EN
https://edu.casio.com
User’s Guide
CASIO Worldwide Education Website
https://world.casio.com/manual/calc/
Manuals are available in multi languages at
Be sure to keep all user documentation handy for future reference.
fx-85GT X
fx-83GT X
Table of Contents
Before Using the Calculator.................................................... 4
About this Manual.................................................................................... 4
Initializing the Calculator..........................................................................4
Precautions..............................................................................................4
Safety Precautions..........................................................................................4
Handling Precautions......................................................................................5
Getting Started.........................................................................................5
Removing the Hard Case................................................................................5
Turning Power On and Off.............................................................................. 5
Adjusting Display Contrast..............................................................................6
Key Markings.................................................................................................. 6
Reading the Display........................................................................................8
Using Menus................................................................................................... 9
Calculation Modes and Calculator Setup.............................10
Calculation Mode................................................................................... 10
Configuring the Calculator Setup........................................................... 11
Items and Available Setting Options............................................................. 11
Initializing the Calculation Mode and Other Settings.....................................16
Inputting Expressions and Values........................................17
Inputting a Calculation Expression Using Values...................................17
Inputting a Calculation Expression Using Standard Format..........................17
Correcting an Expression..............................................................................18
Overwrite Input Mode (LineI/LineO or LineI/DecimalO only).........................19
Inputting an Expression Using Natural Textbook Format (MathI/MathO or
MathI/DecimalO Only)............................................................................20
Natural Textbook Format Input Examples.....................................................21
Undo Operations...........................................................................................22
Incorporating a Value into a Function............................................................22
Displaying Calculation Results in a Form that Includes √
2,
π
, etc.
(Irrational Number Form)....................................................................... 23
Basic Calculations..................................................................25
Recurring Decimal Calculations.............................................................25
Inputting a Recurring Decimal.......................................................................25
Displaying a Calculation Result as a Recurring Decimal Value.................... 26
Conditions for Displaying a Calculation Result as a Recurring Decimal.......28
Recurring Decimal Examples........................................................................29
Toggling Calculation Results..................................................................30
Arithmetic Calculations.......................................................................... 31
Number of Decimal Places and Number of Significant Digits....................... 32
Omitting a Final Closed Parenthesis.............................................................32
Fraction Calculations............................................................................. 32
1
Switching between Improper Fraction and Mixed Fraction Format...............34
Percent Calculations..............................................................................34
Degree, Minute, Second (Sexagesimal) Calculations............................36
Inputting Sexagesimal Values....................................................................... 36
Sexagesimal Calculations.............................................................................36
Converting Values between Sexagesimal and Decimal................................37
Multi-Statements....................................................................................37
Using Engineering Notation................................................................... 38
Prime Factorization................................................................................39
Calculation History and Replay..............................................................40
Calculation History........................................................................................ 40
Replay...........................................................................................................41
Using Memory Functions....................................................................... 42
Answer Memory (Ans)...................................................................................42
Variables (A, B, C, D, E, F, M, x, y)................................................................43
Independent Memory (M)..............................................................................44
Clearing the Contents of All Memories..........................................................46
Function Calculations............................................................47
Pi (
π), Natural Logarithm Base e............................................................ 47
Pi (
π)..............................................................................................................47
Natural Logarithm Base
e..............................................................................47
Trigonometric Functions, Inverse Trigonometric Functions................... 47
Trigonometric Functions................................................................................47
Inverse Trigonometric Functions...................................................................47
Hyperbolic Functions, Inverse Hyperbolic Functions.............................48
Hyperbolic Functions.....................................................................................48
Inverse Hyperbolic Functions........................................................................48
Converting an Input Value to the Calculator’s Default Angle Unit..........49
Exponential Functions, Logarithmic Functions...................................... 50
Exponential Functions...................................................................................50
Logarithmic Functions...................................................................................51
Power Functions and Power Root Functions.........................................52
Rectangular-Polar Coordinate Conversion............................................ 53
Converting to Polar Coordinates (Pol).......................................................... 54
Converting to Rectangular Coordinates (Rec).............................................. 54
Rectangular-Polar Coordinate Conversion Examples...................................54
Factorial (!).............................................................................................55
Absolute Value Calculation (Abs)...........................................................56
Random Number (Ran#), Random Integer (RanInt#)............................56
Random Number (Ran#)...............................................................................56
Random Integer (RanInt#)............................................................................ 57
Permutation (
n
P
r
) and Combination (
n
C
r
)............................................. 57
Rounding Function (Rnd).......................................................................58
2
Using Calculation Modes.......................................................60
Statistical Calculations...........................................................................60
Inputting Data with Statistics Editor...............................................................61
Statistical Calculation Screen........................................................................64
Using the Statistical Menu.............................................................................64
Displaying Statistical Values Based On Input Data.......................................67
Displaying Regression Calculation Results Based On Input Data (Paired-
Variable Data Only)....................................................................................... 67
Single-variable Statistical Calculation Commands........................................68
Single-variable Statistical Calculation Examples.......................................... 69
Linear Regression Calculation (y=a+bx) Commands....................................72
Linear Regression Calculation Examples..................................................... 74
Quadratic Regression Calculation (y=a+bx+cx
2
) Commands.......................77
Quadratic Regression Calculation Examples................................................78
Logarithmic Regression Calculation (y=a+b･ln(x)) Commands....................80
Logarithmic Regression Calculation Examples.............................................80
e Exponential Regression Calculation (y=a･e^(bx)) Commands...................82
e Exponential Regression Calculation Examples..........................................82
ab Exponential Regression Calculation (y=a･b^x) Commands.....................84
ab Exponential Regression Calculation Examples........................................85
Power Regression Calculation (y=a･x^b) Commands..................................87
Power Regression Calculation Examples..................................................... 87
Inverse Regression Calculation (y=a+b/x) Commands.................................89
Inverse Regression Calculation Examples....................................................90
Creating a Number Table.......................................................................92
Configuring a Number Table Generation Function........................................92
Ratio Calculations..................................................................................94
Changing the Ratio Expression Type............................................................95
Ratio Mode Calculation Example..................................................................95
Technical Information............................................................ 96
Errors..................................................................................................... 96
Displaying the Location of an Error...............................................................96
Clearing the Error Message.......................................................................... 96
Error Messages.............................................................................................96
Before Assuming Malfunction of the Calculator... ............................... 98
Replacing the Battery.............................................................................98
Calculation Priority Sequence................................................................99
Stack Limitations..................................................................................100
Calculation Ranges, Number of Digits, and Precision......................... 100
Calculation Range and Precision................................................................101
Function Calculation Input Ranges and Precision...................................... 101
Specifications.......................................................................................103
Frequently Asked Questions...............................................105
Frequently Asked Questions................................................................105
3
Before Using the Calculator
About this Manual
• 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.
• Unless specifically stated, all sample operations in this manual assume
that the calculator is in its initial default setup. Use the procedure under
“Initializing the Calculator” to return the calculator to its initial default
setup.
• The contents of this manual are subject to change without notice.
• The displays and illustrations (such as key markings) shown in this
manual are for illustrative purposes only, and may differ somewhat from
the actual items they represent.
• Company and product names used in this manual may be registered
trademarks or trademarks of their respective owners.
Initializing the Calculator
Perform the following procedure when you want to initialize the calculator
and return the calculation mode and setup (except for the Contrast setting)
to their initial default settings. Note that this operation also clears all data
currently in calculator memory.
(RESET) (Initialize All) (Yes)
Precautions
Be sure to read the following safety precautions before using the
calculator.
Safety Precautions
Battery
•
Keep batteries out of the reach of small children.
4
• Use only the type of battery specified for this calculator in this
manual.
Handling Precautions
• fx-83GT X: Even if the calculator is operating normally, replace the
battery at least once every two years (R03 (UM-4)).
fx-85GT X: Even if the calculator is operating normally, replace the
battery at least once every three years (LR44).
A dead battery can leak, causing damage to and malfunction of the
calculator. Never leave a dead battery in the calculator. Do not try using
the calculator while the battery is completely dead (fx-85GT X).
• The battery that comes with the calculator discharges slightly during
shipment and storage. Because of this, it may require replacement
sooner than the normal expected battery life.
• Avoid use and storage of the calculator in areas subjected to
temperature extremes, and large amounts of humidity and dust.
• Do not subject the calculator to excessive impact, pressure, or bending.
• Never try to take the calculator apart.
• Use a soft, dry cloth to clean the exterior of the calculator.
• Whenever discarding the calculator or batteries, be sure to do so in
accordance with the laws and regulations in your particular area.
Getting Started
Removing the Hard Case
Before using the calculator, slide its hard case downwards to remove it,
and then affix the hard case to the back of the calculator as shown in the
illustration below.
Turning Power On and Off
•
Press to turn on the calculator.
• Press (OFF) to turn off the calculator.
5
Note
• The calculator also will turn off automatically after approximately 10 minutes of non-
use. Press the key to turn the calculator back on.
Adjusting Display Contrast
1. Press
(SETUP).
• This displays the setup menu.
2. Press .
3. Press (Contrast).
• This displays the contrast adjustment screen.
4. Use and to adjust display contrast.
5. After the setting is the way you want, press .
Important!
• If adjusting display contrast does not improve display readability, it probably means
that battery power is low. Replace the battery.
Key Markings
Pressing the
or key followed by a second key performs the
alternate function of the second key. The alternate function is indicated by
the text printed above the key.
(1) Keycap function (2) Alternate function
6
• The following shows what the different colors of the alternate function
key text mean.
If key marking text is
this color:
It means this:
Yellow
Press and then the key to access the
applicable function.
Red
Press and then the key to input the
applicable variable, constant, function, or
symbol.
• The following shows an example of how an alternate function operation
is represented in this manual.
Example: (sin
-1*
)
* Indicates the function that is accessed by the key operation (
) before it. Note that this is not part of the actual key operation
you perform.
• The following shows an example of how a key operation to select an on-
screen menu item is represented in this manual.
Example:
(Input/Output)
* Indicates the menu item that is selected by the number key
operation ( ) before it. Note that this is not part of the actual key
operation you perform.
• The cursor key is marked with four arrows, indicating direction, as
shown in the illustration nearby. In this manual, cursor key operation is
indicated as , , , and .
• Pressing the displays an options screen. The options screen shows
functions that can be used in a calculation. The functions listed on the
options screen depend on the calculation mode.
7
Reading the Display
(1) Input expression
(2) Calculation result
(3) Indicators
• If a or indicator appears on the right side of either the input
expression line (1) or calculation result line (2), it means the displayed
line continues to the right. Use and to scroll the line display.
Note that if you want to scroll the input expression while both the and
indicators are displayed, you will need to press first and then use
and to scroll.
• The table below describes some of the typical indicators that appear at
the top of the screen (3).
This indicator: Means this:
The keypad has been shifted by pressing the
key. The keypad will unshift and this indicator will
disappear when you press a key.
The alpha input mode has been entered by
pressing the key. The alpha input mode will
be exited and this indicator will disappear when
you press a key.
/ /
Indicates the current setting of Angle Unit ( :
Degree, : Radian, or : Gradian) on the setup
menu.
FIX A fixed number of decimal places is in effect.
SCI A fixed number of significant digits is in effect.
M There is a value stored in independent memory.
The calculator is standing by for input of a variable
name to assign a value to the variable. This
indicator appears after you press .
Indicates that MathI/MathO or MathI/DecimalO is
selected for Input/Output on the setup menu.
8
The display currently shows an intermediate result
of a multi-statement calculation.
This indicator is displayed while the calculator is
being powered directly by its solar cells, either
entirely or in some combination with the battery.
(fx-85GT X only)
Using Menus
Some of the operations of this calculator are performed using menus.
Menus are displayed by pressing
or and then (SETUP).
General menu operation operations are described below.
• You can select a menu item by pressing the number key that
corresponds to the number to its left on the menu screen.
• A vertical scroll bar (1) indicates that the menu runs off the screen. In
this case, you can use and to scroll the menu up and down. A
left arrow (2) indicates that the currently displayed menu is a sub-menu.
To return from a sub-menu to its parent menu, press .
• To close a menu without selecting anything, press .
9
Calculation Modes and
Calculator Setup
Calculation Mode
The calculation modes of this calculator are described below.
Icon: Description:
(Calculate)
General calculations
(Statistics)
Statistical and regression calculations
(Table)
Generate a number table based on one or two
functions
(Ratio)
Ratio calculations
Specify the calculation mode that is suitable for the type of calculation you
want to perform.
1. Press to display the Main Menu.
2. Use the cursor keys to move the highlighting to the icon you want.
3. Press to display the initial screen of the mode whose icon you
selected.
10
Note
• You can also enter a mode without highlighting an icon in the Main Menu by inputting
the number or letter marked in the lower right corner of the icon.
• The initial default calculation mode is the Calculate Mode.
Configuring the Calculator Setup
Pressing
(SETUP) displays the setup menu, which you can use to
control how the calculations are executed and displayed.
To change the calculator setup
1. Press (SETUP) to display the setup menu.
2. Use and to scroll the setup menu, and then input the number
displayed to the left of the item whose setting you want to change.
Items and Available Setting Options
“◆” indicates the initial default setting.
Input/Output
Specifies the format to be used by the calculator for formula input and
calculation result output.
To specify this type
of input and output:
Perform this key operation:
Input: Natural
Textbook
Output: Format that
includes a fraction
*1
(SETUP) (Input/Output) (MathI/
MathO)◆
Input: Natural
Textbook
Output: Converted to
decimal value
(SETUP) (Input/Output) (MathI/
DecimalO)
Input: Linear
*2
Output: Decimal or
fraction
(SETUP) (Input/Output) (LineI/
LineO)
11
Input: Linear
*2
Output: Converted to
decimal value
(SETUP) (Input/Output) (LineI/
DecimalO)
*1 Decimal output is applied when this format cannot be output for some
reason.
*2 All calculations, including fractions and functions are input in a single
line. Same output format as that for models without Natural Textbook
Display (S-V.P.A.M. models, etc.)
Input/Output Format Display Examples
MathI/MathO
MathI/DecimalO
LineI/LineO
LineI/DecimalO
Angle Unit
Specifies degree, radian or gradian as the angle unit for value input and
calculation result display.
To specify this as the
default angle unit:
Perform this key operation:
Degrees
(SETUP) (Angle Unit) (Degree)
◆
Radians (SETUP) (Angle Unit) (Radian)
12
Grads
(SETUP) (Angle Unit)
(Gradian)
90°= π/2 radians = 100 grads
Number Format
Specifies the number of digits for display of a calculation result.
To specify this: Perform this key operation:
Number of Decimal
Places
(SETUP) (Number Format)
(Fix) －
Number of Significant
Digits
(SETUP) (Number Format)
(Sci) －
Exponential Display
Range
(SETUP) (Number Format)
(Norm) (Norm 1◆) or (Norm 2)
Calculation Result Display Examples
• Fix: The value you specify (from 0 to 9) controls the number of decimal
places for displayed calculation results. Calculation results are rounded
off to the specified digit before being displayed.
Example: 100
7 (≈)* 14.286 (Fix 3)
14.29 (Fix 2)
• Sci: The value you specify (from 0 to 9) controls the number of
significant digits for displayed calculation results. Calculation results are
rounded off to the specified digit before being displayed.
Example: 1 7 (≈)* 1.4286×10
-1
(Sci 5)
1.429×10
-1
(Sci 4)
• Norm: Selecting one of the two available settings (Norm1, Norm2)
determines the range in which results will be displayed in exponential
format. Outside the specified range, results are displayed using non-
exponential format.
Norm 1: 10
-2
> |x|, |x| ≧ 10
10
Norm 2: 10
-9
> |
x
|, |
x
| ≧ 10
10
Example: 1 200 (≈)* 5×10
-3
(Norm 1)
0.005 (Norm 2)
* Pressing (≈) instead of after inputting a calculation will
display the calculation result in decimal form.
13
Fraction Result
Specifies either mixed fraction or improper fraction for display of fractions
in calculation results.
To specify this
fraction display
format:
Perform this key operation:
Mixed
(SETUP) (Fraction Result)
(ab/c)
Improper
(SETUP) (Fraction Result)
(d/c)◆
Statistics
Specifies whether or not to display a Freq (frequency) column in the
Statistics Mode Statistics Editor.
To specify this: Perform this key operation:
Show frequency
Column
(SETUP) (Statistics) (On)
Hide frequency
Column
(SETUP) (Statistics) (Off)◆
Table
Specifies whether to use function
f
(
x
) only or the two functions
f
(
x
) and
g
(
x
)
in the Table Mode.
To specify this: Perform this key operation:
f(x) only (SETUP) (Table) (f(x))
f(x) and g(x) (SETUP) (Table) (f(x),g(x))◆
14
Recurring Dec
Specifies whether or not to use recurring decimal form in calculation
results.
To specify this: Perform this key operation:
Use recurring decimal
form
(SETUP) (Recurring Dec)
(On)◆
Do not use recurring
decimal form
(SETUP) (Recurring Dec)
(Off)
Decimal Mark
Specifies whether to display a dot or a comma for the calculation result
decimal mark. A dot is always displayed during input.
To specify this
decimal point
display format:
Perform this key operation:
Dot (.)
(SETUP) (Decimal Mark)
(Dot)◆
Comma (,)
(SETUP) (Decimal Mark)
(Comma)
Note
•
When dot is selected as the decimal mark, the separator for multiple results is a
comma (,). When comma is selected, the separator is a semicolon (;).
Digit Separator
Specifies whether or not to use separator symbols in calculation results.
To specify this: Perform this key operation:
Use three-digit
separator character
(SETUP) (Digit Separator)
(On)
Do not use three-digit
separator character
(SETUP) (Digit Separator)
(Off)◆
15
MultiLine Font
Specifies the display font size when LineI/LineO or LineI/DecimalO is
selected for Input/Output. Up to four lines can be displayed while Normal
Font is selected, and up to six lines can be displayed with Small Font.
To specify this: Perform this key operation:
Use normal font
(SETUP) (MultiLine Font)
(Normal Font)◆
Use small font
(SETUP) (MultiLine Font)
(Small Font)
Initializing the Calculation Mode and Other
Settings
Performing the following procedure initializes the calculation mode and
other setup settings as shown below. (except the Contrast setting)
(RESET) (Setup Data) (Yes)
This setting: Is initialized to this:
Calculation Mode Calculate
Input/Output MathI/MathO
Angle Unit Degree
Number Format Norm 1
Fraction Result d/c
Statistics Off
Table
f(x),g(x)
Recurring Dec On
Decimal Mark Dot
Digit Separator Off
MultiLine Font Normal Font
• To cancel initialization without doing anything, press (Cancel) instead
of .
16
Inputting Expressions and
Values
Inputting a Calculation Expression
Using Values
Inputting a Calculation Expression Using Standard
Format
Your calculator lets you input calculation expressions just as they are
written. Then simply press the
key to execute it. The calculator
automatically judges the calculation priority sequence for addition,
subtraction, multiplication, and division, functions, and parentheses.
Example: 2(5 + 4) － 2 × (-3) =
2 5 4 2 3
Note
• If you execute a calculation that includes both division and multiplication operations in
which a multiplication sign has been omitted, parentheses will be inserted
automatically as shown in the examples below.
- When a multiplication sign is omitted immediately before an open parenthesis or
after a closed parenthesis.
Example: 6 ÷ 2(1 + 2) → 6 ÷ (2(1 + 2))
6 2 1 2
- When a multiplication sign is omitted immediately before a variable, a constant,
etc.
Example: 4
π ÷ 2π → 4π ÷ (2π)
4
(π) 2 (π)
17
• Normally the input cursor appears as a straight vertical ( ) or horizontal ( ) flashing
line on the display screen. When there are 10 or fewer bytes of input remaining in the
current expression, the cursor changes shape to to let you know. If the cursor
appears, terminate the expression at a convenient point and calculate the result.
Correcting an Expression
This section explains how to correct an expression as you are inputting it.
The procedure you should use depends on the current Input/Output
setting on the setup menu.
Changing the Character or Function You Just Input
Example: To correct the expression 369 × 13 so it becomes 369 × 12
369 13
2
Deleting a Character or Function
Example: To correct the expression 369 × × 12 so it becomes 369 × 12
369 12
18
Correcting a Calculation
Example: To correct cos(60) so it becomes sin(60)
60
Inserting Input into a Calculation
Use
and to move the cursor to the location where you want to
insert the character or function and then input it. Be sure always to use the
insert mode if LineI/LineO or LineI/DecimalO is selected.
Clearing all of the calculation you are inputting
Press .
Overwrite Input Mode (LineI/LineO or LineI/
DecimalO only)
In the overwrite mode, text you input replaces the text at the current cursor
location. You can toggle between the insert and overwrite modes by
performing the operations:
(INS). The cursor appears as “ ” in the
insert mode and as “ ” in the overwrite mode.
(LineI/LineO or LineI/DecimalO)
(INS)
Deleting a Character or Function
Example: To correct the expression 369 × × 12 so it becomes 369 × 12
19
369 12
Correcting a Calculation
Example: To correct cos(60) so it becomes sin(60)
60
Inputting an Expression Using
Natural Textbook Format (MathI/
MathO or MathI/DecimalO Only)
Formulas and expressions that include fractions and/or special functions
such as √
can be input in natural textbook format by using templates that
appear when certain keys are pressed.
Note
• When you press and obtain a calculation result, part of the expression you input
may be cut off. If you need to view the entire input expression again, press and
then use and to scroll the input expression.
20
Natural Textbook Format Input Examples
• Pay close attention to the location and size of the cursor on the display
when you input using natural textbook format.
Example 1: To input 2
3
+ 1
2 3
1
Example 2: To input 1 + √2 + 3
1 2
3
Example 3: To input 3
1
2
+ 5
3
2
( )
3 1 2
( ) 5 3 2
Example 4: To input ( 1 +
2
5
)
2
× 2
1 2 5 2
21
Example 5: To input
2 + √2
1 + √2
2 2 1 2
Tip: While the input cursor is located within the input area of a template
(mixed fractions), pressing jumps to the position immediately
following (to the right) of the template, while pressing jumps to
the position immediate before (to the left of) it.
Undo Operations
To undo the last key operation, press
(UNDO).
To redo a key operation you have just undone, press (UNDO)
again.
Incorporating a Value into a Function
When using natural textbook format, you can incorporate part of an input
expression (a value, an expression within parentheses, etc.) into a
function.
Example: To incorporate the expression inside of the parentheses of 1 +
(2 + 3) + 4 into the √
function
1
2 3 4
(INS)
This changes the shape of the cursor as shown here.
This incorporates the expression in the parentheses into the function √ .
22
Displaying Calculation Results in a
Form that Includes √2, π, etc.
(Irrational Number Form)
While MathI/MathO is selected for Input/Output on the setup menu, you
can specify whether calculation results should be displayed in a form that
includes expressions like √2 and
π
(irrational number form).
• Pressing after inputting a calculation displays the result using
irrational number form.
• Pressing (≈) after inputting a calculation displays the result using
decimal values.
Note
• When MathI/DecimalO or LineI/DecimalO is selected for Input/Output on the setup
menu, calculation results are always displayed using decimal values (no irrational
number form) regardless of whether you press or (≈).
• The following are the π forms that are supported.
n
π (n is an integer.)
d
c
π or a
b
c
π (depending on fraction display format setting)
Example 1: √
2 + √8 = 3√2 (MathI/MathO)
2 8
2 8 (≈)
Example 2: sin(60) =
√3
2
(MathI/MathO) (Angle Unit: Degree)
60
Example 3: sin
-1
(0.5) =
1
6
π
(MathI/MathO) (Angle Unit: Radian)
23
(sin
-1
) 0.5
24
Basic Calculations
Recurring Decimal Calculations
Your calculator uses a recurring decimal when you input a value.
Calculation results also can be displayed using recurring decimal form
whenever applicable.
Inputting a Recurring Decimal
When inputting a recurrent decimal, press
( ) before inputting its
period (repetend) and then input the period up to the ending value. To
input the recurring decimal 0.909090.... (0.90), perform the following
operation: “0 ( ) 90”.
Important!
•
If the value starts with an integer part (like: 12.3123123...), do not include the integer
part when inputting the period
(12.312).
• Recurring decimal input is possible only when MathI/MathO or MathI/DecimalO is
selected for Input/Output on the setup menu.
Example 1: To input 0.33333… (0.
3)
0
( )
3
Example 2: To input 1.428571428571... (1.428571)
1 ( )
25
428571
Example 3: To calculate 1.021 + 2.312
1 ( ) 021
2 ( ) 312
Calculation result displayed as recurring decimal value:
Displaying a Calculation Result as a Recurring
Decimal Value
Calculation results that can be displayed as recurring decimal values will
be displayed as such when On is selected for the Recurring Dec setting on
the setup menu.
Pressing the
key will cycle between the available calculation result
formats.
Example 1:
1
7
= 0.142857 = 0.1428571429 (Number Format: Norm 1)
1 7
Display as recurring decimal:
Decimal value according to Norm 1 setting:
26
Return to initial display format (fraction):
Example 2: 1 ÷ 7 =
1
7
= 0.142857 = 0.1428571429 (Number Format:
Norm 1)
1 7 (≈)
Display as fraction:
Display as recurring decimal:
Return to initial display format (Norm 1):
Example 3:
1
7
= 0.142857 = 0.1428571429 (Norm 1)
(LineI/LineO)
1 7
Display as recurring decimal:
27
Decimal value according to Norm 1 setting:
Return to initial display format (fraction):
Example 4: 1 ÷ 7 = 0.1428571429 (Norm 1) = 0.142857 =
1
7
(LineI/LineO)
1 7
Display as fraction:
Display as recurring decimal:
Return to initial display format (Norm 1):
Conditions for Displaying a Calculation Result as a
Recurring Decimal
If a calculation result satisfies the following conditions, pressing
will
display it as a recurring decimal value.
• The total number of digits used in the mixed fraction (including integer,
numerator, denominator, and separator symbol) must be no more than
10.
28
Recurring Decimal Examples
Example 1: 0.
3 + 0.45 = 0.78
0 ( ) 3
0 ( ) 45
Example 2: 1.6 + 2.8 = 4.5
1 ( ) 6
2 ( ) 8
Example 3: To confirm the following: 0.123 =
123
999
, 0.1234 =
1234
9999
,
0.12345 =
12345
99999
123 999
1234 9999
12345 99999
29
Toggling Calculation Results
While MathI/MathO or MathI/DecimalO is selected for Input/Output on the
setup menu, each press of
will toggle the currently displayed
calculation result between its fraction form and decimal form, its √ form
and decimal form, or its π form and decimal form.
Example 1: Fraction → Decimal (MathI/MathO) (Recurring Dec: Off)
5 6
Each press of the key toggles between the two forms.
The format of the fraction depends on the currently selected Fraction
Result setting (improper fraction or mixed fraction).
Example 2:
π ÷ 6 =
1
6
π = 0.5235987756 (MathI/MathO)
(π) 6
Example 3: (√2 + 2) × √3 = 5.913591358 = √6 + 2√3
(MathI/DecimalO)
2 2 3
30
While LineI/LineO or LineI/DecimalO is selected for Input/Output on the
setup menu, each press of will toggle the currently displayed
calculation result between its decimal form and fraction form.
Example 4: 1 ÷ 5 = 0.2 =
1
5
(LineI/LineO)
1 5
Example 5: 1 －
4
5
=
1
5
= 0.2 (LineI/LineO)
1 4 5
Important!
• With certain calculation results, pressing the key will not convert the displayed
value.
• You cannot switch from decimal form to mixed fraction form if the total number of digits
used in the mixed fraction (including integer, numerator, denominator, and separator
symbol) is greater than 10.
To obtain a decimal value calculation result while MathI/
MathO or LineI/LineO is selected
Press
(≈) instead of after inputting a calculation.
Arithmetic Calculations
Use the
, , , and keys to perform arithmetic calculations.
Example: To divide the result of 7 × 8 － 4 × 5 = 36
31
7 8 4 5
• The calculator automatically judges the calculation priority sequence.
Number of Decimal Places and Number of
Significant Digits
You can specify a fixed number of decimal places and significant digits for
the calculation result.
Example: 1 ÷ 6 =
Initial default setting (Norm 1)
1 6 (≈)
3 decimal places (Fix 3)
1 6 (≈)
3 significant digits (Sci 3)
1 6 (≈)
Omitting a Final Closed Parenthesis
Example: (2 + 3) × (4 － 1 = 15
2 3 4 1
Fraction Calculations
Note that the input method for fractions depends on the current Input/
Output setting on the setup menu.
32
Improper Fraction Mixed Fraction
MathI/MathO
MathI/DecimalO
7
3
( 7 3 or 7
3 or 7 3)
2
1
3
( ( ) 2 1 3
or ( ) 2 1
3)
LineI/LineO
LineI/DecimalO
(7 3)
(2 1 3)
Note
• Under initial default settings, fractions are displayed as improper fractions.
• Mixing fractions and decimal values in a calculation while something other than MathI/
MathO is selected will cause the result to be displayed as a decimal value.
• Fractions in calculation results are displayed after being reduced to their lowest terms.
Example 1:
2
3
+
1
2
=
7
6
(MathI/MathO)
2 3 1 2
(LineI/LineO)
2 3 1 2
Example 2: 3
1
4
+ 1
2
3
= 4
11
12
(Fraction Result: ab/c)
(MathI/MathO)
( ) 3 1 4
33
( ) 1 2 3
(LineI/LineO)
3 1 4 1 2 3
Example 3: 4 － 3
1
2
=
1
2
(Fraction Result: ab/c)
(MathI/MathO)
4 ( ) 3 1 2
(LineI/LineO)
4 3 1 2
Note
• If the total number of digits used for a mixed fraction (including integer, numerator,
denominator, and separator symbols) is greater than 10, the value is automatically
displayed in decimal format.
• The result of a calculation that involves both fraction and decimal values is displayed
in decimal format.
Switching between Improper Fraction and Mixed
Fraction Format
Pressing the
( ) key toggles the display fraction between
mixed fraction and improper fraction format.
Percent Calculations
Inputting a value and pressing (%) causes the input value to
become a percent.
Example 1: 2% = 0.02 (
2
100
)
34
2 (%) (≈)
Example 2: 150 × 20% = 30 (150 ×
20
100
)
150 20 (%)
Example 3: Calculate what percentage of 880 is 660. (75%)
660 880 (%)
Example 4: Increase 2500 by 15%. (2875)
2500 2500 15 (%)
Example 5: Discount 3500 by 25%. (2625)
3500 3500 25 (%)
Example 6: Discount the sum of 168, 98, and 734 by 20%. (800)
168 98 734
20 (%)
Example 7: 300 grams are added to a test sample originally weighing 500
grams, producing a final test sample of 800 grams. What percent of 500
grams is 800 grams? (160%)
35
500 300 500 (%)
Example 8: What is the percentage change when a value is increased
from 40 to 46? How about to 48? (15%, 20%)
46 40 40 (%)
8
Degree, Minute, Second
(Sexagesimal) Calculations
You can perform calculations using sexagesimal values, and convert
values between sexagesimal and decimal.
Inputting Sexagesimal Values
The following is the syntax for inputting a sexagesimal value.
{Degrees}
{Minutes} {Seconds}
• Note that you must always input something for the degrees and
minutes, even if they are zero.
Example: Input 2°0’30”
2 0 30
Sexagesimal Calculations
Performing the following types of sexagesimal calculations produces a
sexagesimal result.
- Addition or subtraction of two sexagesimal values
- Multiplication or division of a sexagesimal value and a decimal value
Example: 2°20’30” + 39’30” = 3°00’00”
36
2 20 30 0 39 30
Converting Values between Sexagesimal and
Decimal
Pressing
while a calculation result is displayed toggles the value
between sexagesimal and decimal.
Example: Convert 2.255 to its sexagesimal equivalent.
2.255 (≈)
Multi-Statements
You can use the colon character (:) to connect two or more expressions
and execute them in sequence from left to right when you press .
Example: To create a multi-statement that performs the following two
calculations: 3 + 3 and 3 × 3 (MathI/MathO)
3 3 (:) 3 3
“ ” indicates this is an intermediate result of a multi-statement.
Note
• Inputting a colon (:) while LineI/LineO or LineI/DecimalO is selected for the Input/
Output setting on the setup menu causes a newline operation to be performed.
37
(LineI/LineO)
3 3 (:) 3 3
“ ” indicates this is an intermediate result of a multi-statement.
Using Engineering Notation
A simple key operation transforms a displayed value to engineering
notation. Engineering notation converts the exponent part of a displayed
calculation result value to a power of ten that is a multiple of 3, and
displays the result.
Example 1: Transform the value 1234 to engineering notation, shifting the
decimal point to the right.
1234
Example 2: Transform the value 123 to engineering notation, shifting the
decimal point to the left.
123
(←)
38
(←)
Prime Factorization
In the Calculate Mode, a positive integer no more than 10 digits long can
be factored to prime factors.
Example: To perform prime factorization on 1014
1014
(FACT)
• To re-display the unfactored value, press (FACT) or .
Example: To perform prime factorization on 4104676 (= 2
2
× 1013
2
)
4104676
(FACT)
Any one of the following operations will exit prime factorization result
display.
- Pressing
(FACT) or .
- Pressing any of the following keys: or .
Note
• The types of values described below cannot be factored, even if they have 10 or fewer
digits.
- One of the prime factors of the value is 1018081 or greater.
- Two or more of the prime factors of the value have more than three digits.
• The part that cannot be factored will be enclosed in parentheses on the display.
39
Calculation History and Replay
Calculation History
An
and/or at the top of the display indicates that there is more
calculation history content above and/or below. You can scroll through
calculation history contents using and .
Note that calculation history can be used in the Calculate Mode only.
Example: (MathI/MathO)
(1 + 1 = 2)
1 1
(2 + 2 = 4)
2 2
(3 + 3 = 6)
3 3
(Scrolls back.)
(Scrolls back again.)
Note
• Calculation history data is all cleared whenever you press , when you change to a
different calculation mode, when you change the Input/Output setting, or whenever
you perform a RESET operation (“Initialize All” or “Setup Data”).
• Calculation history memory is limited. When the calculation you are performing causes
calculation history memory to become full, the oldest calculation is deleted
automatically to make room for the new calculation.
40
Replay
While a calculation result is on the display, you can press
or to
edit the expression you used for the previous calculation.
Example: 4 × 3 + 2 = 14
4 × 3 − 7 = 5
4 3 2
7
Note
• If you want to edit a calculation when the indicator is on the right side of a
calculation result display, press and then use or to scroll the
calculation.
Example: Pol(2, √2) → Pol(2, 2)
(MathI/MathO) (Angle Unit: Radian)
(Pol) 2 (,) 2
2
41
Using Memory Functions
Answer Memory (Ans)
The last calculation result obtained is stored in Ans (answer) memory.
Note
• Ans Memory contents are updated whenever you execute a calculation using any one
of the following keys: , (≈), , (M−), (RECALL),
.
• Ans Memory contents are not change if an error occurs during the current calculation.
Using Ans Memory to Perform a Series of Calculations
Example: To divide the result of 3 × 4 by 30
3 4
(Continuing) 30
Pressing
automatically inputs “Ans” command.
• With the above procedure, you need to perform the second
calculation immediately after the first one. If you need to recall Ans
Memory contents after pressing
, press the key.
Inputting Ans Memory Contents into an Expression
Example: To perform the calculations shown below:
123 456
(Continuing) 789
42
Variables (A, B, C, D, E, F, M, x, y)
Your calculator has nine preset variables named A, B, C, D, E, F, M,
x
, and
y.
You can assign values to variables and use the variables in calculations.
• You can assign a specific value or a calculation result to a variable.
Example: To assign the result of 3 + 5 to variable A.
3 5 (A)
Example: To assign the result of 4 × 6 to variable x.
4 6 (x)
• Use the following procedure when you want to check the contents of a
variable.
Example: To recall the contents of variable A
(Continuing) (RECALL)
*1
(A)
*1 Pressing (RECALL) displays a screen that shows the values
currently assigned to variables A, B, C, D, E, F, M, x, and y. On this
screen, values are always displayed using the “Norm 1” Number
Format. To close the screen without recalling a variable value, press
.
• The following shows how you can include variables inside of an
expression.
Example: To multiply the contents of variable A by the contents of
variable B
(Continuing) 1 2 (B)
(A) (B)
*2
43
*2 Input a variable as shown here: press and then press the key that
corresponds to the desired variable name. To input x as the variable
name, you can press
(x).
Example:
9×6+3
5×8
= 1.425
9 6 3 (B)
5 8 (C)
(B) (C) (≈)
Clearing the Contents of a Specific Variable
Press 0
and then press the key for the name of the variable whose
contents you want to clear.
Example: To clear the contents of variable A
0 (A)
Independent Memory (M)
You can add calculation results to or subtract results from independent
memory. The “M” appears on the display when independent memory
contains a value.
• The following is a summary of the different operations you can perform
using independent memory.
To do this: Perform this key operation:
Add the displayed
value or result of the
expression to
independent memory
44
Subtract the displayed
value or result of the
expression from
independent memory
(M−)
Recall current
independent memory
contents
(RECALL) (M)
• Variable M is used for independent memory.
• You can also insert the M variable into a calculation, which tells the
calculator to use the current independent memory contents at that
location. The following is the key operation for inserting the M variable.
(M)
• The “M” indicator appears on the display when there is any value other
than zero stored in independent memory.
Calculation Examples Using Independent Memory
• If the “M” indicator is on the display, perform the procedure under
“Clearing Independent Memory” before performing this example.
Example: 23 + 9 = 32
53 - 6 = 47
-) 45 × 2 = 90
99 ÷ 3 = 33
(Total) 22
23 9
53 6
45 2 (M−)
99 3
45
(RECALL) (M)
Clearing Independent Memory
Press 0
(M). This clears independent memory and causes the
“M” indicator to disappear from the display.
0 (M)
Clearing the Contents of All Memories
Ans memory, independent memory, and variable contents are retained
even if you press
, change the calculation mode, or turn off the
calculator.
Perform the procedure below when you want to clear the contents of all
memories.
(RESET) (Memory) (Yes)
• To cancel the clear operation without doing anything, press (Cancel)
instead of .
46
Function Calculations
Pi (
π), Natural Logarithm Base e
Pi (π)
You can input pi (
π) into a calculation.
The following shows the required key operations and the values this
calculator uses for pi (
π).
π = 3.14159265358980 ( (π))
π is displayed as 3.141592654, but π = 3.14159265358980 is used for
internal calculations.
Natural Logarithm Base
e
You can input natural logarithm base e into a calculation.
The following shows the required key operations and the values this
calculator uses for
e.
e = 2.71828182845904 ( (e))
e is displayed as 2.718281828, but e = 2.71828182845904 is used for
internal calculations.
Trigonometric Functions, Inverse
Trigonometric Functions
Trigonometric Functions
• The angle unit required by trigonometric functions is one specified as
the calculator’s default angle unit. Before performing a calculation, be
sure to specify the default angle unit you want to use.
Example: sin 30 =
1
2
(Angle Unit: Degree)
30
Inverse Trigonometric Functions
•
The angle unit required by inverse trigonometric functions is one
specified as the calculator’s default angle unit. Before performing a
calculation, be sure to specify the default angle unit you want to use.
47
Example: sin
-1
0.5 = 30 (Angle Unit: Degree)
(sin
-1
) 0.5
Hyperbolic Functions, Inverse
Hyperbolic Functions
Hyperbolic Functions
• Input a function from the menu that appears when you press
(Hyperbolic Func)*.
* Depending on the calculation mode, you should press .
Example 1: sinh 1 = 1.175201194
(Hyperbolic Func)
(sinh) 1
Example 2: cosh 0 = 1
(Hyperbolic Func)
(cosh) 0
Inverse Hyperbolic Functions
•
Input a function from the menu that appears when you press
(Hyperbolic Func)*.
* Depending on the calculation mode, you should press .
Example : cosh
-1
1 = 0
(Hyperbolic Func)
48
(cosh
-1
) 1
Converting an Input Value to the
Calculator’s Default Angle Unit
After inputting a value, press
(Angle Unit)* to display the angle unit
specification menu shown below. Press the number key that corresponds
to the angle unit of the input value. The calculator will automatically
convert it to the calculator’s default angle unit.
* Depending on the calculation mode, you should press
.
° : Degrees,
r
: Radians,
g
: Gradians
Example 1: To convert the following values to degrees:
π
2
radians = 90°,
50 grads = 45°
The following procedure assumes that the calculator’s default angle unit
is degrees.
(π) 2
(Angle Unit) (
r
)
50 (Angle Unit) (
g
)
Example 2: cos(π radians) = -1, cos(100 grads) = 0
(π)
(Angle Unit) (
r
)
100 (Angle Unit) (
g
)
49
Example 3: cos
-1
(-1) = 180 (Angle Unit: Degree), cos
-1
(-1) = π (Angle
Unit: Radian)
(Angle Unit: Degree)
(cos
-1
) 1
(Angle Unit: Radian)
(cos
-1
) 1
Exponential Functions, Logarithmic
Functions
Exponential Functions
Example 1:
e
5
× 2 = 296.8263182
(MathI/MathO)
( ) 5 2
(LineI/LineO)
( ) 5 2
Example 2: 1.2 × 10
3
= 1200
(MathI/MathO)
1.2 ( ) 3
(LineI/LineO)
1.2 ( ) 3
50
Logarithmic Functions
• For the logarithmic function “log(”, you can specify base m using the
syntax “log (
m, n)”.
If you input only a single value, a base of 10 is used for the calculation.
• “ln(” is a natural logarithm function with base e.
• You can also use the key when inputting an expression with the
form of “log
m
n” while using MathI/MathO or MathI/DecimalO format. For
details, see Example 1. Note that you must input the base (base
m)
when using the
key for input.
Example 1: log
2
16 = 4
(MathI/MathO)
2 16
(LineI/LineO)
(or ) 2 (,) 16
Example 2: log16 = 1.204119983
16
A base of 10 (common logarithm) is used if no base is specified.
Example 3: ln 90 (= log
e
90) = 4.49980967, ln e = 1
90
(e)
51
Power Functions and Power Root
Functions
Example 1: (1 + 1)
2+2
= 16
1 1 2 2
Example 2: (5
2
)
3
= 15625
5
Example 3: (√2 + 1)(√2 － 1) = 1
(MathI/MathO)
2 1 2 1
(LineI/LineO)
2 1 2 1
Example 4:
5
√32 = 2
(MathI/MathO)
( ) 5 32
(LineI/LineO)
5 ( ) 32
Example 5: (-2)
2
3
= 1.587401052
(MathI/MathO)
52
2 2 3
(LineI/LineO)
2 2 3
Example 6:
3
√5 +
3
√-27 = -1.290024053
(MathI/MathO)
( ) 5
( ) 27
(LineI/LineO)
( ) 5
( ) 27
Example 7: = 12
(MathI/MathO)
3 4
Rectangular-Polar Coordinate
Conversion
•
Coordinate conversion can be performed in the Calculate and Statistics
calculation modes.
53
• Pol converts rectangular coordinates to polar coordinates, while Rec
converts polar coordinates to rectangular coordinates.
• Specify the angle unit before performing calculations.
Converting to Polar Coordinates (Pol)
Pol(X, Y) X: Specifies the rectangular coordinate X value
Y: Specifies the rectangular coordinate Y value
• Calculation result θ is displayed in the range of -180° < θ < 180°.
• Calculation result θ is displayed using the calculator’s angle unit.
• Calculation result
r
is assigned to variable X, while
θ
is assigned to Y.
Converting to Rectangular Coordinates (Rec)
Rec(
r, θ) r : Specifies the polar coordinate r value
θ : Specifies the polar coordinate θ value
• Input value θ is treated as an angle value, in accordance with the
calculator’s angle unit setting.
• Calculation result x is assigned to variable X, while y is assigned to Y.
• If you perform coordinate conversion inside of an expression instead of
a stand-alone operation, the calculation is performed using only the first
value (either the r-value or the X-value) produced by the conversion.
Example: Pol (√
2, √2) + 5 = 2 + 5 = 7
Rectangular-Polar Coordinate Conversion
Examples
Example 1: (X, Y) = (√2, √2) → (r, θ) (Angle Unit: Degree)
(MathI/MathO)
(Pol) 2 (,) 2
(LineI/LineO)
(Pol) 2 (,) 2
Example 2: (X, Y) = (√3, 1) → (
r
,
θ
) (Angle Unit: Radian)
(MathI/MathO)
(Pol) 3 (,) 1
54
(LineI/LineO)
(Pol) 3 (,) 1
Example 3: (r, θ) = (√2, 45) → (X, Y) (Angle Unit: Degree)
(MathI/MathO)
(Rec) 2 (,) 45
(LineI/LineO)
(Rec) 2 (,) 45
Example 4: (r, θ) = (2,
π
6
) → (X, Y) (Angle Unit: Radian)
(MathI/MathO)
(Rec)
2 (,) (π) 6
(LineI/LineO)
(Rec) 2 (,) (π) 6
Factorial (!)
This function obtains the factorials of a value that is zero or a positive
integer.
Example: (5 + 3)! = 40320
5 3 (x!)
55
Example:
Absolute Value Calculation (Abs)
When you are performing a real number calculation, this function simply
obtains the absolute value.
Example: Abs(2 － 7) = |2 － 7| = 5
(MathI/MathO)
2 7
(LineI/LineO)
2 7
Random Number (Ran#), Random
Integer (RanInt#)
Random Number (Ran#)
Function that generates a pseudo random number in the range of 0.000 to
0.999.
The result is displayed as a fraction when MathI/MathO is selected for
Input/Output on the setup menu.
Generate three 3-digit random numbers.
The random 3 digit decimal values are converted to 3-digit
integer values by multiplying by 1000.
Note that the values shown here are examples only. Values
actually generated by your calculator will be different.
1000 (Ran#)
56
Example:
Random Integer (RanInt#)
For input of the function of the form RanInt#(
a, b), which generates a
random integer within the range of
a to b.
To generate random integers in the range of 1 to 6.
Note that the values shown here are examples only.
Values actually generated by your calculator will be different.
(RanInt) 1 (,) 6
Permutation (nPr) and Combination
(
nCr)
These functions make it possible to perform permutation and combination
calculations.
n and r must be integers in the range of 0 ≦ r ≦ n < 1 × 10
10
.
Example: To determine the number of permutations and combinations
possible when selecting four people from a group of 10.
Permutations:
10 (nPr) 4
Combinations:
10 (nCr) 4
57
Rounding Function (Rnd)
Using the Rnd function causes decimal fraction values of the argument to
be rounded in accordance with the current Number Format setting.
Number Format: Norm 1 or Norm 2
The argument is rounded off to 10 digits.
Number Format: Fix or Sci
The argument is rounded off to the specified digit.
When Fix 3 is the Number Format setting, for example, the result of 10 ÷ 3
is displayed as 3.333, while the calculator maintains a value of
3.33333333333333 (15 digits) internally for calculation. In the case of
Rnd(10÷3) = 3.333 (with Fix 3), both the displayed value and the
calculator’s internal value become 3.333. Because of this a series of
calculations will produce different results depending on whether Rnd is
used (Rnd(10÷3) × 3 = 9.999) or not used (10 ÷ 3 × 3 = 10.000).
Example: To perform the following calculation when Fix 3 is selected for
the number of display digits: 200 ÷ 7 × 14 = 400 (MathI/DecimalO)
200 7 14
(Calculation is performed internally using 15 digits.)
200 7
14
The following performs the same calculation with rounding.
200 7
(Round the value to the specified number of digits.)
(Rnd)
58
(Check rounded result.)
14
59
Using Calculation Modes
Statistical Calculations
Perform the steps below to start a statistical calculation.
1. Press
, select the Statistics Mode icon, and then press .
2. On the Select Type screen that appears, press one of the keys below to
select a statistical calculation type.
(1-Variable)
Single-variable (x)
(y=a+bx)
Paired-variable (x, y), linear regression
(y=a+bx+cx
2
)
Paired-variable (x, y), quadratic regression
(y=a+b･ln(x))
Paired-variable (x, y), logarithmic regression
(y=a･e^(bx)) Paired-variable (x, y), e exponential regression
(y=a･b^x)
Paired-variable (x, y), ab exponential
regression
(y=a･x^b)
Paired-variable (x, y), power regression
(y=a+b/x)
Paired-variable (x, y), inverse regression
•
Performing any of the above key operations displays the Statistics
Editor.
Note
• When you want to change the calculation type after entering the Statistics Mode,
perform the key operation (Select Type) to display the calculation type
selection screen.
60
Inputting Data with Statistics Editor
Statistics Editor
There are two Statistics Editor formats, depending on the type of
statistical calculation you selected.
Single-variable
Paired-variable
• The first line of the Statistics Editor shows the value for the first
sample or the values for their first pair of samples.
Freq (Frequency) Column
If you turn on the Statistics setting on the setup menu, a column labeled
“Freq” will also be included on the Statistics Editor.
You can use the Freq column to specify the frequency (the number of
times the same sample appears in the group of data) of each sample
value.
Single-variable
Paired-variable
61
Rules for Inputting Sample Data on the Statistics Editor
• Data you input is inserted into the cell where the cursor is located.
Use the cursor keys to move the cursor between cells.
• After inputting a value, press . This registers the value and
displays up to six of its digits in the currently selected cell.
Example 1: To input the value 1234 in cell X1
(Move the cursor to cell X1.)
1234
The value you input appears in the formula area.
Registering a value causes the cursor to move down one cell.
Example 2: To select logarithmic regression and input the following
data: (170, 66), (173, 68), (179, 75)
(Select Type) (y=a+b･ln(x))
170 173 179
66 68 75
Statistics Editor Input Precautions
•
The number of lines in Statistics Editor (the number of sample data
values you can input) depends on the type of statistical calculation
you selected, and on the Statistics setting on the setup menu.
62
Statistics
setting
calculation type
Off
(No Freq column)
On
(Freq column)
Single-variable 160 lines 80 lines
Paired-variable 80 lines 53 lines
• Pressing the key while the Statistics Editor is on the screen will
display a statistical calculation screen for performing calculations
based on the input data. What you need to do to return to the
Statistics Editor from the statistical calculation screen depends on the
calculation type you selected. Press (Data) if you selected
single-variable or (Data) if you selected paired-variable.
Precautions Concerning Sample Data Storage
• All data currently input in the Statistics Editor is deleted whenever you
exit the Statistics Mode, switch between the single-variable and a
paired-variable statistical calculation type, or change the Statistics
setting on the setup menu.
Editing Sample Data
To replacing the data in a cell
1. On the Statistics Editor, move the cursor to the cell you want to edit.
2. Input the new data value or expression, and then press .
Important!
• Note that you must totally replace the existing data of the cell with new input. You
cannot edit parts of the existing data.
To delete a line
1. On the Statistics Editor, move the cursor to the line you want to
delete.
2. Press
.
To insert a line
1. On the Statistics Editor, move the cursor to the line that will be
under the line you will insert.
2. Press
(Editor).
3. Press (Insert Row).
63
Important!
• Note that the insert operation will not work if the maximum number of lines allowed
for the Statistics Editor are already used.
To delete all Statistics Editor contents
1. On the Statistics Editor, press
(Editor).
2. Press (Delete All).
Statistical Calculation Screen
The statistical calculation screen is for performing statistical calculations
with the data you input with the Statistics Editor. Pressing the key
while the Statistics Editor is displayed switches to the statistical calculation
screen.
Using the Statistical Menu
While the Statistics Editor or statistical calculation screen is on the display,
press
to display the statistical menu.
The content to the statistical menu depends on whether the currently
selected statistical operation type uses a single variable or paired
variables.
Statistics Editor: Single-variable
Select this menu
item:
When you want to do this:
(Select Type)
Display the statistical calculation type
selection screen
(Editor)
Display the Editor sub-menu for editing
Statistics Editor contents
(1-Variable Calc) Display statistical values based on input data
64
(Statistics Calc) Display the statistical calculation screen
Statistics Editor: Paired-variable
Select this menu
item:
When you want to do this:
(Select Type)
Display the statistical calculation type
selection screen
(Editor)
Display the Editor sub-menu for editing
Statistics Editor contents
(2-Variable Calc) Display statistical values based on input data
(Regression Calc)
Display regression calculation results based
on input data
(Statistics Calc) Display the statistical calculation screen
Statistical calculation screen: Single-variable
65
Select this menu
item:
When you want to do this:
(Select Type)
Display the statistical calculation type
selection screen
(1-Variable Calc) Display statistical values based on input data
(Data) Display the Statistics Editor
(Summation)
Display the Summation sub-menu of
commands for calculating sums
(Variable)
Display the Variable sub-menu of commands
for calculating the mean, standard deviation,
etc.
(Min/Max)
Display the Min/Max sub-menu of commands
for obtaining maximum and minimum values
Statistical calculation screen: Paired-variable
66
Select this menu
item:
When you want to do this:
(Select Type)
Display the statistical calculation type
selection screen
(2-Variable Calc) Display statistical values based on input data
(Regression Calc)
Display regression calculation results based
on input data
(Data) Display the Statistics Editor
(Summation)
Display the Summation sub-menu of
commands for calculating sums
(Variable)
Display the Variable sub-menu of commands
for calculating the mean, standard deviation,
etc.
(Min/Max)
Display the Min/Max sub-menu of commands
for obtaining maximum and minimum values
(Regression)
Display the Regression sub-menu of
commands for regression calculations
Displaying Statistical Values Based On Input Data
From the Statistics Editor:
(1-Variable Calc or 2-Variable Calc)
From the statistical calculation screen:
(1-Variable Calc or 2-Variable Calc)
Displaying Regression Calculation Results Based
On Input Data (Paired-Variable Data Only)
From the Statistics Editor:
(Regression Calc)
From the statistical calculation screen:
(Regression Calc)
67
Single-variable Statistical Calculation Commands
The following are the commands that appear on the sub-menus that
appear when you select Summation, Variable, or Min/Max on the statistical
menu while a single-variable statistical calculation type is selected.
The following is the calculation formula used for each command.
Summation Sub-menu ( (Summation))
Select this menu
item:
When you want to obtain this:
(Σx)
Sum of the sample data
(Σx
2
)
Sum of squares of the sample data
Variable Sub-menu ( (Variable))
Select this menu
item:
When you want to obtain this:
(x) Mean of the sample data
(σ
2
x
)
Population variance
(σ
x
)
Population standard deviation
(s
2
x
) Sample variance
(s
x
) Sample standard deviation
68
(n)
Number of items
Min/Max Sub-menu ( (Min/Max))
Select this menu
item:
When you want to obtain this:
(min(x))
Minimum value
(Q
1
) First quartile
(Med) Median
(Q
3
) Third quartile
(max(x))
Maximum value
Single-variable Statistical Calculation Examples
Select single-variable and input the following data: {1, 2, 3, 4, 5, 6, 7, 8, 9,
10} (Statistics: On)
(Select Type) (1-Variable)
1 2 3 4 5 6 7 8 9 10
Edit the data to the following, using insert and delete: {0, 1, 2, 3, 4, 5, 6, 7,
9, 10}
(Data)
69
(Editor)
(Insert Row)
Edit the Freq data to the following: {1, 2, 1, 2, 2, 2, 3, 4, 2, 1}
(Data)
2 2 2 2 3 4 2
Display statistical values based on input data.
(1-Variable Calc)
70
Calculate sum of squares of the sample data and sum of the sample data.
(Summation)
(Σx
2
)
(Summation)
(Σx)
Calculate number of samples, mean, and population standard deviation.
(Variable)
(n)
(Variable)
(x)
(Variable)
(σ
x
)
Calculate minimum value and maximum value.
(Min/Max)
(min(x))
(Min/Max)
(max(x))
71
Linear Regression Calculation (y=a+bx)
Commands
With linear regression, regression is performed in accordance with the
following model equation.
y = a + bx
The following is the calculation formula used for each command.
Summation Sub-menu ( (Summation))
Select this menu
item:
When you want to obtain this:
(Σx)
Sum of the x-data
(Σx
2
)
Sum of squares of the x-data
(Σy)
Sum of the y-data
(Σy
2
)
Sum of squares of the y-data
72
(Σxy)
Sum of products of the x-data and y-data
(Σx
3
)
Sum of cubes of the x-data
(Σx
2
y)
Sum of (x-data squares × y-data)
(Σx
4
)
Sum of biquadrate of the x-data
Variable Sub-menu ( (Variable))
Select this menu
item:
When you want to obtain this:
(x) Mean of the x-data
(σ
2
x
)
Population variance of the x-data
(σ
x
)
Population standard deviation of the x-data
(s
2
x
) Sample variance of the x-data
(s
x
) Sample standard deviation of the x-data
(n)
Number of items
(y) Mean of the y-data
(σ
2
y
)
Population variance of the y-data
(σ
y
)
Population standard deviation of the y-data
(s
2
y
) Sample variance of the y-data
(s
y
) Sample standard deviation of the y-data
Min/Max Sub-menu ( (Min/Max))
73
Select this menu
item:
When you want to obtain this:
(min(x))
Minimum value of the x-data
(max(x))
Maximum value of the x-data
(min(y))
Minimum value of the y-data
(max(y))
Maximum value of the y-data
Regression Sub-menu ( (Regression))
Select this menu
item:
When you want to obtain this:
(a)
Regression coefficient constant term a
(b)
Regression coefficient b
(r)
Correlation coefficient r
(xˆ)
Estimated value of x
(yˆ)
Estimated value of y
Linear Regression Calculation Examples
Select linear regression and input the following data (Statistics: Off)
x y x y
1.0 1.0 2.1 1.5
1.2 1.1 2.4 1.6
1.5 1.2 2.5 1.7
1.6 1.3 2.7 1.8
1.9 1.4 3.0 2.0
74
(Select Type) (y=a+bx)
1 1.2 1.5 1.6 1.9
2.1 2.4 2.5 2.7 3
1 1.1 1.2 1.3 1.4
1.5 1.6 1.7 1.8 2
Display statistical values based on input data.
(2-Variable Calc)
Display regression calculation results based on input data.
(Regression Calc)
Calculate sum of products of the x-data and y-data, Population standard
deviation of the x-data, and maximum value of the y-data.
(Summation)
75
(Σxy)
(Variable)
(σ
x
)
(Min/Max)
(max(y))
Calculate regression coefficient constant term a, regression coefficient b,
and correlation coefficient r.
(Regression)
(a)
(Regression)
(b)
(Regression)
(r)
Calculate estimated values.
(y=-3 → xˆ=?)
3 (Regression)
76
(xˆ)
(x=2 → yˆ=?)
2 (Regression)
(yˆ)
Quadratic Regression Calculation (y=a+bx+cx
2
)
Commands
With quadratic regression, regression is performed in accordance with the
following model equation.
y = a + bx + cx
2
The following is the calculation formula used for each command.
•
Summation Sub-menu, Variable Sub-menu, and Min/Max Sub-menu
operations are the same those for linear regression calculations.
Regression Sub-menu ( (Regression))
77
Select this menu item: When you want to obtain this:
(a)
Regression coefficient constant
term a
(b)
Linear coefficient b of the
regression coefficients
(c)
Quadratic coefficient c of the
regression coefficients
(xˆ
1
)
Estimated value of x1
(xˆ
2
)
Estimated value of x2
(yˆ)
Estimated value of y
Quadratic Regression Calculation Examples
Select quadratic regression and input the following data (Statistics: Off)
x y x y
1.0 1.0 2.1 1.5
1.2 1.1 2.4 1.6
1.5 1.2 2.5 1.7
1.6 1.3 2.7 1.8
1.9 1.4 3.0 2.0
(Select Type) (y=a+bx+cx
2
)
1 1.2 1.5 1.6 1.9
2.1 2.4 2.5 2.7 3
1 1.1 1.2 1.3 1.4
1.5 1.6 1.7 1.8 2
78
Display statistical values based on input data.
(2-Variable Calc)
Display regression calculation results based on input data.
(Regression Calc)
Calculate regression coefficient constant term a, linear coefficient b, and
quadratic coefficient c.
(Regression)
(a)
(Regression)
(b)
(Regression)
(c)
79
Logarithmic Regression Calculation (y=a+b･ln(x))
Commands
With logarithmic regression, regression is performed in accordance with
the following model equation.
y = a + blnx
The following is the calculation formula used for each command.
• Summation Sub-menu, Variable Sub-menu, Min/Max Sub-menu, and
Regression Sub-menu operations are the same those for linear
regression calculations.
Logarithmic Regression Calculation Examples
Select logarithmic regression and input the following data (Statistics: Off)
x y
29 1.6
50 23.5
74 38.0
103 46.4
118 48.9
(Select Type) (y=a+b･ln(x))
29 50 74 103 118
80
1.6 23.5 38 46.4 48.9
Display statistical values based on input data.
(2-Variable Calc)
Display regression calculation results based on input data.
(Regression Calc)
Calculate regression coefficient constant term a, regression coefficient b,
and correlation coefficient r.
(Regression)
(a)
(Regression)
(b)
81
(Regression)
(r)
Calculate estimated values.
(y=73 → xˆ=?)
73 (Regression)
(xˆ)
(
x
=80 →
yˆ
=?)
80 (Regression)
(yˆ)
e Exponential Regression Calculation (y=a･e^(bx))
Commands
With
e exponential regression, regression is performed in accordance with
the following model equation.
y = ae
bx
The following is the calculation formula used for each command.
• Summation Sub-menu, Variable Sub-menu, Min/Max Sub-menu, and
Regression Sub-menu operations are the same those for linear
regression calculations.
e Exponential Regression Calculation Examples
Select
e
exponential regression and input the following data (Statistics:
Off)
82
x y
6.9 21.4
12.9 15.7
19.8 12.1
26.7 8.5
35.1 5.2
(Select Type) (y=a･e^(bx))
6.9 12.9 19.8 26.7 35.1
21.4 15.7 12.1 8.5 5.2
Display statistical values based on input data.
(2-Variable Calc)
Display regression calculation results based on input data.
83
(Regression Calc)
Calculate regression coefficient constant term a, regression coefficient b,
and correlation coefficient r.
(Regression)
(a)
(Regression)
(b)
(Regression)
(r)
Calculate estimated values.
(y=20 → xˆ=?)
20 (Regression)
(xˆ)
(x=16 → y
ˆ
=?)
16 (Regression)
(yˆ)
ab Exponential Regression Calculation (y=a･b^x)
Commands
With
ab
exponential regression, regression is performed in accordance
with the following model equation.
y = ab
x
The following is the calculation formula used for each command.
84
• Summation Sub-menu, Variable Sub-menu, Min/Max Sub-menu, and
Regression Sub-menu operations are the same those for linear
regression calculations.
ab Exponential Regression Calculation Examples
Select
ab exponential regression and input the following data (Statistics:
Off)
x y
-1 0.24
3 4
5 16.2
10 513
(Select Type) (y=a･b^x)
1 3 5 10
0.24 4 16.2 513
Display statistical values based on input data.
85
(2-Variable Calc)
Display regression calculation results based on input data.
(Regression Calc)
Calculate regression coefficient constant term a, regression coefficient b,
and correlation coefficient r.
(Regression)
(a)
(Regression)
(b)
(Regression)
(r)
Calculate estimated values.
(
y
=1.02 →
xˆ
=?)
1.02 (Regression)
86
(xˆ)
(x=15 → yˆ=?)
15 (Regression)
(yˆ)
Power Regression Calculation (y=a･x^b)
Commands
With power regression, regression is performed in accordance with the
following model equation.
y = ax
b
The following is the calculation formula used for each command.
• Summation Sub-menu, Variable Sub-menu, Min/Max Sub-menu, and
Regression Sub-menu operations are the same those for linear
regression calculations.
Power Regression Calculation Examples
Select power regression and input the following data (Statistics: Off)
x y
28 2410
30 3033
33 3895
35 4491
38 5717
87
(Select Type) (y=a･x^b)
28 30 33 35 38
2410 3033 3895 4491 5717
Display statistical values based on input data.
(2-Variable Calc)
Display regression calculation results based on input data.
(Regression Calc)
Calculate regression coefficient constant term a, regression coefficient b,
and correlation coefficient r.
(Regression)
88
(a)
(Regression)
(b)
(Regression)
(r)
Calculate estimated values.
(y=1000 → xˆ=?)
1000 (Regression)
(xˆ)
(x=40 → yˆ=?)
40 (Regression)
(yˆ)
Inverse Regression Calculation (y=a+b/x)
Commands
With inverse regression, regression is performed in accordance with the
following model equation.
y = a +
b
x
The following is the calculation formula used for each command.
89
• Summation Sub-menu, Variable Sub-menu, Min/Max Sub-menu, and
Regression Sub-menu operations are the same those for linear
regression calculations.
Inverse Regression Calculation Examples
Select inverse regression and input the following data (Statistics: Off)
x y
1.1 18.3
2.1 9.7
2.9 6.8
4.0 4.9
4.9 4.1
(Select Type) (y=a+b/x)
1.1 2.1 2.9 4 4.9
18.3
9.7 6.8 4.9 4.1
Display statistical values based on input data.
(2-Variable Calc)
90
Display regression calculation results based on input data.
(Regression Calc)
Calculate regression coefficient constant term a, regression coefficient b,
and correlation coefficient r.
(Regression)
(a)
(Regression)
(b)
(Regression)
(r)
Calculate estimated values.
(
y
=15 →
xˆ
=?)
15 (Regression)
(xˆ)
91
(x=3.5 → yˆ=?)
3.5 (Regression)
(yˆ)
Creating a Number Table
The Table Mode generates a number table based on one or two functions.
You can use the function
f(x) or the two functions f(x) and g(x).
Configuring a Number Table Generation Function
Perform the following steps to generate a number table.
1. Press
, select the Table Mode icon, and then press .
• This displays the function input screen.
2. Use the
x
variable to input two functions, one in the format
f
(
x
) and the
other in the format
g(x).
• Be sure to input the x variable ( (x)) when generating a number
table. Any variable other than
x is handled as a constant.
• If you are using a single function, input a function in the format f(x)
only.
3. On the Table Range dialog box that appears, input values for Start, End,
and Step.
For this: Input this:
Start
Input the lower limit of x (Default = 1).
End
Input the upper limit of x (Default = 5).
92
Step
Input the increment step (Default = 1).
Note: The Step specifies by how
much the Start value should be
sequentially incremented as the
number table is generated. If you
specify Start = 1 and Step = 1, x
sequentially will be assigned the
values 1, 2, 3, 4, and so on to
generate the number table until the
End value is reached.
• Pressing generates and displays the number table in accordance
with the Table Range dialog box.
• Pressing while the number table screen is displayed will return to
the function input screen in step 2.
Example: To generate a number table for the functions
f(x) = x
2
+
1
2
and
g(x) = x
2
－
1
2
for the range -1 ≦ x ≦ 1, incremented in steps of 0.5
(x) 1 2
(x) 1 2
1 1 0.5
93
Tip:
• In the number table, you can change the value in the currently
highlighted x cell. Changing the x value causes the f(x) and g(x) values
in the same line to be updated accordingly.
• If there is value in the x cell above the currently highlighted x cell,
pressing
or automatically inputs into the highlighted cell the
value equal to the value of the cell above it plus the step value. So
also, pressing automatically inputs the value equal to the value of
the cell above less the step value. The f(x) and g(x) values in the
same line are also updated accordingly.
Note
• The maximum number of rows in the generated number table depends on the setup
menu table setting. Up to 45 rows are supported for the “f(x)” setting, while 30 rows
are supported for the “
f(x),g(x)” setting.
• The number table generation operation causes the contents of variable x to be
changed.
Important!
• Functions input in this mode are deleted whenever the Input/Output settings are
changed in the Table Mode.
Ratio Calculations
The Ratio Mode lets you determine the value of X in the ratio expression
A : B = X : D (or A : B = C : X) when the values of A, B, C and D are
known. The following shows the general procedure for using Ratio.
1. Press
, select the Ratio Mode icon, and then press .
2. On the menu that appears, select (A:B=X:D) or (A:B=C:X).
3. On the Coefficient Editor screen that appears, input up to 10 digits for
each of the required values (A, B, C, D).
• To solve 3 : 8 = X : 12 for X, for example, press in step 1, and
then input the following for the coefficients (A = 3, B = 8, D = 12): 3
8 12 .
94
• Pressing will reset all of the coefficients to one.
4. After all the values are the way you want, press .
• This displays the solution (value of X).
• Pressing again will return to the Coefficient Editor.
Important!
• A Math ERROR will occur if you perform a calculation while 0 is input for a coefficient.
Changing the Ratio Expression Type
Press
(Select Type) and then select the ratio expression type you
want from the menu that appears. Changing the ratio expression type
causes the values of all Coefficient Editor coefficients to change to one.
Ratio Mode Calculation Example
Example 1: To calculate X in the ratio 1 : 2 = X : 10
(Select Type) (A:B=X:D)
1 2 10
Example 2: To calculate X in the ratio 1 : 2 = 10 : X
(Select Type) (A:B=C:X)
1 2 10
95
Technical Information
Errors
The calculator will display an error message whenever an error occurs for
any reason during a calculation.
Displaying the Location of an Error
While an error message is displayed, press
or return to the
calculation screen. The cursor will be positioned at the location where the
error occurred, ready for input. Make the necessary corrections to the
calculation and execute it again.
Example: When you input 14 ÷ 0 × 2 = by mistake instead of 14 ÷ 10 × 2
=.
14 0 2
(or )
1
Clearing the Error Message
While an error message is displayed, press
to return to the calculation
screen. Note that this also clears the calculation that contained the error.
Error Messages
Math ERROR
Cause:
•
The intermediate or final result of the calculation you are performing
exceeds the allowable calculation range.
•
Your input exceeds the allowable input range (particularly when using
functions).
• The calculation you are performing contains an illegal mathematical
operation (such as division by zero).
96
Action:
• Check the input values, reduce the number of digits, and try again.
• 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.
Stack ERROR
Cause:
• The calculation you are performing has caused 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 stack.
• Try splitting the calculation into two or more parts.
Syntax ERROR
Cause:
• There is a problem with the format of the calculation you are
performing.
Action:
• Make necessary corrections.
Argument ERROR
Cause:
•
There is a problem with the argument of the calculation you are
performing.
Action:
• Make necessary corrections.
Range ERROR
Cause:
•
An attempt to generate a number table in the Table Mode whose
conditions cause it to exceed the maximum number of allowable rows.
The maximum number of rows is 45 when “f(x)” is selected for the
setup menu table setting and 30 when “
f
(
x
),
g
(
x
)” is selected.
Action:
•
Narrow the table calculation range by changing the Start, End, and
Step values, and try again.
97
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 separate copies of important data before
performing these steps.
1. Check the calculation expression to make sure that it does not contain
any errors.
2. Make sure that you are using the correct mode for the type of
calculation you are trying to perform.
3. If the above steps do not correct your problem, press the
key.
• This will cause the calculator to perform a routine that checks whether
calculation functions are operating correctly. If the calculator discovers
any abnormality, it automatically initializes the calculation mode and
clears memory contents.
4. Return the calculation mode and setup (except for the Contrast setting)
to their initial default settings by performing the following operation:
(RESET) (Setup Data) (Yes).
Replacing the Battery
A low battery is indicated by a dim display, even if contrast is adjusted, or
by failure of figures to appear on the display immediately after you turn on
the calculator. If this happens, replace the battery with a new one.
Important!
• Removing the battery will cause all of the calculator’s memory contents to be deleted.
1. Press
(OFF) to turn off the calculator.
•
To ensure that you do not accidentally turn on power while replacing
the battery, slide the hard case onto the front of the calculator.
2. On the back of the calculator, remove the screws and the cover.
98
3. Remove the battery, and then load a new battery with its plus (+) and
minus (−) ends facing correctly.
4. Replace the cover.
5. Initialize the calculator: (RESET) (Initialize All) (Yes).
• Do not skip the above step!
Calculation Priority Sequence
The calculator performs calculations according to a calculation priority
sequence.
• Basically, calculations are performed from left to right.
• Expressions within parentheses have the highest priority.
• The following shows the priority sequence for each individual command.
1 Parenthetical expressions
2
Functions that have parentheses (sin(, log(, etc., functions
that take an argument to the right, functions that require a
closing parenthesis after the argument)
3
Functions that come after the input value (x
2
, x
3
, x
-1
, x!, °’ ”, °,
r
,
g
, %), powers ( ), roots ( )
4 Fractions
5 Negative sign ((-))
6
Statistics Mode estimated values (xˆ, yˆ, xˆ
1
, xˆ
2
)
7 Multiplication where the multiplication sign is omitted
8
Permutation (nPr), combination (nCr)
9 Multiplication (×), division (÷)
99
10 Addition (+), subtraction (−)
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 x
2
is a function
preceded by a value (Priority 3, above), whose priority is greater than the
negative sign, which is a prefix symbol (Priority 5).
Example:
2 -2
2
= -4
2 (-2)
2
= 4
Stack Limitations
This calculator uses memory areas called stacks to temporarily store 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.
A Stack ERROR occurs when the calculation you are performing causes
the capacity of either stack to be exceeded.
Calculation Ranges, Number of
Digits, and Precision
The calculation range, number of digits used for internal calculation, and
calculation precision depends on the type of calculation you are
performing.
100
Calculation Range and Precision
Calculation Range ±1 × 10
-99
to ±9.999999999 × 10
99
or 0
Number of Digits for
Internal Calculation
15 digits
Precision
In general, ±1 at the 10th digit for a single
calculation. Precision for exponential display is
±1 at the least significant digit. Errors are
cumulative in the case of consecutive
calculations.
Function Calculation Input Ranges and Precision
Functions Input Range
sinx
cosx
Degree
0 ≦ |x| < 9 × 10
9
Radian
0 ≦ |x| < 157079632.7
Gradian
0 ≦ |x| < 1 × 10
10
tanx
Degree
Same as sinx, except when
|
x| = (2n−1) × 90.
Radian
Same as sinx, except when
|
x| = (2n−1) × π/2.
Gradian
Same as sinx, except when
|
x| = (2n−1) × 100.
sin
-1
x, cos
-1
x 0 ≦ |x| ≦ 1
tan
-1
x 0 ≦ |x| ≦ 9.999999999 × 10
99
sinhx, coshx 0 ≦ |x| ≦ 230.2585092
sinh
-1
x 0 ≦ |x| ≦ 4.999999999 × 10
99
cosh
-1
x 1 ≦ x ≦ 4.999999999 × 10
99
tanhx 0 ≦ |x| ≦ 9.999999999 × 10
99
tanh
-1
x 0 ≦ |x| ≦ 9.999999999 × 10
-1
101
logx, lnx 0 < x ≦ 9.999999999 × 10
99
10
x
-9.999999999 × 10
99
≦ x ≦ 99.99999999
e
x
-9.999999999 × 10
99
≦ x ≦ 230.2585092
√x 0 ≦ x < 1 × 10
100
x
2
|x| < 1 × 10
50
x
-1
|x| < 1 × 10
100
; x ≠ 0
3
√x |x| < 1 × 10
100
x! 0 ≦ x ≦ 69 (x is an integer)
nPr
0 ≦ n < 1 × 10
10
, 0 ≦ r ≦ n (n, r are integers)
1 ≦ {
n!/(n−r)!} < 1 × 10
100
nCr
0 ≦ n < 1 × 10
10
, 0 ≦ r ≦ n (n, r are integers)
1 ≦
n!/r! < 1 × 10
100
or 1 ≦ n!/(n−r)! < 1 × 10
100
Pol(x, y)
|x|, |y| ≦ 9.999999999 × 10
99
√x
2
+ y
2
≦ 9.999999999 × 10
99
Rec(r, θ)
0 ≦ r ≦ 9.999999999 × 10
99
θ: Same as sinx
°’ ”
a°b’c”: |a|, b, c < 1 × 10
100
; 0 ≦ b, c
The display seconds value is subject to an
error of ±1 at the second decimal place.
°’ ”
←
|x| < 1 × 10
100
Decimal ↔ Sexagesimal Conversions
0°0’0” ≦ |
x
| ≦ 9999999°59’59”
x
y
x > 0: -1 × 10
100
< ylogx < 100
x = 0: y > 0
x < 0: y = n,
m
2n + 1
(m, n are integers)
However: -1 × 10
100
< ylog |x| < 100
102
x
√y
y > 0: x ≠ 0, -1 × 10
100
< 1/x logy < 100
y = 0: x > 0
y < 0: x = 2n+1,
2n + 1
m
(m ≠ 0; m, n are
integers)
However: -1 × 10
100
< 1/x log |y| < 100
a
b
/
c
Total of integer, numerator, and denominator
must be 10 digits or less (including separator
symbol).
RanInt#(a, b) a < b; |a|, |b| < 1 × 10
10
; b − a < 1 × 10
10
• Precision is basically the same as that described under “Calculation
Range and Precision”, above.
• x
y
,
x
√y,
3
√ , x!, nPr, nCr type functions require consecutive internal
calculation, which can cause accumulation of errors that occur with each
calculation.
• Error is cumulative and tends to be large in the vicinity of a function’s
singular point and inflection point.
• The range for calculation results that can be displayed in π form when
MathI/MathO is selected for Input/Output on the setup menu is |
x| < 10
6
.
Note, however, that internal calculation error can make it impossible to
display some calculation results in
π form. It also can cause calculation
results that should be in decimal form to appear in
π form.
Specifications
fx-83GT X
Power Requirements:
AAA-size battery R03 (UM-4) × 1
Approximate Battery Life:
2 years (based on one hour of operation per day)
Power Consumption:
0.0006 W
Operating Temperature:
0°C to 40°C (32°F to 104°F)
103
Dimensions:
13.8 (H) × 77 (W) × 165.5 (D) mm
½" (H) × 3" (W) × 6
1
⁄
2
" (D)
Approximate Weight:
100 g (3.5 oz) including the battery
fx-85GT X
Power Requirements:
Built-in solar cell; button battery LR44 × 1
Approximate Battery Life:
2 years (based on one hour of operation per day)
Operating Temperature:
0°C to 40°C (32°F to 104°F)
Dimensions:
11.1 (H) × 77 (W) × 165.5 (D) mm
⅜" (H) × 3" (W) × 6
1
⁄
2
" (D)
Approximate Weight:
90 g (3.2 oz) including the battery
104
Frequently Asked Questions
Frequently Asked Questions
■ How can I perform input and display results the same way I did on
a model that does not have Natural Textbook Format?
→ Perform the following key operation:
(SETUP) (Input/Output) (LineI/LineO), or
(SETUP) (Input/Output) (LineI/DecimalO).
■ How can I change a fraction form result produced by a division
operation to decimal form?
→ While a fraction calculation result is displayed, press . To have
calculation results initially appear as decimal values, change the setup
menu Input/Output setting to MathI/DecimalO.
■ What is the difference between Ans memory, independent memory,
and variable memory?
→ Each of these types of memory acts like “containers” for temporary
storage of a single value.
Ans Memory: Stores the result of the last calculation performed. Use
this memory to carry the result of one calculation on to the next.
Independent Memory: Use this memory to totalize the results of
multiple calculations.
Variables: This memory is helpful when you need to uses the same
value multiple times in one or more calculations.
■ What is the key operation to take me from the Statistics Mode or
Table Mode to a mode where I can perform arithmetic calculations?
→ Press
(Calculate).
■ How can I return the calculator to its initial default settings?
→ Perform the following operation to initialize calculator settings (except
the Contrast setting): (RESET) (Setup Data) (Yes).
■ When I execute a function calculation, why do I get a calculation
result that is completely different from older CASIO calculator
models?
→ With a Natural Textbook Display model, the argument of a function that
uses parentheses must be followed by a closing parenthesis. Failing to
press
after the argument to close the parentheses may cause
unwanted values or expressions to be included as part of the argument.
105
15.530 15
15.530 15
Failure to press here as shown below will result in calculation of
sin 45.
0.707106781230 15
Example: (sin 30) + 15 (Angle Unit: Degree)
Older (S-V.P.A.M.) Model:
Natural Textbook Display Model:
(LineI/LineO)
106
© 2018 CASIO COMPUTER CO., LTD.
