Casio Calculator fx 50F User Manual

fx-50F PLUS

User's Guide

http://world.casio.com/edu/

RCA502903-001V01

• The following shows the notation used in the manual for menu items that appear on the

display (which are executed by pressing a number key).

Example:

(Contrast)

The notation in parentheses indicates the menu item accessed by the preceding number

key.

• The cursor key is marked with arrows indicating direction as shown in the

illustration nearby. Cursor key operations are notated in this manual as:

REPLAY

, and

f c d

• The displays and illustrations (such as key markings) shown in this User’s Guide are for

illustrative purposes only, and may differ somewhat from the actual items they represent.

• The contents of this manual are subject to change without notice.

• In no event shall CASIO Computer Co., Ltd. be liable to anyone for special, collateral,

incidental, or consequential damages in connection with or arising out of the purchase or

use of this product and items that come with it. Moreover, CASIO Computer Co., Ltd. shall

not be liable for any claim of any kind whatsoever by any other party arising out of the use

of this product and the items that come with it.

Safety Precautions

Be sure to read the following safety precautions before using this calculator. Keep this

manual handy for later reference.

Caution

This symbol is used to indicate information that can result in personal injury or material

damage if ignored.

Battery

• After removing the battery from the calculator, put it in a safe place where it will not

get into the hands of small children and accidentally swallowed.

• Keep batteries out of the reach of small children. If accidentally swallowed, consult

with a physician immediately.

• Never charge the battery, try to take the battery apart, or allow the battery to become

shorted. Never expose the battery to direct heat or dispose of it by incineration.

• Improperly using a battery can cause it to leak and damage nearby items, and can

create the risk of ﬁre and personal injury.

• Always make sure that the battery’s positive

correctly when you load it into the calculator.

and negative

ends are facing

• Use only the type of battery speciﬁed for this calculator in this manual.

Disposing of the Calculator

• Never dispose of the calculator by burning it. Doing so can cause certain components

to suddenly burst, creating the risk of ﬁre and personal injury.

E-2

Operating Precautions

• Be sure to press the

key before using the calculator for the ﬁrst time.

• Even if the calculator is operating normally, replace the battery at least once every

three years.

A dead battery can leak, causing damage to and malfunction of the calculator. Never

leave a dead battery in the calculator.

• The battery that comes with this unit discharges slightly during shipment and

storage. Because of this, it may require replacement sooner than the normal

expected battery life.

• Low battery power can cause memory contents to become corrupted or lost

completely. Always keep written records of all important data.

• Avoid use and storage of the calculator in areas subjected to temperature extremes.

Very low temperatures can cause slow display response, total failure of the display,

and shortening of battery life. Also avoid leaving the calculator in direct sunlight, near a

window, near a heater or anywhere else it might be exposed to very high temperatures.

Heat can cause discoloration or deformation of the calculator’s case, and damage to

internal circuitry.

• Avoid use and storage of the calculator in areas subjected to large amounts of

humidity and dust.

Take care never to leave the calculator where it might be splashed by water or exposed to

large amounts of humidity or dust. Such conditions can damage internal circuitry.

• Never drop the calculator or otherwise subject it to strong impact.

• Never twist or bend the calculator.

Avoid carrying the calculator in the pocket of your trousers or other tight-ﬁtting clothing

where it might be subjected to twisting or bending.

• Never try to take the calculator apart.

• Never press the keys of the calculator with a ballpoint pen or other pointed object.

• Use a soft, dry cloth to clean the exterior of the calculator.

If the calculator becomes very dirty, wipe it off with a cloth moistened in a weak solution

of water and a mild neutral household detergent. Wring out all excess liquid before wiping

the calculator. Never use thinner, benzene or other volatile agents to clean the calculator.

Doing so can remove printed markings and can damage the case.

E-3

Contents

Getting Started .........................................................................................1

Before using the calculator for the ﬁrst time... ....................................................................1

Resetting the Calculator to Initial Defaults..........................................................................1

About this Manual...............................................................................................................1

Safety Precautions ...................................................................................2

Operating Precautions.............................................................................3

Before starting a calculation... ................................................................6

Turning On the Calculator...................................................................................................6

Key Markings......................................................................................................................6

Reading the Display ...........................................................................................................7

Calculation Modes and Setup .................................................................7

Selecting a Calculation Mode.............................................................................................7

Calculator Setup.................................................................................................................8

Clearing the Calculation Mode and Setup Settings..........................................................10

Inputting Calculation Expressions and Values....................................10

Inputting a Calculation Expression (Natural Input)...........................................................10

Editing a Calculation.........................................................................................................12

Finding the Location of an Error.......................................................................................13

Basic Calculations..................................................................................14

Arithmetic Calculations.....................................................................................................14

Fractions...........................................................................................................................14

Percent Calculations.........................................................................................................16

Degree, Minute, Second (Sexagesimal) Calculations ......................................................17

Calculation History and Replay.............................................................18

Accessing Calculation History .........................................................................................18

Using Replay....................................................................................................................19

Calculator Memory Operations.............................................................19

Using Answer Memory (Ans) ...........................................................................................19

Using Independent Memory.............................................................................................21

Using Variables.................................................................................................................22

Clearing All Memory Contents .........................................................................................23

Using , , and Scientiﬁc Constants.....................................................23

π e

Pi (π) and Natural Logarithm Base e ................................................................................23

Scientiﬁc Constants..........................................................................................................24

Scientiﬁc Function Calculations ..........................................................26

Trigonometric and Inverse Trigonometric Functions.........................................................27

Angle Unit Conversion......................................................................................................27

Hyperbolic and Inverse Hyperbolic Functions ..................................................................28

Exponential and Logarithmic Functions ...........................................................................28

Power Functions and Power Root Functions....................................................................29

E-4

↔

Coordinate Conversion (Rectangular

Polar)................................................................29

Other Functions................................................................................................................31

Using 10³Engineering Notation (ENG).................................................33

ENG Calculation Examples..............................................................................................33

Complex Number Calculations (CMPLX) .............................................34

Inputting Complex Numbers.............................................................................................34

Complex Number Calculation Result Display...................................................................34

Calculation Result Display Examples...............................................................................35

Conjugate Complex Number (Conjg) ...............................................................................36

Absolute Value and Argument (Abs, arg) .........................................................................36

Overriding the Default Complex Number Display Format.................................................37

Statistical Calculations (SD/REG) ........................................................38

Statistical Calculation Sample Data .................................................................................38

Performing Single-variable Statistical Calculations ..........................................................38

Performing Paired-variable Statistical Calculations..........................................................42

Statistical Calculation Examples ......................................................................................50

Base- Calculations (BASE)..................................................................52

Performing Base- Calculations .......................................................................................52

Converting a Displayed Result to another Number Base.................................................54

Using the LOGIC Menu....................................................................................................54

Specifying a Number Base for a Particular Value.............................................................54

Performing Calculations Using Logical Operations and Negative Binary Values .............55

Built-in Formulas....................................................................................56

Using Built-in Formulas ....................................................................................................56

Built-in Formula List..........................................................................................................58

Program Mode (PRGM) ..........................................................................62

Program Mode Overview..................................................................................................62

Creating a Program..........................................................................................................63

Running a Program ..........................................................................................................64

Deleting a Program...........................................................................................................64

Inputting Commands ........................................................................................................65

Command Reference .......................................................................................................65

Appendix .................................................................................................71

Calculation Priority Sequence..........................................................................................71

Stack Limitations ..............................................................................................................72

Calculation Ranges, Number of Digits, and Precision......................................................73

Error Messages................................................................................................................74

Before assuming malfunction of the calculator... .............................................................76

Power Requirements..............................................................................76

Speciﬁcations .........................................................................................77

E-5

Before starting a calculation...

Turning On the Calculator

Press

. The calculator will enter the calculation mode (page 7) that it was in the last time

you turned it off.

Adjusting Display Contrast

If the ﬁgures on the display become hard to read, try adjusting display contrast.

1. Press (SETUP) (Contrast).

• This will display the contrast adjustment screen.

L I GHT

DARK

CASIO

2. Use

and

to adjust display contrast.

3. After the setting is the way you want, press

(EXIT).

Note

You can also use

and

to adjust contrast while the calculation mode menu that

appears when you press the

key is on the display.

Important!

If adjusting display contrast does not improve display readability, it probably means that

battery power is low. Replace the battery.

Turning Off the Calculator

Press

(OFF).

The following information is retained when you turn off the calculator.

• Calculation modes and setup (page 7)

• Answer Memory (page 19), independent memory (page 21), and variable memory (page

22) contents

Key Markings

M–

LOGIC

DT CL

Function

M+

Colors

To perform the function

Press the key.

M–

Text: Amber

Text: Red

Press

and then press the key.

Text: Blue

In the SD or REG Mode, press the key.

Text: Amber

Frame: Blue

In the SD or REG Mode, press

the key.

and then press

∠

Text: Amber

Frame: Purple

In the CMPLX Mode, press

key.

and then press the

E-6

Function

Colors

Text: Red

To perform the function

Press

and then press the key (variable A).

Frame: Green

In the BASE Mode, press the key.

LOGIC

Text: Green

In the BASE Mode, press the key.

Reading the Display

Input Expressions and Calculation Results

This calculator can display both the expressions you input and calculation results on the

same screen.

Input expression

(

)

–

Calculation result

Display Symbols

The symbols described below appear on the display of the calculator to indicate the current

calculation mode, the calculator setup, the progress of calculations, and more. In this

manual, the expression “turn on” is used to mean that a symbol appears on the display, and

“turn off” means that it disappears.

The nearby sample screen shows the symbol.

(

)

s i n 30

The symbol turns on when degrees (Deg) are selected for the default angle unit (page

8). For information about the meaning of each symbol, see the section of this manual that

describes each function.

Calculation Modes and Setup

Selecting a Calculation Mode

Your calculator has six “calculation modes”.

Selecting a Calculation Mode

1. Press

• This displays the calculation mode menu.

• The calculation mode menu has two screens. Press

to toggle between them.You

can also switch between menu screens using

and

REG

PRGM

^{COMP CMPLX B}3^ASE

E-7

2. Perform one of the following operations to select the calculation mode you want.

To select this calculation mode:

COMP (Computation)

Press this key:

(COMP)

(CMPLX)

(BASE)

(SD)

CMPLX (Complex Number)

BASE (Base n )

SD (Single Variable Statistics)

REG (Paired Variable Statistics)

PRGM (Program)

(REG)

(PRGM)

• Pressing a number key from

selects the applicable mode, regardless of which

menu screen is currently displayed.

Calculator Setup

The calculator setup can be used to conﬁgure input and output settings, calculation

parameters, and other settings. The setup can be conﬁgured using setup screens, which

you access by pressing

(SETUP). There are six setup screens, and you can use

and

to navigate between them.

Specifying the Angle Unit

You can specify degrees, radians, or grads as the angle unit to be applied for trigonometric

function calculations.

(90˚ =

radians = 100 grads)

Angle Unit

Degrees

Radians

Grads

Perform this key operation:

(Deg)

(Rad)

(Gra)

!,b

!,c

!,d

Specifying the Display Digits

You can select any one of three settings for the calculation result display digits: ﬁxed

number of decimal places (0 to 9 places), ﬁxed number of signiﬁcant digits (1 to 10 digits),

or exponential display range (a choice of two settings).

Exponential Display

Perform this key operation:

(Fix)

!,eb

(0) to (9)

Number of Decimal Places

(Sci)

!,ec

Signiﬁcant Digits

(1) to (9),

(10)

(Norm)

(Norm2)

!,ed

(Norm1) or

Exponential Display Range

E-8

The following explains how calculation results are displayed in accordance with the setting

you specify.

• From zero to nine decimal places are displayed in accordance with the number of decimal

places (Fix) you specify. Calculation results are rounded off to the speciﬁed number of

digits.

Example: 100 ÷ 7 = 14.286 (Fix = 3)

14.29 (Fix = 2)

• After you specify the number of signiﬁcant digits with Sci, calculation results are

displayed using the speciﬁed number of signiﬁcant digits and 10 to the applicable power.

Calculation results are rounded off to the speciﬁed number of digits.

Example: 1 ÷ 7 = 1.4286 × 10^–1(Sci = 5)

1.429 × 10^–1(Sci = 4)

• Selecting Norm1 or Norm2 causes the display to switch to exponential notation whenever

the result is within the ranges deﬁned below.

Norm1: 10^–2> ꢀxꢀ, ꢀxꢀ 10¹⁰

Norm2: 10^–9> ꢀxꢀ, ꢀxꢀ 10¹⁰

Example: 100 ÷ 7 = 14.28571429 (Norm1 or Norm2)

1 ÷ 200 = 5. × 10^–3

0.005

(Norm1)

(Norm2)

Specifying the Fraction Display Format

You can specify either improper fraction or mixed fraction format for display of calculation

results.

Fraction Format

Mixed Fractions

Improper Fractions

Perform this key operation:

(ab/c)

(d/c)

!,eeb

!,eec

Specifying the Complex Number Display Format

You can specify either rectangular coordinate format or polar coordinate format for complex

number calculation results.

Complex Number Format

Rectangular Coordinates

Polar Coordinates

Perform this key operation:

(a +b )

!,eeeb

!,eeec

(r ∠ Ƨ)

Specifying the Statistical Frequency Setting

Use the key operations below to turn statistical frequency on or off during SD Mode and

REG Mode calculations.

Frequency Setting

Frequency On

Perform this key operation:

(FreqOn)

(FreqOff)

!,ddb

!,ddc

Frequency Off

E-9

Clearing the Calculation Mode and Setup Settings

Perform the procedure described below to clear the current calculation mode and all setup

settings and initialize the calculator to the following.

Calculation Mode ................................COMP (Computation Mode)

Angle Unit ...........................................Deg (Degrees)

Exponential Display.............................Norm1

Fraction Format ..................................ab/c (Mixed Fractions)

Complex Number Format ...................a+b (Rectangular Coordinates)

Frequency Setting ..............................FreqOn (Frequency On)

Perform the following key operation to clear the calculation mode and setup settings.

(CLR)

(Setup)

If you do not want to clear the calculator’s settings, press

operation.

in place of

in the above

Inputting Calculation Expressions

and Values

Inputting a Calculation Expression (Natural Input)

The natural input system of your calculator lets you input a calculation expression just as

it is written and execute it by pressing

. The calculator determines the proper priority

sequence for addition, subtraction, multiplication, division, functions and parentheses

automatically.

Example: 2 × (5 + 4) – 2 × (–3) =

(

)

–

³24

2*(5+4)-

2*-3w

Inputting Scientiﬁc Functions with Parentheses (sin, cos,

etc.)

Your calculator supports input of the scientiﬁc functions with parentheses shown below.

Note that after you input the argument, you need to press to close the parentheses.

)

sin(, cos(, tan(, sin^–1(, cos^–1(, tan^–1(, sinh(, cosh(, tanh(, sinh^–1(, cosh^–1(, tanh^–1(, log(, ln(,

e ^(, 10^(,

(, ³(, Abs(, Pol(, Rec(, arg(, Conjg(, Not(, Neg(, Rnd(

Example: sin 30 =

(

)

s i n 30

s30)w

E-10

Omitting the Multiplication Sign

You can omit the multiplication sign in the following cases.

• Immediately before an open parenthesis: 2 × (5 + 4)

• Immediately before a scientiﬁc function with parentheses: 2 × sin(30), 2 ×

• Before a preﬁx symbol (excluding the minus sign): 2 × h123

• Before a variable name, constant, or random number: 20 × A, 2 × π, 2 × i

(3)

Final Closed Parenthesis

You can omit one or more closed parentheses that come at the end of a calculation,

immediately before the key is pressed.

Example: (2 + 3) × (4 – 1) = 15

(

)

(

–

(2+3)*

(4-1w

• Simply press

without closing the parentheses. The above applies to the closing

parentheses at the end of the calculation only.Your calculation will not produce the correct

result if you forget the closing parentheses that are required before the end.

Scrolling the Screen Left and Right

Inputting a mathematical expression that has more than 16 characters in it will cause the

screen to scroll automatically, causing part of the expression to move off of the display. The

“

” symbol on the left edge of the screen indicates that there is additional data off the left

side of the display.

Input Expression

12345 + 12345 + 12345

Displayed Expression

345 12345 12345I

Cursor

• While the

symbol is on the screen, you can use the

key to move the cursor to the

left and scroll the screen.

• Scrolling to the left causes part of the expression to run off the right side of the display,

which is indicated by the symbol on the right. While the symbol is on the screen,

you can use the

key to move the cursor to the right and scroll the screen.

• You can also press

end.

to jump to the beginning of the expression, or

to jump to the

Number of Input Characters (Bytes)

As you input a mathematical expression, it is stored in memory called an “input area,”

which has a capacity of 99 bytes. This means you can input up to 99 bytes for a single

mathematical expression.

Normally, the cursor that indicates the current input location on the display is either a

ﬂ ashing vertical bar ( ) or horizontal bar ( ). When the remaining capacity of the input area

is eight bytes or less, the cursor changes to a ﬂashing box ( ).

If this happens, stop input of the current expression at some suitable location and calculate

its result.

E-11

Editing a Calculation

Insert Mode and Overwrite Mode

The calculator has two input modes. The insert mode inserts your input at the cursor

location, shifting anything to the right of the cursor to make room. The overwrite mode

replaces the key operation at the cursor location with your input.

Original Expression

Pressing

Insert Mode

1+2 34

1+2+ 34

Cursor

Overwrite Mode

1+2 3 4

1+2 + 4

Cursor

A vertical cursor ( ) indicates the insert mode, while a horizontal cursor ( ) indicates the

overwrite mode.

Selecting an Input Mode

The initial default input mode setting is insert mode.

To change to the overwrite mode, press:

(INS).

Editing a Key OperationYou Just Input

When the cursor is located at the end of the input, press

to delete the last key operation

you performed.

Example: To correct 369 × 13 so it becomes 369 × 12

369*13

369 13I

369 1I

369 12I

Deleting a Key Operation

With the insert mode, use

and

to move the cursor to the right of the key operation

you want to delete and then press

. With the overwrite mode, move the cursor to the

key operation you want to delete and then press

operation.

. Each press of

deletes one key

Example: To correct 369 × × 12 so it becomes 369 × 12

Insert Mode

369**12

××

369 12I

××

369 I12

Overwrite Mode

369**12

××

369 12

E-12

ddd

××

369 12

Editing a Key Operation within an Expression

With the insert mode, use

and

to move the cursor to the right of the key operation

you want to edit, press

to delete it, and then perform the correct key operation. With the

overwrite mode, move the cursor to the key operation you want to correct and then perform

the correct key operation.

Example: To correct cos(60) so it becomes sin(60)

Insert Mode

c60)

(

)

cos 60

dddD

)

I60

(

s i n I60

Overwrite Mode

c60)

dddd

(

)

cos 60

(

cos 60

(

s i n 60

Inserting Key Operations into an Expression

Be sure to select the insert mode whenever you want to insert key operations into an

expression. Use and to move the cursor to the location where you want to insert

the key operations, and then perform them.

Finding the Location of an Error

If your calculation expression is incorrect, an error message will appear on the display when

you press to execute it. After an error message appears, press the or key and

the cursor will jump to the location in your calculation that caused the error so you can

correct it.

Example: When you input 14 ÷ 0 × 2 = instead of 14 ÷ 10 × 2 =

(The following examples use the insert mode.)

14/0*2w

Mat h ERROR

14 0I 2

Location of Error

E-13

14 1I0 2

14 10

• Instead of pressing

while an error message is displayed to ﬁnd the location of

the error, you could also press

to clear the calculation.

Basic Calculations

Unless otherwise noted, the calculations in this section can be performed in any of the

calculator’s calculation mode, except for the BASE Mode.

Arithmetic Calculations

Arithmetic calculations can be used to perform addition (

), subtraction (

multiplication (

), and division (

Example 1: 2.5 + 1 − 2 = 1.5

–

2. 5

2.5+1-2w

7*8-4*5w

Example 2: 7 × 8 − 4 × 5 = 36

• The calculator determines the proper priority sequence for addition, subtraction,

multiplication, and division automatically. See “Calculation Priority Sequence” on page 71

for more information.

Fractions

Fractions are input using a special separator symbol ( ).

{

Key Operation

Display

{

Improper

7$3

Fraction

Numerator Denominator

{

Mixed

Fraction

2$1$3

Integer Numerator Denominator

Note

• Under initial default settings, fractions are displayed as mixed fractions.

• Fraction calculation results are always reduced automatically before being displayed.

Executing 2 4 = for example, will display the result 1 2.

{

E-14

Fraction Calculation Examples

Example 1: 3 + 1 = 4

3{1{4

4{^1{1²1^{3{12

3$1$4+

1$2$3w

Example 2: 4 – 3

–

3{1{2

4-3$1$2w

1{2

Example 3:

(Fraction Display Format: d/c)

2{3 1{2

2$3+1$2w

Note

• If the total number of elements (integer + numerator + denominator + separator symbols)

of a fraction calculation result is greater than 10, the result will be displayed in decimal

format.

• If an input calculation includes a mixture of fraction and decimal values, the result will be

displayed in decimal format.

• You can input integers only for the elements of a fraction. Inputting non-integers will

produce a decimal format result.

Switching between Mixed Fraction and Improper Fraction

Format

To convert a mixed fraction to an improper fraction (or an improper fraction to a mixed

fraction), press (d/c).

Switching between Decimal and Fraction Format

Use the procedure below to toggle a displayed calculation result between decimal and

fraction format.

Example: 1.5 = 1 , 1 = 1.5

1.5w

{

The current fraction display format setting determines if a

mixed or improper fraction is displayed.

Note

The calculator cannot switch from decimal to fraction format if the total number of fraction

elements (integer + numerator + denominator + separator symbols) is greater than 10.

E-15

Percent Calculations

Inputting a value and with a percent (%) sign makes the value a percent. The percent (%)

sign uses the value immediately before it as the argument, which is simply divided by 100 to

get the percentage value.

Percent Calculation Examples

Example 1: 2 % = 0.02

(

)

100

(%)

2!(

002

100

Example 2: 150 × 20% = 30 (150 ×

)

150 20%

150*20

(%)

Example 3: What percent of 880 is 660?

Example 4: Increase 2,500 by 15%.

660 880%

660/880

(%)

–

2500

3500

²⁵⁰⁰2¹8⁵7^%5

2500+2500*

(%)

15!(

Example 5: Reduce 3,500 by 25%.

3500-3500*

³⁵⁰⁰2²6⁵2^%5

(%)

25!(

Example 6: Reduce the sum of 168, 98, and 734 by 20%.

168+98+734w

168 98

⁷³1⁴000

–

Ans Ans 20%

(%)

-G*20!(

800

Example 7: If 300 grams are added to a test sample originally weighing 500 grams, what is

the percentage increase in weight?

(

)

500 300 500%

(500+300)

(%)

/500!(

160

E-16

Example 8: What is the percentage change when a value is increased from 40 to 46? How

about to 48?

Insert Mode

(

)

–

^40%15

^40%20

46 40

(46-40)/40

(%)

–

48 40

eeeeY8w

Degree, Minute, Second (Sexagesimal) Calculations

You can perform calculations using sexagesimal values, and you can convert between

sexagesimal and decimal.

Inputting Sexagesimal Values

The following is basic syntax for inputting a sexagesimal value.

{Degrees} {Minutes} {Seconds}

Example: To input 2°30´30˝

30 30

^˚2 30 30

2$30$30$w

• Note that you must always input something for the degrees and minutes, even if they are

zero.

Example: To input 0°00´30˝, press

0$0$30$

Sexagesimal Calculation Examples

The following types of sexagesimal calculations will produce sexagesimal results.

• Addition or subtraction of two sexagesimal values

• Multiplication or division of a sexagesimal value and a decimal value

Example 1: 2°20´30˝ + 39´30˝ = 3°00´00˝

20 30

39 30

2$20$30$+

0$39$30$w

3 0 0

˚ ˚

Example 2: 2°20´00˝ × 3.5 = 8°10´00˝

20 3. 5

2$20$*

3.5w

8 10 0

Converting between Sexagesimal and Decimal

Pressing

while a calculation result is displayed will toggle the value between

sexagesimal and decimal.

E-17

Example: To convert 2.255 to sexagesimal

2.255w

2255

2 15 18

2255

Calculation History and Replay

Calculation history maintains a record of each calculation you perform, including the

expressions you input and calculation results.You can use calculation history in the COMP,

CMPLX, and BASE Modes.

Accessing Calculation History

The

symbol in the upper right corner of the display indicates that there is data stored in

calculation history. To view the data in calculation history, press

. Each press of

will

scroll upwards (back) one calculation, displaying both the calculation expression and its

result.

Example:

1+1w2+2w

3+3w

While scrolling through calculation history records, the

symbol will appear on the display,

which indicates that there are records below (newer than) the current one. When this

symbol is turned on, press

records.

to scroll downwards (forward) through calculation history

Important!

• Calculation history records are all cleared whenever you press

, when you change to a

different calculation mode, and whenever you perform any reset operation.

• Calculation history capacity is limited. Whenever you perform a new calculation while

calculation history is full, the oldest record in calculation history is deleted automatically to

make room for the new one.

E-18

Using Replay

While a calculation history record is on the display, press

to display the cursor

and enter the editing mode. Pressing

displays the cursor at the beginning of the

calculation expression, while

displays it at the end. After you make the changes you

want, press

to execute the calculation.

Example: 4 × 3 + 2.5 = 14.5

4 × 3 – 7.1 = 4.9

2 . 5

4*3+2.5w

145

2 . 5I

DDDD

–

7 . 1

-7.1w

Calculator Memory Operations

Your calculator includes the types of memory described below, which you can use for

storage and recall of values.

Memory Name

Description

Answer Memory contains the result of the last calculation you

performed.

Answer Memory

Independent

Memory

Independent memory can be used in all calculation modes, except

for the SD Mode and the REG Mode.

Six variables named A, B, C, D, X, and Y can be used for temporary

storage of values. Variables can be used in all calculation modes.

Variables

The types of memory described above are not cleared when you press the

to another mode, or turn off the calculator.

key, change

Using Answer Memory (Ans)

The result of any new calculation you perform on the calculator is stored automatically in

Answer Memory (Ans).

E-19

Ans Update and Delete Timing

When using Ans in a calculation, it is important to keep in mind how and when its contents

change. Note the following points.

• The contents of Ans are replaced whenever you perform any of the following operations:

calculate a calculation result, add a value to or subtract a value from independent

memory, assign a value to a variable or recall the value of a variable, or input statistical

data in the SD Mode or REG Mode.

• In the case of a calculation that produces more than one result (like coordinate

calculations), the value that appears ﬁrst on the display is stored in Ans.

• The contents of Ans do not change if the current calculation produces an error.

• When you perform a complex number calculation in the CMPLX Mode, both the real part

and the imaginary part of the result are stored in Ans. Note, however, that the imaginary

part of the value is cleared if you change to another calculation mode.

Automatic Insertion of Ans in Consecutive Calculations

If you start a new calculation while the result of a previous calculation is still on the display,

the calculator will insert Ans into the applicable location of the new calculation automatically.

Example 1: To divide the result of 3 × 4 by 30

3*4w

/30w

Ans 30

(Next)

Pressing

inputs Ans automatically.

Example 2: To determine the square root of the result of 3²+ 4²

3x+4xw

3 ²

(

Ans

Note

• As in the above examples, the calculator automatically inserts Ans as the argument of

any calculation operator or scientiﬁc function you input while a calculation result is on the

display.

• In the case of a function with parenthetical argument (page 10), Ans automatically

becomes the argument only in the case that you input the function alone and then press

• Basically, Ans is inserted automatically only when the result of the previous calculation is

still on the display, immediately after you executed the calculation that produced it. See

the next section for information about inserting Ans into a calculation manually with the

key.

E-20

Inserting Ans into a Calculation Manually

You can insert Ans into a calculation at the current cursor location by pressing the

key.

Example 1: To use the result of 123 + 456 in another calculation as shown below

123 + 456 = 579

789 – 579 = 210

123+456w

579

210

–

789 Ans

789-Kw

Example 2: To determine the square root of 3²+ 4², and then add 5 to the result

3 ²

3x+4xw

9K)+5w

(

)

Ans

Using Independent Memory

Independent memory (M) is used mainly for calculating cumulative totals.

If you can see the M symbol on the display, it means there is a non-zero value in

independent memory.

M symbol

10M

Adding to Independent Memory

While a value you input or the result of a calculation is on the display, press

to add it to

independent memory (M).

Example: To add the result of 105 ÷ 3 to independent memory (M)

105 3M

105/3m

(M–) to

Subtracting from Independent Memory

While a value you input or the result of a calculation is on the display, press

subtract it from independent memory (M).

Example: To subtract the result of 3 × 2 from independent memory (M)

–

(M–)

3*21m

E-21

Note

Pressing

(M–) while a calculation result is on the display will add it to or

subtract it from independent memory.

Important!

The value that appears on the display when you press

(M–) at the end of a

calculation in place of

is the result of the calculation (which is added to or subtracted

from independent memory). It is not the current contents of independent memory.

Viewing Independent Memory Contents

Press

(M).

Clearing Independent Memory Contents (to 0)

01t

(STO)

(M)

Clearing independent memory will cause the M symbol to turn off.

Calculation Example Using Independent Memory

If the M symbol is displayed on your calculator screen, press

(STO) (M) to

01t m

clear independent memory contents before performing the following operation.

Example:

23 + 9 = 32

53 – 6 = 47

23+9m

53-6m

−) 45 × 2 = 90

99 ÷ 3 = 33

(M–)

45*21m

99/3m

(M)

(Total) 22

(Recalls value of M.)

Using Variables

The calculator supports six variables named A, B, C, D, X, and Y, which you can use to store

values as required.

Assigning a Value or Calculation Result to a Variable

Use the procedure shown below to assign a value or a calculation expression to a variable.

Example: To assign 3 + 5 to variable A

(STO)

3+51t

(A)

Viewing the Value Assigned to a Variable

To view the value assigned to a variable, press

and then specify the variable name.

Example: To view the value assigned to variable A

(A)

Using a Variable in a Calculation

You can use variables in calculations the same way you use values.

Example: To calculate 5 + A

(A)

5+a-

E-22

Clearing the Value Assigned to a Variable (to 0)

Example: To clear variable A

(STO)

(A)

01t

Calculation Example Using Variables

Example: To perform calculations that assign results to variables B and C, and then use the

variables to perform another calculation

9 × 6 + 3

= 1.425

5 × 8

→

9*6+3

(STO)

(B)

→

5*8

(STO)

(C)

(B)

(C)

1425

Clearing All Memory Contents

Perform the following key operation when you want to clear the contents of independent

memory, variable memory, and Answer Memory.

(CLR)

(Mem)

• If you do not want to clear the calculator’s settings, press

operation.

in place of

in the above

Using , , and Scientiﬁc

π e

Constants

Pi ( ) and Natural Logarithm Base

The calculator supports input of pi (π) and natural logarithm base e into calculations. π and

e are supported in all modes, except for the BASE Mode. The following are the values that

the calculator applies for each of the built-in constants.

π = 3.14159265358980 (1e(π))

e = 2.71828182845904 (

(e))

E-23

Scientiﬁc Constants

Your calculator has 40 often-used scientiﬁc constants built in. Like π and e, each scientiﬁc

constant has a unique display symbol. Scientiﬁc constants are supported in all modes,

except for the BASE Mode.

Inputting a Scientiﬁc Constant

1. Press

(CONST).

• This displays page 1 of the scientiﬁc constant menu.

mn ne

mμ

2 3 4

• There are 10 scientiﬁc command menu screens, and you can use

and

navigate between them. For more information, see “Table of Scientiﬁc Constants” on

page 25.

2. Use

and

to scroll through the pages and display the one that contains the

scientiﬁc constant you want.

3. Press the number key (from

want to select.

) that corresponds to the scientiﬁc constant you

• This will input the scientiﬁc constant symbol that corresponds to the number key you

press.

mn ne

2 3 4

m I

• Pressing

here will display the value of the scientiﬁc constant whose symbol is

currently on the screen.

167262171^–

Example Calculations Using Scientiﬁc Constants

Example 1: To input the constant for the speed of light in a vacuum

^C0299792458

(CONST)

(c )

dddd4

_{Example 2: To calculate the speed of light in a vacuum (}c₀= 1/

₀µ₀

)

(

1/9

E-24

(

(CONST)

(ε )

ddd4

(

)

(CONST)

(ƫ )

dd1

)

(

299792458

Table of Scientiﬁc Constants

The numbers in the “No.” column show the scientiﬁc constant menu page number on the left

and the number key you need to press to select the constant when the proper menu page is

displayed.

No.

Scientiﬁc Constant

Symbol

m_p

Value

Unit

1-1 Proton mass

1.67262171×10^–27

1.67492728×10^–27

9.1093826×10^–31

1.8835314×10^–28

0.5291772108×10^–10

6.6260693×10^–34

5.05078343×10^–27

927.400949×10^–26

1.05457168×10^–34

7.297352568×10^–3

2.817940325×10^–15

2.426310238×10^–12

2.67522205×10⁸

1.3214098555×10^–15

1.3195909067×10^–15

10973731.568525

1.66053886×10^–27

1.41060671×10^–26

–928.476412×10^–26

–0.96623645×10^–26

–4.49044799×10^–26

96485.3383

1-2 Neutron mass

m_n

1-3 Electron mass

m_e

1-4 Muon mass

2-1 Bohr radius

a₀

2-2 Planck constant

J s

2-3 Nuclear magneton

2-4 Bohr magneton

µ _N

µ _B

J T^–1

J s

3-1 Planck constant, rationalized

3-2 Fine-structure constant

3-3 Classical electron radius

3-4 Compton wavelength

4-1 Proton gyromagnetic ratio

4-2 Proton Compton wavelength

4-3 Neutron Compton wavelength

4-4 Rydberg constant

r_e

−

λ _c

γ _p

s^–1T^–1

λ _cp

λ _cn

R∞

m^–1

5-1 Atomic mass constant

5-2 Proton magnetic moment

5-3 Electron magnetic moment

5-4 Neutron magnetic moment

6-1 Muon magnetic moment

6-2 Faraday constant

µ _p

µ _e

µ _n

µ _ƫ

J T^–1

C mol^–1

6-3 Elementary charge

1.60217653×10^–19

E-25

No.

Scientiﬁc Constant

Symbol

N_A

Value

Unit

mol^–1

J K^–1

6-4 Avogadro constant

6.0221415×10²³

1.3806505×10^–23

7-1 Boltzmann constant

7-2 Molar volume of ideal gas

7-3 Molar gas constant

V_m

22.413996×10^–3m³mol^–1

8.314472 J mol^–1K^–1

7-4 Speed of light in vacuum

8-1 First radiation constant

8-2 Second radiation constant

8-3 Stefan-Boltzmann constant

8-4 Electric constant

C₀

C₁

C₂

299792458

3.74177138×10^–16

1.4387752×10^–2

m s^–1

W m²

m K

5.670400×10^–8W m^–2K^–4

ε ₀

8.854187817×10^–12

12.566370614×10^–7

2.06783372×10^–15

9.80665

F m^–1

N A^–2

9-1 Magnetic constant

µ ₀

9-2 Magnetic ﬂux quantum

9-3 Standard acceleration of gravity

9-4 Conductance quantum

φ ₀

m s^–2

G₀

7.748091733×10^–5

Characteristic impedance of

vacuum

10-1

Z₀

376.730313461

273.15

Ω

10-2 Celsius temperature

10-3 Newtonian constant of gravitation

10-4 Standard atmosphere

6.6742×10^–11m³kg^–1s^–2

atm

101325

• Source: 2000 CODATA recommended values

Scientiﬁc Function Calculations

Unless otherwise noted, the functions in this section can be used in any of the calculator’s

calculation modes, except for the BASE Mode.

Scientiﬁc Function Calculation Precautions

• When performing a calculation that includes a built-in scientiﬁc function, it may take

some time before the calculation result appears. Do not perform any key operation on the

calculator until the calculation result appears.

• To interrupt and on-going calculation operation, press

Interpreting Scientiﬁc Function Syntax

• Text that represents a function’s argument is enclosed in braces ({ }). Arguments are

normally {value} or {expression}.

• When braces ({ }) are enclosed within parentheses, it means that input of everything

inside the parentheses is mandatory.

E-26

Trigonometric and Inverse Trigonometric Functions

sin(, cos(, tan(, sin^–1(, cos^–1(, tan^–1

(

Syntax and Input

sin({n}), cos({n}), tan({n}), sin^–1({n}), cos^–1({n}), tan^–1({n})

Example: sin 30 = 0.5, sin^–10.5 = 30 (Angle Unit: Deg)

(

)

s i n 30

s30)w

)

0.5)w

s i n^–10. 5

(

)

(sin^–1

Notes

• These functions can be used in the CMPLX Mode, as long as a complex number is not

used in the argument. A calculation like × sin(30) is supported for example, but sin(1 + )

is not.

• The angle unit you need to use in a calculation is the one that is currently selected as the

default angle unit.

Angle Unit Conversion

You can convert a value that was input using one angle unit to another angle unit.

After you input a value, press (DRG ) to display the menu screen shown below.

(D): Degrees

(R): Radians

(G): Grads

1 2 3

Example: To convert

radians and 50 grads both to degrees

The following procedure assumes that Deg (degrees) is currently speciﬁed for the default

angle unit.

(

)

(π)

(1e /2)

π÷

(DRG

)

(R)

1G ' 2 E

50^g

(DRG

501G

)

(G)

E-27

Hyperbolic and Inverse Hyperbolic Functions

sinh(, cosh(, tanh(, sinh^–1(, cosh^–1(, tanh^–1

(

Syntax and Input

sinh({n}), cosh({n}), tanh({n}), sinh^–1({n}), cosh^–1({n}), tanh^–1({n})

Example: sinh 1 = 1.175201194

(

)

s i nh

(sinh)

1)E

1175201194

Notes

• After pressing

to specify a hyperbolic function or

to specify an inverse

hyperbolic function, press

, or

s c

• These functions can be used in the CMPLX Mode, but complex number arguments are

not supported.

Exponential and Logarithmic Functions

10^(, e ^(, log(, ln(,

Syntax and Input

{

}

10^({n}) .......................... 10

(Same applies to e^(.)

(Common Logarithm)

(Base {m} Logarithm)

(Natural Logarithm)

log({n}) ........................... log₁₀{n}

log({m},{n})..................... log_{{ }}{n}

ln({n}) ............................. log {n}

Example 1: log₂16 = 4, log16 = 1.204119983

l2,16)E

(

)

l o 2, 16

(

)

l o 16

l16)E

1204119983

Base 10 (common logarithm) is assumed when no base is speciﬁed.

Example 2: ln 90 (log 90) = 4.49980967

(

)

^{I n}4⁹4⁰9980967

I90)E

Example 3: e¹⁰= 22026.46579

(

)

(e^x)

10)E

2202646579

E-28

Power Functions and Power Root Functions

x ², x ³, x ^–1, ^(,

(, ³(,

(

Syntax and Input

{n} x²............................... {n}²

{n} x³............................... {n}³

{n} x^–1............................. {n}^–1

(Square)

(Cube)

(Reciprocal)

(Power)

{

}

{(m)}^({n})....................... {m}

({n}) .......................... {n}

(Square Root)

(Cube Root)

(Power Root)

({n}) ......................... ³{n}

}

({n}) .................. ^{{n}

({m})

Example 1: ( 2 + 1) ( 2 – 1) = 1, (1 + 1)²⁺²= 16

(

)

) (

(

)

–

(

(92)+1)

(92)-1)E

(

⁾16

)

(1+1)M2+2)E

Example 2: –2 = –1.587401052

(

–

2{3

-2M2$3)E

1587401052

Notes

• The functions x², x³, and x^–1can be used in complex number calculations in the CMPLX

Mode. Complex number arguments are also supported for these functions.

(, ³(,

( are also supported in the CMPLX Mode, but complex number

• ^(,

arguments are not supported for these functions.

↔

Coordinate Conversion (Rectangular

Polar)

Pol(, Rec(

Your calculator can convert between rectangular coordinates and polar coordinates.

Rectangular Coordinates (Rec)

Polar Coordinates (Pol)

E-29

Syntax and Input

Rectangular-to-Polar Coordinate Conversion (Pol)

Pol(x, y)

x : Rectangular coordinate x-value

y: Rectangular coordinate y-value

Polar-to-Rectangular Coordinate Conversion (Rec)

Rec(r, Ƨ)

r : Polar coordinate r-value

Ƨ: Polar coordinate Ƨ-value

Example 1: To convert the rectangular coordinates ( 2, 2 ) to polar coordinates

(Angle Unit: Deg)

(

)

(

⁾2⁾

(Pol)

92)

,92))E

Po l

(View the value of Ƨ)

(Y)

Example 2: To convert the polar coordinates (2, 30°) to rectangular coordinates

(Angle Unit: Deg)

(

)

(Rec)

30)E

Rec 2, 30

1732050808

(View the value of y)

(Y)

Notes

• These functions can be used in the COMP, SD, and REG Modes.

• Calculation results show the ﬁrst r value or x value only.

• The r-value (or x-value) produced by the calculation is assigned to variable X, while the

Ƨ-value (or y-value) is assigned to variable Y (page 22). To view the Ƨ-value (or y-value),

display the value assigned to variable Y, as shown in the example.

• The values obtained for Ƨ when converting from rectangular coordinates to polar

coordinates is within the range –180°< Ƨ 180°.

• When executing a coordinate conversion function inside of a calculation expression, the

calculation is performed using the ﬁrst value produced by the conversion (r-value or x-

value).

Example: Pol ( 2, 2 ) + 5 = 2 + 5 = 7

E-30

Other Functions

x !, Abs(, Ran#, n Pr , n Cr , Rnd(

The x!, nPr, and nCr functions can be used in the CMPLX Mode, but complex number

arguments are not supported.

Factorial (!)

Syntax: {n}! ({n} must be a natural number or 0.)

Example: (5 + 3)!

(

)

(5+3)

(x!)

40320

Absolute Value (Abs)

When you are performing a real number calculation, Abs( simply obtains the absolute value.

This function can be used in the CMPLX Mode to determine the absolute value (size) of a

complex number. See “Complex Number Calculations” on page 34 for more information.

Syntax: Abs({n})

Example: Abs (2 – 7) = 5

(

)

–

Abs

(Abs)

2-7)E

Random Number (Ran#)

This function generates a three-decimal place (0.000 to 0.999) pseudo random number. It

does not require an argument, and can be used the same way as a variable.

Syntax: Ran#

Example: To use 1000Ran# to obtain three 3-digit random numbers.

1000Ran#

(Ran#)

10001.

287

613

118

1000Ran#

• The above values are provided for example only. The actual values produced by your

calculator for this function will be different.

E-31

Permutation ( P )/Combination ( C )

Syntax: {n}P{m}, {n}C{m}

Example: How many four-person permutations and combinations are possible for a group

of 10 people?

10P4

(nPr)

101*

101/

5040

210

10C4

(nCr)

Rounding Function (Rnd)

You can use the rounding function (Rnd) to round the value, expression, or calculation result

speciﬁed by the argument. Rounding is performed to the number of signiﬁcant digits in

accordance with the number of display digits setting.

Rounding for Norm1 or Norm2

The mantissa is rounded off to 10 digits.

Rounding for Fix or Sci

The value is rounded to the speciﬁed number of digits.

Example: 200 ÷ 7 × 14 = 400

200

Ans

200/7*14E

400

(3 decimal places)

(Fix)

1Ne1

400000

(Internal calculation uses 15 digits.)

200/7E

*14E

28571

¹⁴400000

Now perform the same calculation using the rounding (Rnd) function.

200

(

200/7E

28571

(Calculation uses rounded value.)

^Ans28571

Rnd

(Rnd)

E-32

Ans

¹⁴399994

(Rounded result)

*14E

Using 10³Engineering Notation

(ENG)

Engineering notation (ENG) expresses quantities as a product of a positive number

between 1 and 10 and a power of 10 that is always a multiple of three. There are two types

of engineering notation, ENG and ENG

Function

Key Operation

ENG

(

)

1W ,

ENG Calculation Examples

Example 1: To convert 1234 to engineering notation using ENG

1234

1234E

1234

Example 2: To convert 123 to engineering notation using ENG

123

123E

123

0123

(

)

1W ,

(

1W ,

0000123

E-33

Complex Number Calculations

(CMPLX)

To perform the example operations in this section, ﬁrst select CMPLX (

calculation mode.

) as the

Inputting Complex Numbers

Inputting Imaginary Numbers ( )

In the CMPLX Mode, the

key is used to input the imaginary number . Use

( ) when

W i

inputting complex numbers using rectangular coordinate format (a+bi).

Example: To input 2 + 3

( )

2+3W i

3 iI

Inputting Complex Number Values Using Polar Coordinate

Format

Complex numbers can also be input using polar coordinate format (r Ƨ).

∠

Example: To input 5 30

∠

(

)

51- ∠ 30

30I

Important!

When inputting argument Ƨ, enter a value that indicates an angle in accordance with the

calculator’s current default angle unit setting.

Complex Number Calculation Result Display

When a calculation produces a complex number result, R⇔I symbol turns on in the upper

right corner of the display and the only the real part appears at ﬁrst. To toggle the display

between the real part and the imaginary part, press

(Re⇔Im).

Example: To input 2 + 1 and display its calculation result

Before starting the calculation, you need to perform the following operation to change the

a b

complex number display setting to “ + ” as shown below.

To select rectangular coordinate format:

(SETUP)

(a+bi)

eee1

( )

2+W i E

Displays real part.

E-34

(Re⇔Im)

Displays imaginary part.

(

symbol turns on during imaginary part display.)

Default Complex Number Calculation Result Display Format

You can select either rectangular coordinate format or polar coordinate format for complex

number calculation results.

Imaginary axis

a + bi

Real axis

Rectangular Coordinates

Polar Coordinates

Use the setup screens to specify the default display format you want. For details, see

“Specifying the Complex Number Display Format” (page 9).

Calculation Result Display Examples

a bi

Rectangular Coordinate Format ( + )

a b

( +

(SETUP)

eee1

)

Example 1: 2 × ( 3 + i) = 2 3 + 2i = 3.464101615 + 2i

(

)

( )

2*(93)+W i )E

3464101615

(

)

(Re⇔Im)

Example 2: 2 ∠ 45 = 1 + 1i (Angle Unit: Deg)

(

)

(∠)

45E

92)1-

(

(Re⇔Im)

E-35

r∠Ƨ

Polar Coordinate Format (

)

(SETUP)

eee2

(r∠Ƨ)

Example 1: 2 × ( 3 + i) = 2 3 + 2i = 4 30

∠

(

)

( )

2*(93)+W i )E

(

(Re⇔Im)

^{symbol turns on during display of}Ƨ^-value.

∠

Example 2: 1 + 1 = 1.414213562 ∠ 45 (Angle Unit: Deg)

1 i

( )

1+1W i E

1414213562

1 i

(Re⇔Im)

Conjugate Complex Number (Conjg)

¯z

(

)

You can perform the operation below to obtain conjugate complex number

for the

complex number

Example: Obtain the conjugate complex number of 2 + 3

Con

3 i

(Conjg)

( )

2+3W i )E

)

(Re⇔Im)

Absolute Value and Argument (Abs, arg)

You can use the procedure shown below to obtain the absolute value (|z|) and argument (arg)

on the Gaussian plane for a complex number in the format

Example:

Imaginary axis

To obtain the absolute value and argument of 2 + 2

(Angle Unit: Deg)

b = 2

Real axis

a = 2

E-36

Absolute Value:

Argument:

(

)

Abs

2 i

(Abs)

( )

2+2W i )E

2828427125

(

)

2 i

(arg)

( )

2+2W i )E

Overriding the Default Complex Number Display Format

You can use the procedures described below to override the default complex number

display format and specify a particular display format for the calculation you are currently

inputting.

Specifying Rectangular Coordinate Format for a Calculation

1- '

Input

a b

) at the end of the calculation.

(

Example: 2 2 ∠ 45 = 2 + 2i (Angle Unit: Deg)

(

)

⁺^b2ⁱ

(∠)

292)1- 45

a b

(

)

1- '

i E

(Re⇔Im)

Specifying Polar Coordinate Format for a Calculation

Input

(

r∠Ƨ) at the end of the calculation.

1+ '

Example: 2 + 2i = 2 2 ∠ 45 = 2.828427125 ∠ 45 (Angle Unit: Deg)

( )

2+2W i

2 i

(

r∠Ƨ)

1+ '

2828427125

2 i

(Re⇔Im)

E-37

Statistical Calculations (SD/REG)

Statistical Calculation Sample Data

Inputting Sample Data

You can input sample data either with statistical frequency turned on (FreqOn) or off (FreqOff).

The calculator’s initial default setting is FreqOn. You can select the input method you want

to use with the setup screen statistical frequency setting (page 9).

Maximum Number of Input Data Items

The maximum number of data items you can input depends on whether frequency is on

(FreqOn) or off (FreqOff).

Frequency Setting

FreqOn

FreqOff

Calculation Mode

SD Mode

40 items

26 items

80 items

40 items

REG Mode

Sample Data Clear

All sample data currently in memory is cleared whenever you change to another calculation

mode and when you change the statistical frequency setting.

Performing Single-variable Statistical Calculations

To perform the example operations in this section, ﬁrst select SD (

) as the calculation

mode.

Inputting Sample Data

Frequency On (FreqOn)

The following shows the key operations required when inputting class values x1, x2, ...xn,

and frequencies Freq1, Freq2, ... Freqn.

{x1}

{x2}

(;) {Freq1}

(;) {Freq2}

(DT)

{xn}

(;) {Freqn}

(DT)

Note

If the frequency of a class value is only one, you can input it by pressing {xn}

(DT) only

(without specifying the frequency).

E-38

Example: To input the following data

Class Value (x )

Frequency (Freq)

24.5

25.5

26.5

;

(;)

24.51,

L i ne

(DT)

(DT) tells the calculator this is the end of the ﬁrst data item.

L i ne

(;)

25.51, 6m

(DT)

(;)

26.51, 2m

Frequency Off (FreqOff)

In this case, input each individual data item as shown below.

... xn

{x1}

(DT) {x2}

(DT)

{

}

(DT)

Viewing Current Sample Data

After inputting sample data, you can press

to scroll through the data in the sequence

you input it. The

symbol indicates there is data below the sample that is currently on the

display. The

symbol indicates there is data above.

Example: To view the data you input in the example under “Inputting Sample Data” on page

38 (Frequency Setting: FreqOn)

x 1

245

F r e

E-39

x 2

255

F r e

When the statistical frequency setting is FreqOn, data is displayed in the sequence: x1,

Freq1, x2, Freq2, and so on. In the case of FreqOff, it is displayed in the sequence: x1, x2,

x3, and so on. You can also use

to scroll in the reverse direction.

Editing a Data Sample

To edit a data sample, recall it, input the new value(s), and then press

Example: To edit the “Freq3” data sample input under “Inputting Sample Data” on page 38

F r e

Deleting a Data Sample

To delete a data sample, recall it and then press

(CL).

Example: To delete the “x2” data sample input under “Inputting Sample Data” on page 38

x 2

Accc

255

L i ne

(CL)

Note

• The following shows images of how the data appears before and after the delete

operation.

Before

After

x 1: 24.5

x 2: 25.5

x 3: 26.5

Freq1: 4

Freq2: 6

Freq3: 2

x 1: 24.5

x 2: 26.5

Freq1: 4

Freq2: 2

Shifted upwards.

• When the statistical frequency setting is turned on (FreqOn), the applicable x-data and

Freq data pair is deleted.

E-40

Deleting All Sample Data

Perform the following key operation to delete all sample data.

(CLR) (Stat)

If you do not want to delete all sample data, press

in place of

in the above operation.

Statistical Calculations Using Input Sample Data

To perform a statistical calculation, input the applicable command and then press

. To

determine the mean ( ) value of the current input sample data, for example, perform the

operation shown below.

xσn xσn–

1 2 3 ¹

(S-VAR)

2533333333

* This is one example of possible calculation results.

SD Mode Statistical Command Reference

ƙx²

(S-SUM)

(S-VAR)

12 2

Obtains the sum of squares of the sample

data.

Obtains the population standard deviation.

Σ(x_i– o)

x²x ²

xσn

(S-SUM)

ƙx

12(S-VAR)3

–1

Obtains the sum of the sample data.

Obtains the sample standard deviation.

Σ(x_i– o)

n – 1

xσn–1

(S-SUM)

(S-VAR)

12 e1

minX

Obtains the number of samples.

= (number of -data items)

Determines the minimum value of the

samples.

(S-VAR)

x¯

Obtains the mean.

(S-VAR)

12 e2

maxX

Σx

n ⁱ

Determines the maximum value of the

samples.

E-41

Performing Paired-variable Statistical Calculations

To perform the example operations in this section, ﬁrst select REG (

) as the

calculation mode.

Regression Calculation Types

The REG Mode lets you perform the seven types of regression listed below. The ﬁgures in

the parentheses show the theoretical formulas.

• Linear

(y = a + bx)

• Quadratic

• Logarithmic

• e Exponential

• ab Exponential

• Power

(y = a+ bx + cx²)

(y = a + b lnx)

(y = ae^bx

(y = ab^x)

(y = ax^b)

)

• Inverse

(y = a + b/x)

Each time you enter the REG Mode, you must select the type of regression calculation you

plan to perform.

Selecting the Regression Calculation Type

1. Press

(REG) to enter the REG Mode.

• This displays the initial regression calculation selection menu. The menu has two

screens, and you can use

and

to navigate between them.

–

I nv Quad AB

L i n Lo E x

1 2 3 4

1 2 3 ^Ex

2. Perform one of the following operations to select the regression calculation you want.

To select this regression type:

Linear

And press this key:

(Lin)

Logarithmic

e Exponential

Power

(Log)

(Exp)

(Pwr)

Inverse

(Inv)

Quadratic

(Quad)

(AB-Exp)

ab Exponential

Note

You can switch to another regression calculation type from within the REG Mode, if you

want. Pressing (S-VAR) (TYPE) will display a menu screen like the one shown in

step 1 above. Perform the same operation as the above procedure to select the regression

calculation type you want.

E-42

Inputting Sample Data

Frequency On (FreqOn)

The following shows the key operations required when inputting class values (x1, y1), (x2,

y2), ...(xn, yn), and frequencies Freq1, Freq2, ... Freqn.

{x1}

{x2}

{y1}

{y2}

(;) {Freq1}

(;) {Freq2}

(DT)

{xn} {yn}

(;) {Freqn}

(DT)

Note

If the frequency of a class value is only one, you can input it by pressing {xn} {yn} (DT)

only (without specifying the frequency).

Frequency Off (FreqOff)

In this case, input each individual data item as shown below.

{x1}

{x2}

{y1}

{y2}

(DT)

{xn} {yn}

(DT)

Viewing Current Sample Data

After inputting sample data, you can press

to scroll through the data in the sequence

you input it. The

symbol indicates there is data below the sample that is currently on the

display. The

symbol indicates there is data above.

When the statistical frequency setting is FreqOn, data is displayed in the sequence: x1, y1,

Freq1, x2, y2, Freq2, and so on. In the case of FreqOff, it is displayed in the sequence: x1,

y1, x2, y2, x3, y3, and so on. You can also use

to scroll in the reverse direction.

Editing a Data Sample

To edit a data sample, recall it, input the new value(s), and then press

Deleting a Data Sample

To delete a data sample, recall it and then press

(CL).

Deleting All Sample Data

See “Deleting All Sample Data” (page 41).

Statistical Calculations Using Input Sample Data

To perform a statistical calculation, input the applicable command and then press

. To

determine the mean ( or ) value of the current sample data, for example, perform the

operation shown below.

xσn xσn–

1 2 3¹

(S-VAR)

(VAR)

115

E-43

σn

σn–

1 2 3 ¹

(S-VAR)

(VAR)

* This is one example of possible calculation results.

REG Mode Statistical Command Reference

Sum and Number of Sample Command (S-SUM Menu)

ƙx²

ƙxy

(S-SUM)

Obtains the sum of squares of the sample

Obtains the sum of products of the sample

x-data.

x-data and y-data.

x²x ²

xy x y

ƙx²y

(S-SUM)

ƙx

Obtains the sum of squares of the sample

Obtains the sum of the sample x-data.

x-data multiplied by the sample y-data.

x y x ²y

(S-SUM)

ƙx³

(S-SUM)

Obtains the number of samples.

Obtains the sum of cubes of the sample

= (number of -data items)

x-data.

x³x ³

ƙy²

(S-SUM)

Obtains the sum of squares of the sample

ƙx⁴

(S-SUM)

y-data.

y²y ²

Obtains the sum of the fourth power of the

sample x-data.

(S-SUM)

ƙy

x⁴x ⁴

Obtains the sum of the sample y-data.

Mean and Standard Deviation Commands (VAR Menu)

(S-VAR)

(VAR)

(S-VAR) (VAR)

1 2

x¯

σⁿ

Obtains the population standard deviation

Obtains the mean of the sample x-data.

of the sample x-data.

Σx

n ⁱ

Σ(x_i– o)

xσn

E-44

(S-VAR)

(VAR)

(S-VAR) (VAR)

1 e2

–1

σⁿ

Obtains the sample standard deviation of

Obtains the population standard deviation

the sample x-data.

of the sample y-data.

Σ (y_i– y)

Σ(x_i– o)

yσn

xσn–1

n – 1

(S-VAR)

(VAR)

_–112

σⁿ

Obtains the sample standard deviation of

the sample y-data.

(S-VAR)

(VAR)

1 e1

y¯

Obtains the mean of the sample y-data.

Σ (y_i– y)

Σy_i

yσn–1

n – 1

Regression Coefﬁcient and Estimated Value Commands for Non-

quadratic Regression (VAR Menu)

The calculation that is performed when one of these commands is performed depends on

the regression type that is currently selected. For details about each regression calculation

formula, see “Regression Coefﬁcient and Estimated Value Calculation Formula Table” (page

47).

(S-VAR)

(VAR)

ee1

ee2

ee3

Obtains constant term a of the regression formula.

Obtains coefﬁcient b of the regression formula.

Obtains correlation coefﬁcient r.

(S-VAR)

(VAR)

xˆ

Taking the value input immediately before this command as the y-value, obtains the

estimated value of x based on the regression formula for the currently selected regression

calculation.

(S-VAR) (VAR)

1 d2

yˆ

Taking the value input immediately before this command as the x-value, obtains the

estimated value of y based on the regression formula for the currently selected regression

calculation.

E-45

Regression Coefﬁcient and Estimated Value Commands for Quadratic

Regression (VAR Menu)

For details about the formula that is executed by each of these commands, see “Regression

Coefﬁcient and Estimated Value Calculation Formula Table” (page 47).

(S-VAR)

(VAR)

ee1

ee2

ee3

Obtains constant term a of the regression formula.

Obtains coefﬁcient b of the regression formula.

Obtains coefﬁcient c of the regression formula.

(S-VAR)

(VAR)

xˆ ¹

Taking the value input immediately before this command as the y-value, uses the formula on

page 47 to determine one estimated value of x.

(S-VAR) (VAR)

1 d2

xˆ ²

Taking the value input immediately before this command as the y-value, uses the formula on

page 47 to determine one more estimated value of x.

(S-VAR) (VAR)

1 d3

yˆ

Taking the value input immediately before this command as the x-value, uses the formula on

page 47 to determine the estimated value of y.

Minimum and Maximum Value Commands (MINMAX Menu)

(S-VAR)

(MINMAX)

minX

Obtains the minimum value of the sample x-data.

(S-VAR)

(MINMAX)

maxX

Obtains the maximum value of the sample x-data.

(S-VAR)

(MINMAX)

minY

Obtains the minimum value of the sample y-data.

(S-VAR)

maxY

Obtains the maximum value of the sample y-data.

E-46

Regression Coefﬁcient and Estimated Value Calculation

Formula Table

The following table shows the calculation formulas used by the regression coefﬁcient and

estimated value commands for each regression calculation type.

Linear Regression

Command

Calculation Formula

Regression Formula

Constant Term a

Σy_i– b Σx_i

a =

b =

n Σx_iy_i– Σx_iΣy_i

Regression Coefﬁcient b

Correlation Coefﬁcient r

(

)

n Σx_i– Σx_i

n Σx_iy_i– Σx_iΣy_i

r =

(

)

(

)

{n Σx_i– Σx_i}{n Σy_i– Σy_i

}

y – a

Estimated Value

n = a + bx

Estimated Value ţ

Quadratic Regression

Command

Calculation Formula

Σy_i

Σx_i

Regression Formula

Constant Term a

a =

b =

– b

– c

(

)

(

)

Sxy Sx x – Sx y Sxx

Regression Coefﬁcient b

Sxx Sx x – (Sxx )

Sx y Sxx – Sxy Sxx

Regression Coefﬁcient c

However,

c =

Sxx Sx x – (Sxx )

(Σx_iΣx_i)

Sxx = Σx_i

–

(Σx_i)

Sxx = Σx_i–

(Σx_i)

Sx x = Σx_i

–

(Σx_iΣy_i)

Sxy = Σx_iy_i

–

(Σx_iΣy_i)

Sx y = Σx_iy_i

–

Command

Calculation Formula

(

)

– b + b – 4c a – y

Estimated Value

m1 =

m₁

(

)

– b – b – 4c a – y

Estimated Value

m₂

m2 =

n = a + bx + cx

E-47

Logarithmic Regression

Command

Calculation Formula

Σy – b Σlnx

Regression Formula

Constant Term a

a =

b =

(

n Σ lnx

– Σlnx Σy

Regression Coefﬁcient b

Correlation Coefﬁcient r

(

)

(

)

n Σ lnx – Σlnx

(

– Σlnx Σy

n Σ lnx

r =

(

)

(

)

(

)

{n Σ lnx – Σlnx }{n Σy – Σy

}

m = e^{y – a}

Estimated Value

n = a + blnx

e Exponential Regression

Command

Calculation Formula

Regression Formula

Constant Term a

Σlny – b Σx

a = exp

(

)

n Σx_iln _i– Σx_iΣlny_i

Regression Coefﬁcient b

Correlation Coefﬁcient r

b =

r =

(

)

n Σx_i– Σx_i

n Σx_iln _i– Σx_iΣlny_i

(

)

(

)

(

)

{n Σx_i– Σx_i}{n Σ lny_i– Σlny_i

}

lny – lna

Estimated Value

m =

n = ae

ab Exponential Regression

Command

Calculation Formula

Regression Formula

Constant Term a

Σlny_i– ln^bΣx_i

a = exp

(

)

n Σx_iln _i– Σx_iΣlny_i

Regression Coefﬁcient b

Correlation Coefﬁcient r

b = exp

(

)

(

)

n Σx_i– Σx_i

n Σx_iln _i– Σx_iΣlny_i

r =

(

)

(

)

(

)

{n Σx_i– Σx_i}{n Σ lny_i– Σlny_i

}

E-48

Command

Calculation Formula

lny – lna

Estimated Value

m =

lnb

Estimated Value

n = ab

Power Regression

Command

Calculation Formula

Regression Formula

Constant Term a

Σlny_i– b Σlnx_i

a = exp

(

)

n Σlnx_iln _i– Σlnx_iΣlny_i

Regression Coefﬁcient b

Correlation Coefﬁcient r

b =

r =

(

)

(

)

n Σ lnx_i– Σlnx_i

n Σlnx_iln _i– Σlnx_iΣlny_i

(

)

(

)

(

)

(

)

{n Σ lnx_i– Σlnx_i}{n Σ lny_i– Σlny_i

}

m = e^{ln y – ln a}

Estimated Value

n = ax

Inverse Regression

Command

Calculation Formula

–1

Σy_i– b Σx_i

Regression Formula

Constant Term a

a =

b =

r =

Sxy

Sxx

Regression Coefﬁcient b

Sxy

Correlation Coefﬁcient r

However,

Sxx Syy

–1

(Σx_i

)

–1

Sxx = Σ(x_i) –

(Σy_i)

Syy = Σy_i–

–1

Σx_iΣy_i

–1

Sxy = Σ(x_i)y_i–

E-49

Command

Calculation Formula

y ^b– a

m =

Estimated Value

n = a +

Estimated Value

Statistical Calculation Examples

This section provides some actual examples of statistical calculation examples as they are

performed on your calculator.

Example 1: The nearby table shows the pulse rates of 50

Pulse Rate Students

students who attend a high school for boys

54 – 56

56 – 58

58 – 60

60 – 62

62 – 64

64 – 66

66 – 68

68 – 70

70 – 72

72 – 74

74 – 76

that has a total enrollment of 1,000 students.

Determine the mean and standard deviation of the

sample data.

Operation Procedure

Select the SD Mode:

(SD)

Select FreqOn for the statistical frequency setting:

(SETUP) (FreqOn)

dd1

Input the sample data:

(DT)

(;)

571, 2m

(DT)

(;) (DT)

591, 2m

55m

(;)

(DT)

(;)

(DT)

611, 5m

631, 8m

(;)

651, 9m

(;)

691, 6m

(;)

731, 3m

(;)

671, 8m

(;)

711, 4m

(;)

751, 2m

Obtain the mean:

(S-VAR)

( )

6568

Obtain the sample standard deviation:

xσn–1

(S-VAR) (xσ

)

–1

4635444632

E-50

Example 2: The nearby data shows how the weight of a

Number

of Days

110

140

170

200

230

260

290

320

Weight

(g)

newborn at various numbers of days after birth.

3150

4800

6420

7310

7940

8690

8800

9130

9270

9310

9390

Obtain the regression formula and correlation coefﬁcient

produced by linear regression of the data.

Obtain the regression formula and correlation coefﬁcient

produced by logarithmic regression of the data.

Predict the weight 350 days after birth based on the

regression formula that best ﬁts the trend of the data in

accordance with the regression results.

Operation Procedure

Enter the REG Mode and select linear regression:

(REG)

(Lin)

Select FreqOff for the statistical frequency setting:

(SETUP) (FreqOff)

Input the sample data:

dd2

(DT)

20,3150m

80,6420m

140,7940m

200,8800m

260,9270m

320,9390m

50,4800m

(DT)

110,7310m

170,8690m

230,9130m

290,9310m

(DT)

Linear Regression

Regression Formula Contant Term a:

(S-VAR)

(VAR)

(a)

(b)

ee1

4446575758

Regression Coefﬁcient b:

(S-VAR)

ee2

1887575758

Correlation Coefﬁcient:

(S-VAR)

(VAR) (r)

ee3

0904793561

Logarithmic Regression

Select logarithmic regression:

(S-VAR)

(TYPE)

(Log)

Regression Formula Contant Term a:

(S-VAR)

(VAR)

ee1

(a)

A12

–

4209356544

E-51

Regression Coefﬁcient b:

(S-VAR)

(VAR) (b)

ee2

2425756228

Correlation Coefﬁcient:

(S-VAR)

(VAR) (r)

ee3

0991493123

Weight Prediction

The absolute value of the correlation coefﬁcient for logarithmic regression is closer to 1, so

perform the weight prediction calculation using logarithmic regression.

Obtain ţ when x = 350:

350

(VAR) ( )

d2 n E

(S-VAR)

1000056129

Base-n Calculations (BASE)

To perform the example operations in this section, ﬁrst select BASE (

calculation mode.

) as the

Performing Base-n Calculations

Specifying the Default Number Base

Use the following keys to select a default number base.

DEC ' HEX 10 BIN

e^xOCT e

w M l i

To select this number

base:

Press this key:

Screen Indicator

Decimal

Hexadecimal

Binary

(DEC)

(HEX)

(BIN)

Octal

(OCT)

Number base indicator

E-52

Example Base- Calculations

Example 1: To select binary as the number base and calculate 1₂+ 1₂

(BIN)

1+1E

Example 2: To select octal as the number base and calculate 7₈+ 1₈

(OCT)

7+1E

• Inputting an invalid value causes a Syntax ERROR.

• In the BASE Mode, input of fractional (decimal) values and exponential values is not

supported. Anything to the right of the decimal point of calculation results is cut off.

Hexadecimal Value Input and Calculation Example

Use the following keys to input the letters required for hexadecimal values (A, B, C, D, E, F).

{

}{A} {B}

{C} sin^–1{D} cos^–1tan^–1

y e w s c t

Example: To select hexadecimal as the number base and calculate 1F₁₆+ 1₁₆

(HEX)

(F)

1t +1E

Effective Calculation Ranges

Number Base

Effective Range

Positive: 0

111111111

Binary

Negative: 1000000000

1111111111

7777777777

Positive: 0

3777777777

Octal

Negative: 4000000000

Decimal

Hexadecimal

–2147483648

2147483647

Positive: 0

7FFFFFFF

FFFFFFFF

Negative: 80000000

A Math ERROR occurs when a calculation result is outside of the applicable range for the

current default number base.

E-53

Converting a Displayed Result to another Number Base

Pressing

(DEC),

(HEX),

(BIN), or

(OCT) while a calculation result is displayed

will convert the result to the corresponding number base.

Example: To convert the decimal value 30₁₀to binary, octal, and hexadecimal format

(DEC)

Ax 30E

11110

(BIN)

(OCT)

(HEX)

Using the LOGIC Menu

In the BASE Mode, the

key changes function to become a LOGIC menu display key.

The LOGIC menu has three screens, and you can use

them.

and

to navigate between

o r

xno r

^a1^nd

Screen 1

^x1^{o r}

^N3^e

No t

1 2 3 4

Screen 3

Screen 2

Specifying a Number Base for a Particular Value

You can specify a number base that is different from the current default number base while

inputting a value.

Specifying the Number Base during Input

Inputting a decimal value of 3, for example, can be performed using the following key

operation.

(LOGIC)

(d)

d3I

E-54

Example Calculation Using Base- Speciﬁcation

Example: To perform the calculation 5₁₀+ 5₁₆, and display the result in binary

d5 h5

(BIN)

(LOGIC)

(d)

(h)

d2 5E

(LOGIC)

5+X

1010

Performing Calculations Using Logical Operations and

Negative Binary Values

Your calculator can perform 10-digit (10-bit) binary logical operations and negative value

calculations. All of the examples shown below are performed with BIN (binary) set as the

default number base.

Logical Product (and)

Returns the result of a bitwise product.

Example: 1010₂and 1100₂= 1000₂

^1010and111⁰⁰000

(LOGIC)

1100E

(and)

1010X

Logical Sum (or)

Returns the result of a bitwise sum.

Example: 1011₂or 11010₂= 11011₂

1011o r 11010

(LOGIC)

(or)

1011X

11010E

11011

Exclusive Logical Sum (xor)

Returns the result of a bitwise exclusive logical sum.

Example: 1010₂xor 1100₂= 110₂

1010xo r 1100

(LOGIC)

(xor)

1010X

1100E

110

Exclusive Logical Sum Negation (xnor)

Returns the result of the negation of a bitwise exclusive logical sum.

Example: 1111₂xnor 101₂= 1111110101₂

1111xno r 101

1111110101

(LOGIC)

(xnor)

1111X

101E

E-55

Complement/Inversion (Not)

Returns the complement (bitwise inversion) of a value.

Example: Not(1010₂) = 1111110101₂

(

)

No t 1010

(LOGIC)

(Not)

1010)

1111110101

Negation (Neg)

Returns the twos complement of a value.

Example: Neg(101101₂) = 1111010011₂

(

)

Ne 10 1101

(LOGIC)

(Neg)

101101)E

1111010011

Built-in Formulas

Your calculator has 23 built-in formulas for mathematics and physics, which can be used in

the COMP Mode.

Using Built-in Formulas

Selecting a Built-in Formula by Its Formula Number

1. Press

• This will display the message “Formula No.?”.

2. Input the two-digit formula number (01 to 23) of the formula you want to recall.

• For a list of formulas and their numbers, see the “Built-in Formula List” (page 58).

Fo rmu l a

^N–^o0^{. ?}6–

Selecting a Built-in Formula by Scrolling

1. Press

2. Use

and

to scroll through the built-in formulas until the one you want to recall is

on the display.

Performing Calculation with a Built-in Formula

The following example shows how to use Heron’s formula to determine the area of a triangle

when the lengths of its three sides (8, 5, 5) are known.

Operation Procedure

Recall Heron’s formula:

03 He r onFormul a

Gccc

E-56

(Prompt for input for variable a)

Input 8 for variable a:

Input 5 for variable b:

Input 5 for variable c:

03 He r onFormul a

• As shown above, the calculation result appears after you assign values to all of the

required variables.

• Pressing

while a calculation result is on the display will re-execute the formula from

the beginning.

Special Built-in Formula Variables (Formula Variables)

When you perform a calculation using a built-in formula, you assign values to the variables

of the formula and calculate the result. In addition to the a, b, and c variables we saw

in Heron's formula above, there are also variables named r, t, v, ρ, and Ƨ. Since these

variables are used only in built-in formulas, they are called formula variables.

Values you assign to formula variables when you perform a calculation with a built-in

formula are retained until you change to another calculation mode, perform a memory clear

operation (

(CLR)

(Mem)), or reset the calculator (

(CLR)

(All)). This

means that you can execute a built-in calculation multiple times leaving one or more of the

variables assigned with the same values as a previous execution, if you want.

Pressing

after performing the operation under “Performing Calculation with a Built-in

Formula” will display the variable assignment screen again, with the previously assigned

values as the initial defaults.

Prompt for input for variable a

Value previously assigned to variable a

If you want to leave the displayed value assigned to the variable, press . In this case,

pressing

will leave 8 assigned to variable a.

Note

Even if you select a different built-in formula, all variables that have the same names as the

previously used formula will retain their current values.

E-57

Displaying a Built-in Formula

While inputting values for the variables of a formula, you can display the formula by pressing

(LOOK).

(Value Input Screen)

(LOOK)

(

) (

–

• If the formula is too long to ﬁt on the display use the

the missing part.

key to scroll to the right to view

• To clear the formula from the display, press

(EXIT) or

Built-in Formula List

No. 01 Quadratic Equation Solution

Solves a quadratic equation using values you specify for a, b, and c.

(a ≠ 0, b − 4ac ≧ 0)

ax + bx + c = 0

No. 02 Cosine Theorem

For a triangle for which the lengths of two sides (b and c) and the angle (Ƨ) formed by them

are known, determines the length of remaining side.

a =

+ c − 2bc cos

(b, c > 0, 0˚< ≦ 180˚)

No. 03 Heron’s Formula

Determines the area (S) of a triangle when the lengths of its three sides (a, b, c) are known.

(a + b + c)

S = s(s − a)(s − b)(s − c) , s=

(a + b > c > 0, b + c > a > 0, c + a > b > 0)

No. 04 Normal Probability Function P(x)

Uses Hastings’ estimate formula to determine the probability of a standard normal

distribution P(x) illustrated below when the standardized variate (x) is known.

P（x）

2π

−

P(x) =

_−∞e dt

∫

(0 ≦ x < 1 × 10⁵⁰

)

Important!

Since this is an estimate formula, proper precision may not be obtainable.

E-58

No. 05 Normal Probability Function Q(x)

Uses Hastings’ estimate formula to determine the probability of a standard normal

distribution Q(x) illustrated below when the standardized variate (x) is known.

Q（x）

2π

−

Q(x) =

∫

(0 ≦ x < 1 × 10⁵⁰

)

Important!

Since this is an estimate formula, proper precision may not be obtainable.

No. 06 Coulomb’s Law

Determines the force (F) between two charges of quantities Q and q, over a separation of r.

4πε₀

F =

(Ƥ₀: permittivity)

(r > 0)

Units: Q, q : C, r : m

No. 07 Resistance of a Conductor

Determines resistance R of a conductor when its length ( ) and cross sectional area (S),

and the resistance of its component material ( ρ) are known.

Units:

: m, S : m², ρ : Ω ·m, R : Ω

R =

(S, , > 0)

No. 08 Magnetic Force

Determines the motive force (F) in a conductor with electric current (I) ﬂowing through it

and placed in a magnetic ﬁeld of uniform magnetic force density (B), when the length of the

conductor is and the angle formed by the conductor and magnetic ﬁeld is

(

> 0, 0˚≦ θ ≦90˚)

F = IB sinθ

Units: B : T, I : A, : m, Ƨ: ° (degrees), F : N

No. 09 Change in Terminal Voltage of R in an RC Series Circuit

Determines the terminal voltage (V_R) of terminal R at time t in an RC series circuit when

voltage V is applied to a circuit with a resistance of R and capacitance of C.

−t/CR

VR = V•e

(C, R, t > 0)

Units: R : Ω , C : F, t : seconds, V and V _R: V

E-59

No. 10 Voltage Gain

Determines the voltage gain (G) of an ampliﬁer circuit when input voltage (E) and output

voltage (E´) are known.

Units: E and E Ϣ: V, G : d B

G[dB] = 20 log10

[dB]

(E E >0)

(

)

No. 11 Impedance in an LRC Series Circuit

Determines the impedance (Z) of an LRC series circuit of frequency f, when resistance (R),

coil inductance (L), and capacitance (C) are known.

^ωC

Z = R + 2π f L−

R + ωL−

(

)

(

)

2π f C

(R, f, L, C>0)

Units: f : Hz, L : H, C : F, R and Z : Ω

No. 12 Impedance in an LRC Parallel Circuit

Determines the impedance (Z) of an LRC parallel circuit of frequency f, when resistance (R),

coil inductance (L), and capacitance (C) are known.

Z =

(R, f, L, C>0)

2π f C−

( ) (

)

2π f L

Units: f : Hz, C : F, L : H, R and Z : Ω

No. 13 Frequency of Electric Oscillation

Determines the harmonic oscillation frequency (f₁) of a series resonance circuit when the

coil self-inductance (L) and capacitance (C) are known.

(L, C>0)

Units:

: H, : F, ₁: Hz

2π LC

No. 14 Distance of Drop

Determines the distance of drop (S) after t seconds of an object dropped straight down

(gravitational direction) at an initial velocity of v₁(air friction disregarded).

(g: gravitational acceleration, t > 0)

S = v1t + gt

Units: v ₁: m/s, t : seconds, S : m

E-60

No. 15 Cycle of Simple Pendulum

Determines the cycle (T) of a simple pendulum with a string of length

Units:

: m, T : seconds

T = 2π

(g: gravitational acceleration, >0)

No. 16 Cycle of Spring Pendulum

Determines the cycle of simple oscillation (T) of a spring pendulum when the mass of the

weight (m) and the spring constant of the spring (k) are known.

(m, k > 0)

T = 2π

Units: m : kg, k : N/m, T : seconds

No. 17 Doppler Effect

Determines the oscillation frequency (f) heard by an observer when both the sound source

and observer are moving, when the sound source oscillation frequency (f₁), acoustic velocity

(v), sound source movement speed (v₁) and observer movement speed (u) are known.

v− u

f = f

v ≠ v1, f > 0, (v− u)/( v− v1) > 0

(

)

v− v

Units: v , v ₁and u : m/s, f ₁and f : Hz

No. 18 Equation of State of Ideal Gas

Determines the pressure (P) of a gas when the number of mols (n), absolute temperature (T),

and volume (V) are known.

nRT

Units: n : mol, T : K, V : m³, P : N/m³

P =

(R: gas constant, n, T, V > 0)

No. 19 Centrifugal Force

Determines the centrifugal force (F) for an object of mass m moving at velocity v in a circular

pattern of radius r.

Units: m : kg, v : m/s, r : m, F : N

F = m

(m, v, r > 0)

No. 20 Elastic Energy

Determines the elastic energy (U) of an object when its elastic constant (K) and elongated

length (x) are known.

Units: K : N/m, x : m, U : J

(K, x > 0)

U= Kx

E-61

No. 21 Bernoulli’s Theorem

Determines the ﬁxed value (C) of an inviscid ﬂuid (steady ﬂow, incompressible ﬂuid) when

the ﬂow velocity (v), location (height) (z), speciﬁc weight ( ρ), and pressure (P) are known.

(g: gravitational acceleration, v, z, , P > 0)

Units: v : m/s, z : m, ρ : kgf/m³, P : kgf/m², C : m²/s²

C = v + +gz

No. 22 Calculations Using a Stadia (Height)

Determines the difference in elevation (h) from the transit to the leveling rod after a transit

is used to read the length on the leveling rod ( ) between the upper and lower stadia lines,

and the angle of elevation (Ƨ).

(K and C: stadia constants, 0° <

Units:

90°, > 0)

h = K sin2θ + Csinθ

: m, Ƨ: ° (degrees), h : m

No. 23 Calculations Using a Stadia (Distance)

Determines the horizontal distance (S) from the transit to the leveling rod after a transit is

used to read the length on the leveling rod ( ) between the upper and lower stadia lines,

and the angle of elevation (Ƨ).

(K and C: stadia constants, 0° < θ < 90°, > 0)

S = K cos θ+ Ccosθ

Units:

: m, Ƨ: ° (degrees), S : m

Program Mode (PRGM)

You can use the PRGM Mode (

) to create and store programs for calculations you

need to perform on a regular basis.You can include any calculation that can be performed

in the COMP, CMPLX, BASE, SD, or REG Mode in a program.

Program Mode Overview

Specifying a Program Run Mode

Though you create and run programs in the PRGM Mode, each program has a “run mode”

that it runs in.You can specify COMP, CMPLX, BASE, SD, or REG as a program’s run

mode. This means you need to think about what you want your program to do and select the

appropriate run mode.

Program Memory

Program memory has a total capacity of 680 bytes, which can be shared by up to four

programs. Further program storage is not possible after program memory becomes full.

E-62

Creating a Program

Creating a New Program

Example: To create a program that converts inches to centimeters (1 inch = 2.54 cm)

? → A : A × 2.54

1. Press

2. Press

(PRGM) to enter the PRGM Mode.

ED I T RUN DEL

(EDIT).

Program areas that already contain program data (P1 through P4)

EDI T Pr o

P-1234 ^{r a}6^m70

Remaining program memory capacity

3. Press the number key that corresponds to an unused program area number.

• This displays the run mode selection menu. Use

screen 1 and screen 2.

and

to switch between menu

MODE COMP CMPLX

MODE BASE SD REG

3 4 5

Screen 1

Screen 2

4. Press the number key that corresponds to the mode you want to assign as the program’s

run mode.

• Here, select

(COMP) on screen 1. This selects COMP

as the run mode, and displays the program editing

screen.

000

Important!

You cannot change the run mode of a program once it has been assigned. A run mode can

be assigned only when you are creating a new program.

5. Input the program.

→

A A

^{2. 54}010

• Here we will input the program shown below.

Program

? → A : A × 2.54

(P-CMD)

(?)

(A)

Key Operation

(STO)

- w

(A)

a- *c.fe

•

(P-CMD) displays a special program command input screen. See “Inputting

Commands” on page 65 for more information.

E-63

6. After inputting the program, press

(EXIT).

• To run the program you just created, press

here to display the RUN Program

screen. For more information, see “Running a Program” below.

• To return to the normal calculation screen, press

to enter the COMP Mode.

Editing an Existing Program

1. Press

(PRGM)

(EDIT) to display the EDIT Program screen.

2. Use number keys

you want to edit.

through

to select the program area that contains the program

3. Use

and

to move the cursor around the program, and perform the required

operations to edit the contents of the program or to add new contents.

• Pressing jumps to the beginning of the program, while jumps to the end.

4. After you ﬁnish editing the program, press

(EXIT).

Running a Program

You can run a program in the PRGM Mode or from another mode.

Running a Program from Outside the PRGM Mode

1. Press

P1 P2 P3 P4

1 2 3 4

2. Use number keys

through

to select a program area and execute its program.

Running a Program in the PRGM Mode

1. Press

(PRGM) to display the PRGM Mode initial screen.

2. Press

(RUN).

• This will display the RUN Program screen.

Program areas that already contain program data (P1 through P4)

RUN P r o r am

Remaining program memory capacity

P-1234 670

3. Use number keys

you want to run.

through

to select the program area that contains the program

• This will execute the program in the program area you select.

What to do if an error message appears

Press

. This will display the editing screen for the program, with the cursor located

at the location where the error was generated so you can correct the problem.

Deleting a Program

You can delete an existing program by specifying its program area number.

Deleting the Program in a Speciﬁc Program Area

1. Press

(PRGM) to display the PRGM Mode initial screen.

E-64

2. Press

(DEL).

Program areas that already contain program data (P1 through P4)

Remaining program memory capacity

DELETE Pr o r am

P-1234 670

3. Use number keys

to delete.

through

to select the program area whose program you want

• The symbol next to the number of the program area

that contained the program you just deleted will turn off,

and the remaining program memory capacity value will

increase.

DELETE Pr o r am

P-1234 680

Inputting Commands

Inputting Special Program Commands

1. While the program editing screen is on the display, press

(P-CMD).

• This displays page 1 of the command menu.

→

1 2 3 4

to scroll through the pages and display the one that contains the

2. Use

and

command you want.

3. Use number keys

through

to select and input the command you want.

Note

To input a separator symbol (:), press

Functions that Can be Input as Program Commands

You can input the settings and other operations that you perform during normal calculations

as program commands. For more information, see the “Command Reference” below.

Command Reference

This section provides details on each of the commands that you can use in programs.

Commands that have in the title can be input on the screen that appears when you

press

(P-CMD) or

Basic Operation Commands

? (Input Prompt)

Syntax ? → {variable}

Function

Displays the input prompt “{variable}?” and assigns the input value to a

variable.

Example

? → A

E-65

→ (Variable Assignment)

Syntax {expression ; ?} → {variable}

Function

Assigns the value obtained by the element on the left to the variable on the

right.

Example

A+5 → A

: (Separator Code)

Syntax {statement} : {statement} : ... : {statement}

Function

Example

Separates statements. Does not stop program execution.

? → A : A²: Ans²

(Output Command)

Syntax

{statement}

Function

Pauses program execution and displays the result of the current execution.

The

symbol is turned on while program execution is paused by this

command.

Example

? → A : A²

Ans²

Unconditional Jump Command

Goto ~ Lbl

Syntax

Function

Example

Goto n : .... : Lbl n or Lbl n : .... : Goto n (n = integer from 0 to 9)

Execution of Goto n jumps to corresponding Lbl n.

? → A : Lbl 1 : ? → B : A × B ÷ 2

Goto 1

Important!

A Syntax ERROR occurs if there is no corresponding Lbl n in the same program where

Goto n is located.

Conditional Jump Commands and Conditional Expressions

Syntax

{expression} {relational operator} {expression}

{statement2} : ....

{statement1} :

{expression}

{statement1} : {statement2} : ....

Function

Conditional branching command used in combination with relational

operators (=, ≠, >, , <, ).

Syntax : {statement1} is executed if the condition to the left of the

command is true, and then {statement2} and everything after it is executed

in sequence. {statement1} is skipped if the condition to the left of the

command is false, and then {statement2} and everything after it is executed.

Syntax : A non-zero evaluation result of the condition to the left of the

command is interpreted as “true”, so {statement1} is executed, followed by

{statement2} and everything after it in succession. A zero evaluation result

of the condition to the left of the

command is interpreted as “false”, so

{statement1} is skipped, and {statement2} and everything after it is executed.

E-66

Example

Lbl 1 : ? → A : A

(A)

S '

Goto 1

=, ≠, >, , <, (Relational Operators)

Syntax

{expression} {relational operator} {expression}

Function

These commands evaluate the expressions on either side, and return a value

of true (1) or false (0). These commands are used in combination with the

branching command , and when structuring the {conditional expression} of

If statements and While statements.

Example

See the entries for

(page 68).

(page 66), If statement (page 67), and While statement

Note

These commands evaluate the expressions on either side, and return 1 if true and 0 if false,

and store the result in Ans.

Control Structure Commands/If Statement

The If statement is used to control program execution branching according to whether the

expression following If (which is the branching condition) is true or false.

If Statement Precautions

• An If must always be accompanied by a Then. Using an If without a corresponding Then

will result in a Syntax ERROR.

• An expression, Goto command, or Break command can be used for the {expression*}

following Then and Else.

If~Then (~Else) ~IfEnd

Syntax

If {conditional expression} : Then {expression*} : Else {expression*} : IfEnd :

{statement} : ...

Function

• The statements following Then are executed up to Else, and then the

statements following IfEnd are executed when the conditional statement

following If is true. The statements following Else and then the statements

following IfEnd are executed when the conditional statement following If is

false.

• Else {expression} may be omitted.

• Always include the IfEnd:{statement}. Omitting it will not cause an error,

but certain program contents can cause unexpected execution results by

everything after the If statement.

Example 1

Example 2

? → A : If A < 10 : Then 10A

Else 9A

IfEnd : Ans×1.05

? → A : If A > 0 : Then A × 10 → A : IfEnd : Ans×1.05

Control Structure Commands/For Statement

The For statement repeats execution of the statements between For and Next as long as

the value assigned to the control variable is within the speciﬁed range.

For Statement Precautions

A For statement must always be accompanied by a Next statement. Using a For without a

corresponding Next will result in a Syntax ERROR.

E-67

For~To~Next

Syntax

For {expression (starting value)} → {variable (control variable)} To {expression

(ending value)} : {statement} : ... {statement} : Next : ....

Function

Execution of the statements from For to Next repeats as the control variable

is incremented by 1 with each execution, starting from the starting value.

When the value of the control value reaches the ending value, execution

jumps to the statement following Next. Program execution stops if there is no

statement following Next.

Example

For 1 → A To 10 : A²→ B : B

For~To~Step~Next

Syntax

For {expression (starting value)} → {variable (control variable)} To {expression

(ending value)} Step {expression (step)} : {statement} : ... {statement} :

Next : ....

Function

Example

Execution of the statements from For to Next repeats as the control variable

is incremented by the step amount with each execution, starting from the

starting value. Except for that, this command is the same as For~To~Next.

For 1 → A To 10 Step 0.5 : A²→ B : B

Control Structure Commands/While Statement

While~WhileEnd

Syntax

Function

While {conditional expression} : {statement} : ... {statement} : WhileEnd : ....

The statements from While to WhileEnd are repeated while the conditional

expression following While is true (non-zero). When the conditional

expression following While becomes false (0), the statement following

WhileEnd is executed.

Example

? → A : While A < 10 : A²

A+1 → A : WhileEnd : A÷2

Note

If the condition of the While statement is false the ﬁrst time this command is executed,

execution jumps directly to the statement following WhileEnd without executing the

statements from While to WhileEnd even once.

Program Control Commands

Break

Syntax

.. : {Then ; Else ; } Break : ..

Function

This command forces a break in a For or While loop, and jumps to the next

command. Normally, this command is used inside of a Then statement in

order to apply a Break condition.

Example

? → A : While A > 0 : If A > 2 : Then Break : IfEnd : WhileEnd : A

Setup Commands

These commands function the same way as the calculator’s various setup settings. For

more information, see “Calculator Setup” on page 8.

E-68

Important!

With some setup commands, the settings you conﬁgure remain in effect even after you

ﬁ nish running the program.

Angle Unit Commands

Deg, Rad, Gra

(COMP, CMPLX, SD, REG)

Syntax

.. : Deg : ..

.. : Rad : ..

.. : Gra : ..

Operation

Function

(SETUP)

(Deg)

(Rad)

(Gra)

These commands specify the angle unit setting.

Display Format Command

Fix

(COMP, CMPLX, SD, REG)

Syntax

Operation

.. : Fix {n} : .. (n = an integer from 0 to 9)

(SETUP) (Fix) to

!, eb

Function

This command ﬁxes the number of decimal places (from 0 to 9) for output of

calculation results.

Sci

(COMP, CMPLX, SD, REG)

Syntax

.. : Sci {n} : .. (n = an integer from 0 to 9)

Operation

(SETUP)

!, ec

(Sci)

Function

This command ﬁxes the number of signiﬁcant digits (from 1 to 10) for output

of calculation results.

Pressing

digits.

(SETUP)

(Sci) and then

speciﬁes 10 signiﬁcant

Norm

(COMP, CMPLX, SD, REG)

Syntax

.. : Norm {1 ; 2} : ..

Operation

Function

(SETUP)

(Norm)

!, ed

This command speciﬁes either Norm1 or Norm2 for output of calculation

results.

Statistical Frequency Command

FreqOn, FreqOff

(SD, REG)

Syntax

.. : FreqOn : ..

.. : FreqOff : ..

Operation

Function

(SETUP)

(FreqOn)

(FreqOff)

(SETUP)

This command turns statistical frequency on (FreqOn) or off (FreqOff).

E-69

Clear Commands

ClrMemory

(COMP, CMPLX, BASE)

Syntax

Operation

Function

.. : ClrMemory : ..

(CLR)

This command clears all variables (A, B, C, D, X, Y, M) to zero.

(Mem)

Note

To clear a speciﬁc variable, use 0 → {variable}.

ClrStat

(SD, REG)

Syntax

Operation

Function

.. : ClrStat : ..

(CLR)

(Stat)

This command clears all statistical sample data currently in memory.

Independent Memory Commands

M+, M–

(COMP, CMPLX, BASE)

Syntax

Operation

Function

.. : {expression} M+ : .. / .. : {expression} M– : ..

(M–)

M+ adds the value of the expression to independent memory, while M–

subtracts it.

l !l

Rounding (Rnd) Command

Rnd(

(COMP, CMPLX, SD, REG)

Syntax

.. : {expression} : Rnd(Ans : ..

Operation

Function

(Rnd)

This command rounds a calculation result in accordance with the number of

digits speciﬁed by the display format.

Number Base Commands

Dec, Hex, Bin, Oct

(BASE)

Syntax

Operation

Function

.. : Dec : .. / .. : Hex : .. / .. : Bin : .. / .. : Oct : ..

(DEC)/ (HEX)/ (BIN)/ (OCT)

These commands specify the number base for base-n calculations.

Statistical Data Input Command

(SD, REG)

Syntax

.. : {expression (x-value)} ; {expression (Freq-value)} DT : ..

..................... SD Mode, FreqOn

.. : {expression (x-value)} DT : ..

..................... SD Mode, FreqOff

.. : {expression (x-value)} , {expression (y-value)} ; {expression (Freq-value)}

DT : ..

...................REG Mode, FreqOn

.. : {expression (x-value)} , {expression (y-value)} DT : ..

...................REG Mode, FreqOff

E-70

Important!

To input a semicolon (;) in the above syntax, press

(;). To input a comma (,), press

Operation

Function

(Inputs DT.)

Use this command to input one set of sample data. The DT command

functions the same way as the

Mode.

key (DT key) in the SD Mode and REG

Functions Not Supported in Programs

The following functions are not supported inside of functions.

• Calculation result conversion functions (ENG , ENG , Sexagesimal ↔ Decimal

Conversion, Fraction ↔ Decimal Conversion)

• Display switching (

displayed

(Re⇔Im)) while a complex number calculation result is

• Reset (

(CLR)

(All)

)

• Setup information clear (

(CLR)

(Setup)

)

Appendix

Calculation Priority Sequence

The calculator performs calculations you input in accordance with the priority sequence shown

below.

•

Basically, calculations are performed from left to right.

Calculations enclosed in parentheses are given priority.

Sequence

Operation Type

Description

Parenthetical Functions

Pol(, Rec(

sin(, cos(, tan(, sin (, cos (, tan (, sinh(, cosh(,

–1

tanh(, sinh (, cosh (, tanh

(

log(, ln(, ^(, 10^(,

(

arg(, Abs(, Conjg(

Not(, Neg(, Rnd(

–1

Functions Preceded by Values

Power, Power Root

Percent

!, ° ´ ˝, °, ,

(

^(,

Fractions

Preﬁx Symbols

(–) (minus sign)

d, h, b, o (number base symbol)

Statistical Estimated Value

Calculations

Permutation, Combination

Complex Number Symbol

P ,

∠

E-71

Sequence

Operation Type

Multiplication, Division

Omitted Multiplication Sign

Description

×, ÷

Multiplication sign can be omitted immediately

before π , e, variables, scientiﬁc constants (2π , 5A,

π A, 3mp, 2i, etc.), and parenthetical functions

(2 (3), Asin(30), etc.)

Addition, Subtraction

Relational Operators

Logical Product

+, −

=, ≠, >, <,

and

Logical Sum, Exclusive Logical or, xor, xnor

Sum, Exclusive Negative

Logical Sum

Note

•

If a calculation contains a negative value, you may need to enclose the negative value in

parentheses. If you want to square the value –2, for example, you need to input: (–2)². This is

because x²is a function preceded by a value (Priority 2, above), whose priority is greater than the

negative sign, which is a preﬁx symbol (Priority 4).

–2²= –4

-cxw

(–2)²= 4

(-c)xw

•

Multiplication and division, and multiplication where the sign is omitted are the same priority

(Priority 7), so these operations are performed from left to right when both types are mixed in the

same calculation. Enclosing an operation in parentheses causes it to be performed ﬁrst, so the

use of parentheses can result in different calculation results.

( )

c. i w

{

( )

(c. i )w

(2 ) = –

Stack Limitations

This calculator uses memory areas called “stacks” for temporary storage of lower calculation priority

sequence values, commands, and functions. The “numeric stack” has 10 levels and the “command

stack” has 24 levels as shown in the illustration below.

Numeric Stack Command Stack

A Stack ERROR occurs when the calculation you are performing causes the capacity of a stack to

be exceeded.

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Note

When inputting a value in the CMPLX Mode, each value takes up two stack levels: one for the real

part and one for the imaginary part. This means that the numeric stack has only ﬁve levels in the

CMPLX Mode.

Calculation Ranges, Number of Digits, and Precision

The following table shows the general calculation range (value input and output range), number of

digits used for internal calculations, and calculation precision.

–99

Calculation Range

Internal Calculation

1×10

15 digits

to 9.999999999×10 or 0

In general, 1 at the 10th digit for a single calculation. Error in the

case of a calculation result in exponential format is 1 at the least

signiﬁcant digits of the mantissa. Errors are cumulative in the case of

consecutive calculations.

Precision

Function Calculation Input Ranges and Precision

Functions

Input Range

DEG

RAD

GRA

DEG

RAD

GRA

DEG

RAD

GRA

| < 9×10

sin

| < 157079632.7

| < 1×10

| < 9×10

cos

| < 157079632.7

| < 1×10

Same as sin , except when

| = (2 –1)×90.

tan

Same as sin , except when

| = (2 –1)×π/2.

Same as sin , except when

| = (2 –1)×100.

^–1x

sin

cos

tan

9.999999999×10

230.2585092

sinh

coshx

^–1x

sinh

4.999999999×10

cosh

4.999999999×10

–1

tanh

9.999999999×10

^–1x

tanh

9.999999999×10

log /ln

0 <

9.999999999×10

–9.999999999×10

99.99999999

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Functions

Input Range

230.2585092

–9.999999999×10

100

< 1×10

x²

| < 1×10⁵⁰

| < 1×10¹⁰⁰

;

< 1×10¹⁰⁰

69 ( is an integer)

< 1×10 , 0

n n r

(

are integers)

n n r

{

n n r

n r

100

!/( – )!} < 1×10

< 1×10 , 0

(

n r

100

!/ ! < 1×10

or 1

!/( – )! < 1×10

n n r

|, | | < 9.999999999×10

Pol(

x y

)

9.999999999×10

Rec( , θ)

θ: Same as sinx

100

b c

< 1×10

°’ ”

100

| < 1×10

Decimal ↔ Sexagesimal Conversions

0°0 0 9999999°59 59

´ ˝ <

100

> 0: –1×10

log < 100

= 0: > 0

)

< 0:

(

m n

are integers)

100

However: –1×10

log | | < 100

100

> 0:

= 0: > 0

< 0: = 2 +1,

0, –1×10

< 1/ log < 100

(

m n

are integers)

100

However: –1×10

< 1/ log | | < 100

Total of integer, numerator, and denominator must be 10 digits or less (including

separtor symbols).

•

^( ),

!, P ,

type functions require consecutive internal calculation, which can

x n r n r

result in accumulation of errors that occur within each individual calculation.

Errors are cumulative and tend to be large in the vicinity of a function’s singular point and

inﬂection point.

Error Messages

An error message will appear on the screen if you perform a

calculation that causes a calculator’s limit to be exceeded, or if you

try to perform some operation that is not allowed.

Mat h ERROR

Sample Error Message

E-74

Recovering from an Error Message

You can recover from an error message by performing the key operations described below,

regardless of the error type.

•

Press

to display the editing screen for the calculation expression you input immediately

before the error occurred, with the cursor positioned at the location that caused the error. For

more information, see “Finding the Location of an Error” on page 13.

•

Pressing

will clear the calculation expression you input immediately before the error occurred.

Note that a calculation expression that causes an error will not be included in calculation history.

Error Message Reference

This section lists all of the error messages that the calculator displays, as well as their causes and

what you need to do to avoid them.

Math ERROR

Cause

Action

• An intermediate or the ﬁnal result of the calculation falls outside of the

allowable calculation range.

• An input value is outside the allowable input range.

• You are trying to perform an illegal mathematical operation (such as

division by zero).

• Check your input values and reduce the number of digits, if required.

• When using independent memory or a variable as the argument of a

function, make sure that the memory or variable value is within the

allowable range for the function.

For information about the allowable value input range, see “Calculation Ranges, Number of Digits,

and Precision” on page 73.

Stack ERROR

Cause

The calculation has causes the capacity of the numeric stack or the

command stack to be exceeded.

Action

• Simplify the calculation expression so it does not exceed the capacity of

the stacks.

• Try splitting the calculation into two or more parts.

For information about the capacities of the stacks, see “Stack Limitations” on page 72.

Syntax ERROR

Cause

Action

The calculation has a format problem.

Check the syntax and make the required corrections.

Arg ERROR

Cause

Action

The calculation has a problem with how an argument being used.

Check how arguments are being used and make the required corrections.

E-75

Data Full

Cause

You are attempting to store sample data in the SD Mode or REG Mode

when the allowable number of data samples are already stored in memory.

Action

Keep the number of data samples within the allowable limit. For more

information, see “Maximum Number of Input Data Items” on page 38.

Go ERROR

Cause

A program (that you created in the PRGM Mode) has a “Goto ” command

without a corresponding “Lbl ” label.

Action

Either add a “Lbl ” for the “Goto ” command, or delete the applicable “Goto

” command.

Before assuming malfunction of the calculator...

Perform the following steps whenever an error occurs during a calculation or when calculation

results are not what you expected. If one step does not correct the problem, move on to the next

step. Note that you should make copies of important copies of important data before performing

these steps.

Check the calculation expression to make sure it does not include any errors.

Make sure that you are using the correct mode for the type of calculation you are trying to

perform.

If the above steps do not restore normal operation, press the

a self-check of its status as it starts up. If the calculator discovers a problem, it will return its

calculation mode and setup to their initial defaults, and clear all data currently in memory.

key. The calculator will perform

If step

does not restore normal operation, initialize all modes and settings by pressing

(CLR)

(All)

Power Requirements

Your calculator has a TWO WAY POWER system that combines a solar cell with a button

battery (LR44). Unlike solar cell-only calculators that operate only when light is present, a

TWO WAY POWER system calculator keeps on operating even in the dark. (Of course, you

will need enough light to be able to read the display contents.)

Replacing the Battery

Dim display characters, especially when using the calculator where lighting is dim, or slow

display response when you turn on the calculator indicates that button battery power is low.

Replace the battery whenever you notice these symptoms.You should also regularly replace

the battery at least once every three years, even if the calculator is operating normally.

Important!

Removing the button battery from the calculator causes independent memory contents and

values assigned to variables to be cleared.

E-76

Screw

1. Press

(OFF) to turn off the calculator.

To ensure that you do not accidentally turn on the

calculator while replacing the battery, slide the hard case

into the front of the calculator.

2. On the back of the calculator, remove the screw and the

battery cover.

3. Remove the old battery.

4. After wiping a new battery with a dry cloth, load it into the

battery compartment with its plus

you can see it).

side facing upwards (so

5. Replace the battery cover and secure it in place with the

screw.

6. Initialize the calculator by pressing

(CLR)

(All)

Be sure to perform this step! Do not skip it!

Auto Power Off

Your calculator will turn off automatically if you do not perform any operation for about 10

minutes. If this happens, press the

key to turn the calculator back on.

Speciﬁcations

Power Requirements:

Solar Cell: Built into front of calculator (ﬁxed)

Button Battery: G13 type (LR44) × 1

Approximate Battery Life:

3 years (based on 1 hour of operation per day)

Operating Temperature: 0˚C to 40˚C (32˚F to 104˚F)

Dimensions: 12.2 (H) × 80 (W) × 161 (D) mm

¹/₂" (H) × 3¹/₈" (W) × 6⁵/₁₆" (D)

Approximate Weight: 105 g (3.7 oz) including the battery

Bundled Accessories: Hard Case

E-77

CASIO Europe GmbH

Bornbarch 10, 22848 Norderstedt,

Germany

This mark applies in EU countries only.

CASIO COMPUTER CO., LTD.

6-2, Hon-machi 1-chome

Shibuya-ku, Tokyo 151-8543, Japan

SA0603-A

Printed in China

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