Casio Fx 3650P II 3650PII EN
User Manual: Casio fx-3650PII fx-3650P II | Calculators | Manuals | CASIO
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E
fx-3650P II
User's Guide
CASIO Worldwide Education Website
http://edu.casio.com
CASIO EDUCATIONAL FORUM
http://edu.casio.com/forum/
RJA527880-001V01
Getting Started
Thank you for purchasing this CASIO product.
k Before using the calculator for the first time...
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 nearby.
A After you are finished using the calculator...
Remove the hard case from the back of the calculator, and re-install it onto the front.
k Resetting the Calculator to Initial Defaults
Perform the operation below when you want to return the calculator’s setup to its initial
defaults. Note that this procedure will also clear all memory contents (independent memory,
variable memory, Answer Memory, statistical calculation sample data, and program data).
!9(CLR)3(All)w
k About this Manual
• 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
Battery
• Keep batteries out of the reach of small children.
• Use only the type of battery specified for this calculator in this manual.
E-1
Operating Precautions
• Even if the calculator is operating normally, replace the battery at least once every
three years (LR44 (GPA76)).
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.
• 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.
• Do not use an oxyride battery* or any other type of nickel-based primary
battery with this product. Incompatibility between such batteries and product
specifications can result in shorter battery life and product malfunction.
• 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, 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.
• Be sure to keep all user documentation handy for future reference.
* Company and product names used in this manual may be registered trademarks or
trademarks of their respective owners.
E-2
Contents
Getting Started..........................................................................................1
Safety Precautions ...................................................................................1
Operating Precautions .............................................................................2
Before starting a calculation... ................................................................4
Calculation Modes and Setup .................................................................5
Inputting Calculation Expressions and Values......................................7
Basic Calculations.................................................................................. 11
Calculation History and Replay.............................................................13
Calculator Memory Operations .............................................................14
Scientific Function Calculations ..........................................................17
3
Using 10 Engineering Notation (ENG) .................................................25
Complex Number Calculations (CMPLX) .............................................25
Statistical Calculations (SD/REG) .........................................................29
Base-n Calculations (BASE)..................................................................40
Program Mode (PRGM) ..........................................................................43
Appendix .................................................................................................53
Power Requirements ..............................................................................57
Specifications .........................................................................................58
E-3
Before starting a calculation...
k Turning On the Calculator
Press O. The calculator will enter the calculation mode (page 5) that it was in the last time
you turned it off.
A Adjusting Display Contrast
If the figures on the display become hard to read, try adjusting display contrast.
1. Press !N(SETUP) db(Contrast).
L I GHT
• This will display the contrast adjustment screen.
DARK
CASIO
2. Use d and e to adjust display contrast.
3. After the setting is the way you want, press A or !p(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.
A Turning Off the Calculator
Press !A(OFF).
The following information is retained when you turn off the calculator.
• Calculation modes and setup (page 5)
• Answer Memory (page 14), independent memory (page 15), and variable memory (page
16) contents
k Key Markings
M–
x!
A
M
8
LOGIC
DT CL
Function
Colors
To perform the function
1
M+
2
M–
Text: Amber
Press ! and then press the key.
3
M
Text: Red
Press a and then press the key.
4
DT
Text: Blue
In the SD or REG Mode, press the key.
5
CL
Text: Amber
Frame: Blue
In the SD or REG Mode, press ! and then press
the key.
6
∠
Text: Amber
Frame: Purple
In the CMPLX Mode, press ! and then press the
key.
Press the key.
E-4
Function
7
A
8
LOGIC
Colors
To perform the function
Text: Red
Frame: Green
Press a and then press the key (variable A).
In the BASE Mode, press the key.
Text: Green
In the BASE Mode, press the key.
k Reading the Display
A Input Expressions and Calculation Results
This calculator can display both the expressions you input and calculation results on the
same screen.
2× ( 5+ 4 ) – 2× - 3
Input expression
24
Calculation result
A 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 7 symbol.
Calculation Modes and Setup
k Selecting a Calculation Mode
Your calculator has six “calculation modes”.
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 d and e.
COMP CMPLX BASE
SD
REG
1
4
5
2
3
PRGM
6
2. Perform one of the following operations to select the calculation mode you want.
b(COMP): COMP(Computation)
d(BASE): BASE (Base n)
f(REG): REG (Paired Variable Statistics)
c(CMPLX): CMPLX (Complex Number)
e(SD): SD (Single Variable Statistics)
g(PRGM): PRGM (Program)
• Pressing a number key from b to g selects the applicable mode, regardless of which
menu screen is currently displayed.
E-5
k 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
d and e to navigate between them.
A Specifying the Angle Unit
90˚ =
π
radians = 100 grads
2
Angle Unit
Perform this key operation:
Degrees
!,b(Deg)
Radians
!,c(Rad)
Grads
!,d(Gra)
A Specifying the Display Digits
Exponential Display
Perform this key operation:
Number of Decimal Places
!,eb(Fix)a(0) to j(9)
Significant Digits
!,ec(Sci)b(1) to j(9), a(10)
Exponential Display Range
!,ed(Norm)b(Norm1) or c(Norm2)
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)
• After you specify the number of significant digits with Sci, calculation results are displayed
using the specified number of significant digits and 10 digits to the applicable power.
Calculation results are rounded off to the specified number of digits.
–1
(Sci = 5)
Example: 1 ÷ 7 = 1.4286 × 10
• Selecting Norm1 or Norm2 causes the display to switch to exponential notation whenever
the result is within the ranges defined below.
–2
10
–9
10
Norm2: 10 > x, x > 10
Norm1: 10 > x, x > 10
Example: 1 ÷ 200 = 5. × 10
–3
(Norm1)
0.005 (Norm2)
A Specifying the Fraction Display Format
Fraction Format
Perform this key operation:
Mixed Fractions
!,eeb(ab/c)
Improper Fractions
!,eec(d/c)
E-6
A Specifying the Complex Number Display Format
Complex Number Format
Perform this key operation:
Rectangular Coordinates
!,eeeb(a+bi)
Polar Coordinates
!,eeec(r∠)
A Specifying the Statistical Frequency Setting
Frequency Setting
Perform this key operation:
Frequency On
!,ddb(FreqOn)
Frequency Off
!,ddc(FreqOff)
k 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+bi (Rectangular Coordinates)
Frequency Setting .............................. FreqOn (Frequency On)
Perform the following key operation to clear the calculation mode and setup settings.
!9(CLR)2(Setup)w
If you do not want to clear the calculator’s settings, press A in place of w in the above
operation.
Inputting Calculation Expressions
and Values
k Inputting a Calculation Expression
Your calculator lets you input a calculation expression just as it is written and execute
it by pressing w. The calculator determines the proper priority sequence for addition,
subtraction, multiplication, division, functions and parentheses automatically.
Example: 2 × (5 + 4) – 2 × (–3) =
2*(5+4)2*-3w
E-7
2× ( 5+ 4 ) – 2× - 3
24
A 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.
–1
–1
–1
–1
–1
–1
sin(, cos(, tan(, sin (, cos (, tan (, sinh(, cosh(, tanh(, sinh (, cosh (, tanh (, log(, ln(,
e^(, 10^(, '(, 3'(, Abs(, Pol(, Rec(, arg(, Conjg(, Not(, Neg(, Rnd(, ∫(, d/dx(
Example: sin 30 =
s30)w
s i n ( 30 )
05
A 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 × '(3)
• Before a prefix symbol (excluding the minus sign): 2 × h123
• Before a variable name, constant, or random number: 20 × A, 2 × π
Important!
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.
6 ÷ 2 (1 + 2) p 6 ÷ (2 (1 + 2))
6 ÷ A (1 + 2) p 6 ÷ (A (1 + 2))
1 ÷ (2 + 3) sin(30) p 1 ÷ ((2 + 3) sin(30))
• When a multiplication sign is omitted immediately before a variable, a constant, etc.
6 ÷ 2π p 6 ÷ (2π)
2 ÷ 2'(2) p 2 ÷ (2'(2))
4π ÷ 2π p 4π ÷ (2π)
• When inputting a function that uses commas (such as Pol, Rec), be sure to input the
closed parentheses required by the expression. If you do not input closed parentheses,
parentheses may not be inserted automatically as described above.
A Final Closed Parenthesis
You can omit one or more closed parentheses that come at the end of a calculation,
immediately before the w key is pressed.
Example: (2 + 3) × (4 – 1) = 15
(2+3)*
(4-1w
( 2+ 3 ) × ( 4– 1
15
A Scrolling the Screen Left and Right
Input Expression
12345 + 12345 + 12345
345 + 12345 + 12345I
Displayed Expression
Cursor
E-8
• While the b symbol is on the screen, you can use the d 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 e key to move the cursor to the right and scroll the screen.
• You can also press f to jump to the beginning of the expression, or c to jump to the
end.
A 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
flashing vertical bar (|) or horizontal bar ( ). When the remaining capacity of the input area
is 10 bytes or less, the cursor changes to a flashing box (k).
If this happens, stop input of the current expression at some suitable location and calculate
its result.
k Editing a Calculation
A 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.
Pressing +
Original Expression
Insert Mode
1+2|34
1+2+|34
1+2 3 4
1+2 + 4
Cursor
Overwrite Mode
Cursor
The initial default input mode setting is insert mode.
To change to the overwrite mode, press: 1D(INS).
A Editing a Key Operation You Just Input
Example: To correct 369 × 13 so it becomes 369 × 12
369*13
369 × 13I
D2
369 × 12I
E-9
A Deleting a Key Operation
Example: To correct 369 × × 12 so it becomes 369 × 12
Insert Mode
369**12
ddD
369 ×× 12I
369 ×I12
Overwrite Mode
369**12
dddD
369 ×× 12
369 × 12
A Editing a Key Operation within an Expression
With the insert mode, use d and e to move the cursor to the right of the key operation
you want to edit, press D 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.
A Inserting Key Operations into an Expression
Be sure to select the insert mode whenever you want to insert key operations into an
expression. Use d and e to move the cursor to the location where you want to insert
the key operations, and then perform them.
k Finding the Location of an Error
If your calculation expression is incorrect, an error message will appear on the display when
you press w to execute it. After an error message appears, press the d or e 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
e or d
Mat h ERROR
14 ÷ 0I×2
Location of Error
d1w
E-10
14 ÷ 10 × 2
28
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.
k Arithmetic Calculations
Arithmetic calculations can be used to perform addition (+), subtraction (-),
multiplication (*), and division (/).
Example: 7 × 8 − 4 × 5 = 36
7*8-4*5w
36
k Fractions
Fractions are input using a special separator symbol ({).
A Fraction Calculation Examples
Example 1: 3
Example 2:
1
2
11
+1 =4
4
3
12
3$1$4+
1$2$3w
2
1
7
+
=
(Fraction Display Format: d/c)
3
2
6
2$3+1$2w
4{11{12
7{6
Note
• If the total number of elements (integer + numerator + denominator + separator symbols)
of a fraction calculation result is greater than 10 digits, the result will be displayed in
decimal format.
• If an input calculation includes a mixture of fraction and decimal values, the result will be
displayed in decimal format.
• You can input integers only for the elements of a fraction. Inputting non-integers will
produce a decimal format result.
A Switching between Mixed Fraction and Improper Fraction
Format
To convert a mixed fraction to an improper fraction (or an improper fraction to a mixed
fraction), press !$(d/c).
A Switching between Decimal and Fraction Format
Press $ to toggle between decimal value and fraction display format.
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 digits.
E-11
k Percent Calculations
Inputting a value and with a percent (%) sign makes the value a percent.
A Percent Calculation Examples
Example 1: 2 % = 0.02
(
2
)
10 0
2!((%)w
002
150*20
!((%)w
30
Example 3: What percent of 880 is 660?
660/880
!((%)w
75
Example 2: 150 × 20% = 30
(150 ×
20
)
100
Example 4: Increase 2,500 by 15%.
2500+2500*
15!((%)w
2875
Example 5: Reduce 3,500 by 25%.
3500-3500*
25!((%)w
2625
Example 6: Reduce the sum of 168, 98, and 734 by 20%.
168+98+734w
1000
-G*20!((%)w
800
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?
(500+300)
/500!((%)w
160
Example 8: What is the percentage change when a value is increased from 40 to 46?
(46-40)/40
!((%)w
E-12
15
k Degree, Minute, Second (Sexagesimal) Calculations
A Inputting Sexagesimal Values
The following is basic syntax for inputting a sexagesimal value.
{Degrees} $ {Minutes} $ {Seconds} $
Example: To input 2°30´30˝
2$30$30$w
2 ˚ 30 ˚ 30 ˚
2 ˚ 30 ˚ 30
• Note that you must always input something for the degrees and minutes, even if they are
zero.
A 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: 2°20´30˝ + 39´30˝ = 3°00´00˝
2$20$30$+
0$39$30$w
3 ˚ 0˚ 0
A Converting between Sexagesimal and Decimal
Pressing $ while a calculation result is displayed will toggle the value between
sexagesimal and decimal.
Example: To convert 2.255 to sexagesimal
2 ˚ 15˚ 18
2.255w$
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.
k 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 f. Each press of f
will scroll upwards (back) one calculation, displaying both the calculation expression and its
result.
Example: 1+1w2+2w3+3w
3+ 3
6
f
2+2
4
E-13
f
1+1
2
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 c to scroll downwards (forward) through calculation history
records.
Important!
• Calculation history records are all cleared whenever you press p, 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.
k Using Replay
While a calculation history record is on the display, press d or e to display the cursor
and enter the editing mode. Pressing e displays the cursor at the beginning of the
calculation expression, while d displays it at the end. After you make the changes you
want, press w to execute the calculation.
Example: 4 × 3 + 2.5 = 14.5
4 × 3 – 7.1 = 4.9
4*3+2.5w
d
DDDD-7.1w
4×3+ 2 . 5
145
4 × 3 + 2 . 5I
4×3 –7 . 1
49
Calculator Memory Operations
k Using Answer Memory (Ans)
The result of any new calculation you perform on the calculator is stored automatically in
Answer Memory (Ans).
A 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.
E-14
• 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.
A Automatic Insertion of Ans in Consecutive Calculations
Example: To divide the result of 3 × 4 by 30
12
3*4w
(Next) /30w
Ans ÷ 30
04
Pressing / inputs Ans automatically.
Note
In the case of a function with parenthetical argument (page 8), Ans automatically becomes
the argument only in the case that you input the function alone and then press w.
A Inserting Ans into a Calculation Manually
Example: To use the result of 123 + 456 in another calculation as shown below
123 + 456 = 579
789 – 579 = 210
123+456w
579
789-Kw
210
k 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. Independent memory can be used in all calculation modes, except
for the SD Mode and the REG Mode.
M symbol
10M+
A Adding to Independent Memory
While a value you input or the result of a calculation is on the display, press m to add it to
independent memory (M).
Example: To add the result of 105 ÷ 3 to independent memory (M)
105/3m
E-15
35
A Subtracting from Independent Memory
While a value you input or the result of a calculation is on the display, press 1m(M–) to
subtract it from independent memory (M).
Example: To subtract the result of 3 × 2 from independent memory (M)
3*21m(M–)
6
Note
Pressing m or 1m(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 or 1m(M–) at the end of a
calculation in place of w is the result of the calculation (which is added to or subtracted
from independent memory). It is not the current contents of independent memory.
A Viewing Independent Memory Contents
Press tm(M).
A Clearing Independent Memory Contents (to 0)
01t(STO)m(M)
Clearing independent memory will cause the M symbol to turn off.
k Using Variables
The calculator supports six variables named A, B, C, D, X, and Y, which you can use to
store values as required. Variables can be used in all calculation modes.
A 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
3+51t(STO)-(A)
A Viewing the Value Assigned to a Variable
To view the value assigned to a variable, press t and then specify the variable name.
Example: To view the value assigned to variable A
t-(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
5+a-(A)w
A Clearing the Value Assigned to a Variable (to 0)
Example: To clear variable A
01t(STO)-(A)
E-16
k Clearing All Memory Contents
Perform the following key operation when you want to clear the contents of independent
memory, variable memory, and Answer Memory.
19(CLR)1(Mem)w
• If you do not want to clear the calculator’s settings, press A in place of w in the above
operation.
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 A.
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.
k Pi (π) and Natural Logarithm Base e
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 (Si(e))
k Trigonometric and Inverse Trigonometric Functions
A Syntax and Input
–1
–1
–1
sin({n}), cos({n}), tan({n}), sin ({n}), cos ({n}), tan ({n})
–1
Example: sin 30 = 0.5, sin 0.5 = 30 (Angle Unit: Deg)
s30)w
05
1s(sin )0.5)w
30
–1
E-17
A 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 i × sin(30) is supported for example, but sin(1 + i)
is not.
• The angle unit you need to use in a calculation is the one that is currently selected as the
default angle unit.
k 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 1G(DRG') to display the menu screen shown below.
D
R
1(D): Degrees
2(R): Radians
3(G): Grads
G
1 2 3
Example: To convert
π
radians to degrees (Angle Unit: Deg)
2
(1e(π)/2)
1G(DRG')2(R)E
( π ÷2 ) r
90
k Hyperbolic and Inverse Hyperbolic Functions
A Syntax and Input
–1
–1
–1
sinh({n}), cosh({n}), tanh({n}), sinh ({n}), cosh ({n}), tanh ({n})
Example: sinh 1 = 1.175201194
ws(sinh)1)E
1175201194
A Notes
• After pressing w to specify a hyperbolic function or 1w to specify an inverse
hyperbolic function, press s, c, or t.
• These functions can be used in the CMPLX Mode, but complex number arguments are
not supported.
k Exponential and Logarithmic Functions
A Syntax and Input
10^({n}) .......................... 10 n
e^({n}) ............................. e{n}
log({n}) ........................... log10{n}
log({m},{n}) ..................... log{m}{n}
ln({n}) ............................. loge{n}
{ }
(Common Logarithm)
(Base {m} Logarithm)
(Natural Logarithm)
E-18
Example 1: log216 = 4, log16 = 1.204119983
4
l2,16)E
l16)E
l o g ( 16 )
1204119983
Base 10 (common logarithm) is assumed when no base is specified.
Example 2: ln 90 (loge 90) = 4.49980967
I90)E
449980967
k Power Functions and Power Root Functions
A Syntax and Input
2
2
{n} x ............................... {n}
3
3
{n} x ............................... {n}
–1
–1
{n} x ............................. {n}
{ }
{(m)}^({n}) ....................... {m} n
'({n}) .......................... {n}
3
3
'({n}) ......................... {n}
{ }
({m})x'({n}) .................. m {n}
(Square)
(Cube)
(Reciprocal)
(Power)
(Square Root)
(Cube Root)
(Power Root)
Example 1: ('
2 + 1) ('
2 – 1) = 1
(92)+1)
(92)-1)E
('( 2 ) + 1 ) ('( 2 ) – 1 )
1
2
Example 2: –2 3 = –1.587401052
-2M2$3)E
– 2 ˆ ( 2{3 )
-1587401052
A Notes
2
3
–1
• The functions x , x , and x can be used in complex number calculations in the CMPLX
Mode. Complex number arguments are also supported for these functions.
3
• ^(, '(, '(, x'( are also supported in the CMPLX Mode, but complex number
arguments are not supported for these functions.
E-19
k Coordinate Conversion (Rectangular ↔ Polar)
Your calculator can convert between rectangular coordinates and polar coordinates.
o
o
Rectangular Coordinates (Rec)
Polar Coordinates (Pol)
A 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, )
r: Polar coordinate r-value
: Polar coordinate -value
Example 1: To convert the rectangular coordinates ('
2, '
2 ) to polar coordinates
(Angle Unit: Deg)
1+(Pol)92)
,92))E
2
t,(Y)
45
(View the value of )
Example 2: To convert the polar coordinates (2, 30°) to rectangular coordinates
(Angle Unit: Deg)
1-(Rec)2,
30)E
1732050808
t,(Y)
1
(View the value of y)
A 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
-value (or y-value) is assigned to variable Y (page 16). To view the -value (or y-value),
display the value assigned to variable Y, as shown in the example.
• The values obtained for when converting from rectangular coordinates to polar
coordinates is within the range –180°< < 180°.
E-20
• 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 xvalue).
Example: Pol ('
2, '
2)+5=2+5=7
k Integration Calculation and Differential Calculation
A Integration Calculation
Your calculator performs integration using the Gauss-Kronrod method.
Syntax and Input
∫ ( f (x), a, b, tol)
f (x):
a:
b:
tol:
Function of X (Input the function used by variable X.)
Lower limit of region of integration
Upper limit of region of integration
Error tolerance range
–5
• This parameter can be omitted. In that case, a tolerance of 1 × 10 is used.
e
Example: ∫1 In( x ) = 1
fIa0(X)),1,aI(e))E
∫ ( I n ( X ) , 1, e )
1
A Differential Calculation
Your calculator approximates the derivative based on the central difference method.
Syntax and Input
d/dx( f (x), a, tol)
f (x): Function of X (Input the function used by variable X.)
a: Input value of point (differential point) of desired differential coefficient
tol: Error tolerance range
• This parameter can be omitted. In that case, a tolerance of 1 × 10
–10
is used.
π for the function y = sin(x) (Angle Unit: Rad)
Example: To obtain the derivative at point x = 2
1f(d/dx)sa0(X)),
1e(π)/2)E
d/ dx ( s i n ( X ) , π ÷2 )
0
A Integration and Differential Calculation Precautions
• Integration and differential calculations can be performed in the COMP Mode and PRGM
Mode (run mode: COMP) only.
• The following cannot be used in f(x): Pol, Rec. The following cannot be used in f(x), a, b,
or tol: ∫, d/dx.
• When using a trigonometric function in f(x), specify Rad as the angle unit.
E-21
• A smaller tol value increases precision, but it also increases calculation time. When
specifying tol, use value that is 1 × 10–14 or greater.
Precautions for Integration Calculation Only
• Integration normally requires considerable time to perform.
1
• For f(x) 0 where a x b (as in the case of ∫0 3x2 – 2 = –1), calculation will produce a
negative result.
• Depending on the content of f(x) and the region of integration, calculation error that
exceeds the tolerance may be generated, causing the calculator to display an error
message.
Precautions for Differential Calculation Only
• If convergence to a solution cannot be found when tol input is omitted, the tol value will
be adjusted automatically to determine the solution.
• Non-consecutive points, abrupt fluctuation, extremely large or small points, inflection
points, and the inclusion of points that cannot be differentiated, or a differential point or
differential calculation result that approaches zero can cause poor precision or error.
A Tips for Successful Integration Calculations
When a periodic function or integration interval results in positive
and negative f(x) function values
Perform separate integrations for each cycle, or for the positive part and the negative part,
and then combine the results.
∫
S Positive
c
a
f(x)dx + (–
∫
b
c
f(x)dx)
Positive Part Negative Part
(S Negative)
(S Positive)
S Negative
When integration values fluctuate widely due to minute shifts in the
integration interval
Divide the integration interval into multiple parts (in a way that breaks areas of wide
fluctuation into small parts), perform integration on each part, and then combine the results.
f (x)
0
∫
a
x1
x2
x3
x4
b
x
b
a
+
∫
f(x)dx =
b
x4
∫
x1
a
f(x)dx
E-22
f(x)dx +
∫
x2
x1
f(x)dx + .....
k Other Functions
x!, Abs(, Ran#, nPr, nCr, Rnd(
The x!, nPr, and nCr functions can be used in the CMPLX Mode, but complex number
arguments are not supported.
A Factorial (!)
Syntax: {n}! ({n} must be a natural number or 0.)
Example: (5 + 3)!
(5+3)
1X(x!)E
40320
A 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 25 for more information.
Syntax: Abs({n})
Example: Abs (2 – 7) = 5
1)(Abs)2-7)E
5
A 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.
10001.(Ran#)E
E
E
287
613
118
• The above values are provided for example only. The actual values produced by your
calculator for this function will be different.
E-23
A Permutation (nPr)/Combination (nCr)
Syntax: {n}P{m}, {n}C{m}
Example: How many four-person permutations and combinations are possible for a group
of 10 people?
101*(nPr)4E
5040
101/(nCr)4E
210
A 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
(3 decimal places)
(Internal calculation uses 15 digits.)
1Ne1(Fix)3
200/7E
*14E
28571
400000
Now perform the same calculation using the rounding (Rnd) function.
(Calculation uses rounded value.)
200/7E
10(Rnd)E
*14E
(Rounded result)
E-24
28571
399994
Using 103 Engineering 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,.
The CMPLX Mode does not support use of engineering notation.
k ENG Calculation Examples
Example 1: To convert 1234 to engineering notation using ENG/
1234
1234 03
1234 00
1234E
W
W
Example 2: To convert 123 to engineering notation using ENG,
123
0123 03
0000123 06
123E
1W(,)
1W(,)
Complex Number Calculations
(CMPLX)
To perform the example operations in this section, first select CMPLX as the calculation
mode.
k Inputting Complex Numbers
A Inputting Imaginary Numbers (i)
Example: To input 2 + 3i
2+3W(i)
E-25
2 + 3 iI
A Inputting Complex Number Values Using Polar Coordinate
Format
Example: To input 5 ∠ 30
51-(∠)30
5 30I
Important!
When inputting argument , enter a value that indicates an angle in accordance with the
calculator’s current default angle unit setting.
k 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 1E(Re⇔Im).
Example: To input 2 + 1i and display its calculation result
1,(SETUP)eee1(a+bi)
2+W(i)E
2+ i
2
Displays real part.
1
1E(Re⇔Im)
Displays imaginary part.
(i symbol turns on during imaginary part display.)
A 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
r ⬔
a + bi
b
o
Imaginary axis
a
Real axis
o
Rectangular Coordinates
Real axis
Polar Coordinates
Use the setup screens to specify the default display format you want. For details, see
“Specifying the Complex Number Display Format” (page 7).
E-26
k Calculation Result Display Examples
A Rectangular Coordinate Format (a+bi)
1,(SETUP)eee1(a+bi)
Example 1: 2 × ('
3 + i) = 2'
3 + 2i = 3.464101615 + 2i
2*(93)+W(i))E
3464101615
1E(Re⇔Im)
2
Example 2: '
2 ∠ 45 = 1 + 1i (Angle Unit: Deg)
92)1-(∠)
45E
1
1E(Re⇔Im)
1
2*(93)+W(i))E
4
1E(Re⇔Im)
30
A Polar Coordinate Format (r∠)
1,(SETUP)eee2(r∠)
3 + i) = 2'
3 + 2i = 4 ∠ 30
Example 1: 2 × ('
∠ symbol turns on during display of -value.
Example 2: 1 + 1i = 1.414213562 ∠ 45 (Angle Unit: Deg)
1+1W(i)E
1414213562
1E(Re⇔Im)
45
k Conjugate Complex Number (Conjg)
Example: Obtain the conjugate complex number of 2 + 3i
1,(Conjg)2+3W(i))E
1E(Re⇔Im)
E-27
2
-3
k Absolute Value and Argument (Abs, arg)
Example:
To obtain the absolute value and argument of 2 + 2i
(Angle Unit: Deg)
Imaginary axis
b=2
o
Absolute Value:
Argument:
1)(Abs)2+2W(i))E
1((arg)2+2W(i))E
a=2
Real axis
2828427125
45
k Overriding the Default Complex Number Display Format
A Specifying Rectangular Coordinate Format for a Calculation
Input 1-('a+bi) at the end of the calculation.
Example: 2'
2 ∠ 45 = 2 + 2i (Angle Unit: Deg)
292)1-(∠)45
1-('a+bi)E
2
1E(Re⇔Im)
2
A Specifying Polar Coordinate Format for a Calculation
Input 1+('r∠) at the end of the calculation.
2 ∠ 45 = 2.828427125 ∠ 45 (Angle Unit: Deg)
Example: 2 + 2i = 2'
2+2W(i)
1+('r∠)E
1E(Re⇔Im)
E-28
2828427125
45
Statistical Calculations (SD/REG)
k Statistical Calculation Sample Data
A 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 7).
A 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).
SD Mode......40 items (FreqOn), 80 items (FreqOff)
REG Mode ...26 items (FreqOn), 40 items (FreqOff)
A 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.
k Performing Single-variable Statistical Calculations
To perform the example operations in this section, first select SD as the calculation mode.
A 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}1,(;) {Freq1}m(DT)
{x2}1,(;) {Freq2}m(DT)
{xn}1,(;) {Freqn}m(DT)
Note
If the frequency of a class value is only one, you can input it by pressing {xn}m(DT) only
(without specifying the frequency).
Example: To input the following data: (x, Freq) = (24.5, 4), (25.5, 6), (26.5, 2)
24.51,(;)4
m(DT)
24 .5 ; 4I
0
L i ne =
1
m(DT) tells the calculator this is the end of the first data item.
E-29
25.51,(;)6m(DT)
26.51,(;)2m(DT)
L i ne =
3
Frequency Off (FreqOff)
In this case, input each individual data item as shown below.
{x1}m(DT) {x2}m(DT) ... {xn}m(DT)
A Viewing Current Sample Data
After inputting sample data, you can press c 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 29 (Frequency Setting: FreqOn)
Ac
c
x 1=
245
F r e q 1=
4
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 f to scroll in the reverse direction.
A Editing a Data Sample
To edit a data sample, recall it, input the new value(s), and then press E.
Example: To edit the “Freq3” data sample input under “Inputting Sample Data” on page 29
Af
3E
F r eq3=
2
F r eq3=
3
A Deleting a Data Sample
To delete a data sample, recall it and then press 1m(CL).
Example: To delete the “x2” data sample input under “Inputting Sample Data” on page 29
Accc
E-30
x 2=
255
L i ne =
1m(CL)
2
Note
• The following shows images of how the data appears before and after the delete
operation.
Before
After
x1: 24.5
Freq1: 4
x1: 24.5
Freq1: 4
x2: 25.5
Freq2: 6
x2: 26.5
Freq2: 2
x3: 26.5
Freq3: 2
Shifted upwards.
• When the statistical frequency setting is turned on (FreqOn), the applicable x-data and
Freq data pair is deleted.
A Deleting All Sample Data
Perform the following key operation to delete all sample data.
19(CLR)1(Stat)E
If you do not want to delete all sample data, press A in place of E in the above operation.
A Statistical Calculations Using Input Sample Data
To perform a statistical calculation, input the applicable command and then press E.
A SD Mode Statistical Command Reference
11(S-SUM)1
x2
Obtains the sum of squares of the sample
data.
Σx
2
Obtains the sum of the sample data.
Σx = Σxi
= Σxi
2
11(S-SUM)3
n
Obtains the number of samples.
11(S-SUM)2
x
12(S-VAR)1
x̄
Obtains the mean.
Σx
o= ni
σx
12(S-VAR)2
Obtains the population standard deviation.
σx =
minX
Obtains the sample standard deviation.
Σ(xi – o)2
n
sx =
12(S-VAR)e1
Determines the minimum value of the
samples.
12(S-VAR)3
sx
maxX
Σ(xi – o)2
n–1
12(S-VAR)e2
Determines the maximum value of the
samples.
E-31
k Performing Paired-variable Statistical Calculations
To perform the example operations in this section, first select REG as the calculation mode.
A Regression Calculation Types
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. Enter the REG Mode.
• This displays the initial regression calculation selection menu. The menu has two
screens, and you can use d and e to navigate between them.
2. Perform one of the following operations to select the regression calculation you want.
To select this regression type:
And press this key:
Linear (y = a + bx)
1(Lin)
Logarithmic (y = a + b Inx)
2(Log)
e Exponential (y = aebx)
3(Exp)
Power (y = axb)
4(Pwr)
Inverse (y = a + b/x)
e1(Inv)
2
Quadratic (y = a + bx + cx )
e2(Quad)
ab Exponential (y = abx)
e3(AB-Exp)
Note
You can switch to another regression calculation type from within the REG Mode, if you
want. Pressing 12(S-VAR)3(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.
A 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},{y1}1,(;) {Freq1} m(DT)
{x2},{y2}1,(;) {Freq2} m(DT)
{xn},{yn}1,(;) {Freqn} m(DT)
Note
If the frequency of a class value is only one, you can input it by pressing {xn},{yn}m(DT)
only (without specifying the frequency).
E-32
Frequency Off (FreqOff)
In this case, input each individual data item as shown below.
{x1},{y1} m(DT)
{x2},{y2} m(DT)
{xn},{yn} m(DT)
A Viewing Current Sample Data
After inputting sample data, you can press c 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 f to scroll in the reverse direction.
A Editing a Data Sample
To edit a data sample, recall it, input the new value(s), and then press E.
A Deleting a Data Sample
To delete a data sample, recall it and then press 1m(CL).
A Deleting All Sample Data
See “Deleting All Sample Data” (page 31).
A Statistical Calculations Using Input Sample Data
To perform a statistical calculation, input the applicable command and then press E.
A REG Mode Statistical Command Reference
Sum and Number of Sample Command (S-SUM Menu)
11(S-SUM)1
x2
Obtains the sum of squares of the sample
x-data.
Σx
2
n
x
Obtains the sum of the sample x-data.
Σx = Σxi
= Σxi
2
11(S-SUM)3
Obtains the number of samples.
11(S-SUM)2
y2
11(S-SUM)e1
Obtains the sum of squares of the sample
y-data.
Σy2 = Σyi2
y
11(S-SUM)e2
Obtains the sum of the sample y-data.
Σy = Σyi
xy
11(S-SUM)e3
Obtains the sum of products of the sample
x-data and y-data.
Σxy = Σxiyi
E-33
11(S-SUM)d1
x2y
11(S-SUM)d2
x3
Obtains the sum of squares of the sample
x-data multiplied by the sample y-data.
Obtains the sum of cubes of the sample
x-data.
Σx2y = Σxi2yi
Σx3 = Σxi3
11(S-SUM)d3
x4
Obtains the sum of the fourth power of the
sample x-data.
Σx4 = Σxi4
Mean and Standard Deviation Commands (VAR Menu)
x̄
σx
12(S-VAR)1(VAR)1
Obtains the mean of the sample x-data.
Obtains the population standard deviation
of the sample x-data.
Σx
o= ni
sx
σx =
ȳ
12(S-VAR)1(VAR)3
Σ(xi – o)
n–1
12(S-VAR)1(VAR)e2
sy
Obtains the population standard deviation
of the sample y-data.
σy =
12(S-VAR)1(VAR)e1
Σy
p = ni
2
σy
Σ(xi – o)2
n
Obtains the mean of the sample y-data.
Obtains the sample standard deviation of
the sample x-data.
sx =
12(S-VAR)1(VAR)2
12(S-VAR)1(VAR)e3
Obtains the sample standard deviation of
the sample y-data.
Σ (yi – y)2
n
sy =
Σ (yi – y)2
n–1
Regression Coefficient and Estimated Value Commands for Nonquadratic Regression (VAR Menu)
12(S-VAR)1(VAR)ee1
a
Obtains constant term a of the regression formula.
12(S-VAR)1(VAR)ee2
b
Obtains coefficient b of the regression formula.
E-34
12(S-VAR)1(VAR)ee3
r
Obtains correlation coefficient r.
12(S-VAR)1(VAR)d1
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.
12(S-VAR)1(VAR)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.
Regression Coefficient and Estimated Value Commands for Quadratic
Regression (VAR Menu)
12(S-VAR)1(VAR)ee1
a
Obtains constant term a of the regression formula.
12(S-VAR)1(VAR)ee2
b
Obtains coefficient b of the regression formula.
12(S-VAR)1(VAR)ee3
c
Obtains coefficient c of the regression formula.
12(S-VAR)1(VAR)d1
xˆ 1
Taking the value input immediately before this command as the y-value, uses the formula
on page 37 to determine one estimated value of x.
12(S-VAR)1(VAR)d2
xˆ 2
Taking the value input immediately before this command as the y-value, uses the formula
on page 37 to determine one more estimated value of x.
12(S-VAR)1(VAR)d3
yˆ
Taking the value input immediately before this command as the x-value, uses the formula
on page 37 to determine the estimated value of y.
Minimum and Maximum Value Commands (MINMAX Menu)
12(S-VAR)2(MINMAX)1
minX
Obtains the minimum value of the sample x-data.
E-35
12(S-VAR)2(MINMAX)2
maxX
Obtains the maximum value of the sample x-data.
12(S-VAR)2(MINMAX)e1
minY
Obtains the minimum value of the sample y-data.
12(S-VAR)2(MINMAX)e2
maxY
Obtains the maximum value of the sample y-data.
A Regression Coefficient and Estimated Value Calculation
Formula Table
Linear Regression
Command
Regression Formula
Constant Term a
Regression Coefficient b
Correlation Coefficient r
Estimated Value m
Estimated Value
Calculation Formula
Σyi – b.Σxi
n
n.Σxiyi – Σxi.Σyi
b= . 2
n Σxi – (Σxi)2
n.Σxiyi – Σxi.Σyi
r=
{n.Σxi2 – (Σxi)2}{n.Σyi2 – (Σyi)2}
y–a
m=
b
n = a + bx
a=
Quadratic Regression
Command
Regression Formula
Constant Term a
Regression Coefficient b
Regression Coefficient c
Calculation Formula
a=
b=
c=
However,
2
Sxx = Σxi 2– (Σxi )
n
(Σx .Σy )
Sxy = Σxi yi – i i
n
Σyi
Σxi
Σxi2
–b
–c
n
n
n
( ) ( )
Sxy.Sx 2x 2 – Sx 2y.Sxx 2
Sxx.Sx2x2 – (Sxx2)2
Sx 2y.Sxx – Sxy.Sxx2
Sxx.Sx2x2 – (Sxx2)2
. 2
Sxx2 = Σxi 3 – (Σxi Σxi )
n
2 2
Sx2x2 = Σxi 4 – (Σxi )
n
2.
Sx2y = Σxi 2yi – (Σxi Σyi )
n
E-36
Command
Calculation Formula
Estimated Value m1
– b + b2 – 4c(a – y)
m1 =
2c
Estimated Value m2
– b – b2 – 4c(a – y)
m2 =
2c
Estimated Value n
n = a + bx + cx 2
Logarithmic Regression
Command
Regression Formula
Constant Term a
Regression Coefficient b
Correlation Coefficient r
Estimated Value m
Estimated Value n
Calculation Formula
Σyi – b.Σlnxi
a=
n
n.Σ(lnxi)yi – Σlnxi .Σyi
b=
n.Σ(lnxi)2 – (Σlnxi)2
n.Σ(lnxi)yi – Σlnxi.Σyi
r=
{n.Σ(lnxi)2 – (Σlnxi)2}{n.Σyi2 – (Σyi)2}
y–a
b
m=e
n = a + blnx
e Exponential Regression
Command
Regression Formula
Constant Term a
Regression Coefficient b
Correlation Coefficient r
Calculation Formula
.
a = exp Σlnyi – b Σxi
(
n
)
n.Σxilnyi – Σxi.Σlnyi
b=
n.Σxi2 – (Σxi)2
n.Σxilnyi – Σxi.Σlnyi
r=
{n.Σxi2 – (Σxi)2}{n.Σ(lnyi)2 – (Σlnyi)2}
lny – lna
Estimated Value m
m=
Estimated Value n
n = aebx
b
E-37
ab Exponential Regression
Command
Regression Formula
Constant Term a
Regression Coefficient b
Calculation Formula
Σlnyi – lnb.Σxi
n
n.Σxilnyi – Σxi.Σlnyi
b = exp
n.Σxi2 – (Σxi)2
(
(
)
a = exp
)
Correlation Coefficient r
n.Σxilnyi – Σxi.Σlnyi
r=
{n.Σxi2 – (Σxi)2}{n.Σ(lnyi)2 – (Σlnyi)2}
Estimated Value m
m=
Estimated Value n
n = abx
lny – lna
lnb
Power Regression
Command
Regression Formula
Constant Term a
Regression Coefficient b
Correlation Coefficient r
Calculation Formula
.
a = exp Σlnyi – b Σlnxi
(
n
)
n.Σlnxilnyi – Σlnxi.Σlnyi
n.Σ(ln xi)2 – (Σln xi)2
n.Σlnxilnyi – Σlnxi.Σlnyi
r=
{n.Σ(lnxi)2 – (Σlnxi)2}{n.Σ(lnyi)2 – (Σlnyi)2}
b=
ln y – ln a
b
Estimated Value m
m=e
Estimated Value n
n = a xb
Inverse Regression
Command
Regression Formula
Constant Term a
Regression Coefficient b
Calculation Formula
Σyi – b.Σxi–1
a=
n
Sxy
b=
Sxx
E-38
Command
Calculation Formula
r=
Correlation Coefficient r
However,
Sxx = Σ(xi–1)2 –
(Σxi–1)2
n
Sxy
Sxx.Syy
Syy = Σyi2– (Σyi)
n
Command
2
Sxy = Σ(xi–1)yi –
Σxi–1.Σyi
n
Calculation Formula
b
Estimated Value m
m=
Estimated Value n
n=a+
y–a
b
x
k Statistical Calculation Example
The nearby data shows how the weight of a newborn at various
numbers of days after birth.
1 Obtain the regression formula and correlation coefficient
produced by linear regression of the data.
2 Obtain the regression formula and correlation coefficient
produced by logarithmic regression of the data.
3 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
Number
of Days
20
50
80
110
140
170
200
230
260
290
320
Weight
(g)
3150
4800
6420
7310
7940
8690
8800
9130
9270
9310
9390
Enter the REG Mode and select linear regression:
N5(REG)1(Lin)
Select FreqOff for the statistical frequency setting:
1N(SETUP)dd2(FreqOff)
Input the sample data:
20,3150m(DT)50,4800m(DT)
80,6420m(DT)110,7310m(DT)
140,7940m(DT)170,8690m(DT)
200,8800m(DT)230,9130m(DT)
260,9270m(DT)290,9310m(DT)
320,9390m(DT)
1 Linear Regression
Regression Formula Contant Term a:
12(S-VAR)1(VAR)ee1(a)E
E-39
4446575758
Regression Coefficient b:
12(S-VAR)1(VAR)ee2(b)E
1887575758
Correlation Coefficient:
12(S-VAR)1(VAR)ee3(r)E
0904793561
2 Logarithmic Regression
Select logarithmic regression:
12(S-VAR)3(TYPE)2(Log)
x1=
20
Regression Formula Contant Term a:
A12(S-VAR)1(VAR)ee1(a)E
–4209356544
Regression Coefficient b:
12(S-VAR)1(VAR)ee2(b)E
2425756228
Correlation Coefficient:
12(S-VAR)1(VAR)ee3(r)E
0991493123
3 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 when x = 350:
350
12(S-VAR)1(VAR)d2(n)E
350 y
1000056129
Base-n Calculations (BASE)
To perform the example operations in this section, first select BASE as the calculation
mode.
k Performing Base-n Calculations
A Specifying the Default Number Base
Use the following keys to select a default number base x(DEC) for decimal, M(HEX) for
hexadecimal, l(BIN) for binary, or i(OCT) for octal.
E-40
A Example Base-n Calculations
Example: To select binary as the number base and calculate 12 + 12
Al(BIN)1+1E
1+ 1
10
b
Number base indicator
(d: decimal, H: hexadecimal, b: binary, o: octal)
• 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.
A Hexadecimal Value Input and Calculation Example
Use the following keys to input the letters required for hexadecimal values: -(A), $(B),
w(C), s(D), c(E), t(F).
Example: To select hexadecimal as the number base and calculate 1F16 + 116
AM(HEX)1t(F)+1E
20
H
A Effective Calculation Ranges
Number Base
Effective Range
Binary
Positive: 0 < x < 111111111
Negative: 1000000000 < x < 1111111111
Octal
Positive: 0 < x < 3777777777
Negative: 4000000000 < x < 7777777777
Decimal
–2147483648 < x < 2147483647
Hexadecimal
Positive: 0 < x < 7FFFFFFF
Negative: 80000000 < x < FFFFFFFF
A Math ERROR occurs when a calculation result is outside of the applicable range for the
current default number base.
k Converting a Displayed Result to another Number Base
Pressing x(DEC), M(HEX), l(BIN), or i(OCT) while a calculation result is displayed
will convert the result to the corresponding number base.
Example: To convert the decimal value 3010 to binary, octal, and hexadecimal format
Ax(DEC)30E
l(BIN)
i(OCT)
E-41
30
11110
36
d
b
o
1E
M(HEX)
H
k Using the LOGIC Menu
In the BASE Mode, the X key changes function to become a LOGIC menu display key.
The LOGIC menu has three screens, and you can use d and e to navigate between
them.
k 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.
A Example Calculation Using Base-n Specification
Example: To perform the calculation 510 + 516, and display the result in binary
Al(BIN)X(LOGIC)d1(d)
5+X(LOGIC)d2(h)5E
d5 + h5
1010
b
k 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.
A Logical Product (and)
Returns the result of a bitwise product.
Example: 10102 and 11002 = 10002
1010X(LOGIC)1(and)1100E
1000
b
11011
b
110
b
A Logical Sum (or)
Returns the result of a bitwise sum.
Example: 10112 or 110102 = 110112
1011X(LOGIC)2(or)11010E
A Exclusive Logical Sum (xor)
Returns the result of a bitwise exclusive logical sum.
Example: 10102 xor 11002 = 1102
1010X(LOGIC)e1(xor)1100E
E-42
A Exclusive Logical Sum Negation (xnor)
Returns the result of the negation of a bitwise exclusive logical sum.
Example: 11112 xnor 1012 = 11111101012
1111X(LOGIC)3(xnor)101E
1111110101
b
1111110101
b
1111010011
b
A Complement/Inversion (Not)
Returns the complement (bitwise inversion) of a value.
Example: Not(10102) = 11111101012
X(LOGIC)e2(Not)1010)E
A Negation (Neg)
Returns the two’s complement of a value.
Example: Neg(1011012) = 11110100112
X(LOGIC)e3(Neg)101101)E
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.
k Program Mode Overview
A 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.
A Program Memory
Program memory has a total capacity of 390 bytes, which can be shared by up to four
programs. Further program storage is not possible after program memory becomes full.
k Creating a Program
A Creating a New Program
Example: To create a program that converts inches to centimeters (1 inch = 2.54 cm)
? → A : A × 2.54
E-43
1. Press ,g(PRGM) to enter the PRGM Mode.
ED I T RUN DEL
1
2
3
2. Press b(EDIT).
Program areas that already contain program data (P1 through P4)
EDI T Pr o g r am
P-1234 380
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 e and d to switch between menu
screen 1 and screen 2.
MODE : COMP CMPLX
1
MODE : BASE SD REG
2
3 45
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 b(COMP) on screen 1. This selects COMP
I
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.
? →A : A × 2. 54
5. Input the program.
010
• Here we will input the program shown below.
Program
? → A : A × 2.54
Key Operation
!d(P-CMD)b(?)
!~(→)-(A)w
a-(A)*c.fe
• !d(P-CMD) displays a special program command input screen. See “Inputting
Commands” on page 46 for more information.
6. After inputting the program, press A or !5(EXIT).
• To run the program you just created, press w here to display the RUN Program
screen. For more information, see “Running a Program” below.
• To return to the normal calculation screen, press ,b to enter the COMP Mode.
E-44
A Editing an Existing Program
1. Press ,g(PRGM)b(EDIT) to display the EDIT Program screen.
2. Use number keys b through e to select the program area that contains the program
you want to edit.
3. Use e and d 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 f jumps to the beginning of the program, while c jumps to the end.
4. After you finish editing the program, press A or !5(EXIT).
k Running a Program
You can run a program in the PRGM Mode or from another mode.
A Running a Program from Outside the PRGM Mode
1. Press 5.
2. Use number keys b through e to select a program area and execute its program.
A Running a Program in the PRGM Mode
1. Press ,g(PRGM) to display the PRGM Mode initial screen.
2. Press c(RUN).
• This will display the RUN Program screen.
Program areas that already contain program data (P1 through P4)
RUN Pr o g r am
P-1234 380
Remaining program memory capacity
3. Use number keys b through e to select the program area that contains the program
you want to run.
• This will execute the program in the program area you select.
A What to do if an error message appears
Press d or e. 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.
k Deleting a Program
You can delete an existing program by specifying its program area number.
A Deleting the Program in a Specific Program Area
1. Press ,g(PRGM) to display the PRGM Mode initial screen.
2. Press d(DEL).
Program areas that already contain program data (P1 through P4)
DELETE Pr o g r am
P-1234 380
Remaining program memory capacity
E-45
3. Use number keys b through e to select the program area whose program you want
to delete.
• The symbol next to the number of the program area
that contained the program you just deleted will turn off,
DELETE Pr o g r am
and the remaining program memory capacity value will
increase.
P-1234 390
k Inputting Commands
A Inputting Special Program Commands
1. While the program editing screen is on the display, press !d (P-CMD).
• This displays page 1 of the command menu.
2. Use e and d to scroll through the pages and display the one that contains the
command you want.
3. Use number keys b through e to select and input the command you want.
Note
To input a separator symbol (:), press w.
A 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.
k Command Reference
This section provides details on each of the commands that you can use in programs.
Commands that have g in the title can be input on the screen that appears when you
press !d(P-CMD) or 5.
A Basic Operation Commands g
? (Input Prompt)
Syntax
Function
Example
? → {variable}
Displays the input prompt “{variable}?” and assigns the input value to a
variable.
?→A
→ (Variable Assignment)
Syntax
Function
Example
{expression ; ?} → {variable}
Assigns the value obtained by the element on the left to the variable on the
right.
A+5 → A
: (Separator Code)
Syntax
Function
Example
{statement} : {statement} : ... : {statement}
Separates statements. Does not stop program execution.
2
2
? → A : A : Ans
E-46
^ (Output Command)
Syntax
Function
Example
{statement} ^ {statement}
Pauses program execution and displays the result of the current execution.
The Q symbol is turned on while program execution is paused by this
command.
2
2
? → A : A ^ Ans
A Unconditional Jump Command g
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.
A Conditional Jump Commands and Conditional Expressions
g
S
Syntax
Function
Example
1 {expression} {relational operator} {expression} S {statement1} :
{statement2} : ....
2 {expression} S {statement1} : {statement2} : ....
Conditional branching command used in combination with relational
operators (=, ≠, >, >, <, <).
Syntax 1: {statement1} is executed if the condition to the left of the S
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 S
command is false, and then {statement2} and everything after it is executed.
Syntax 2: A non-zero evaluation result of the condition to the left of the S
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 S command is interpreted as “false”, so
{statement1} is skipped, and {statement2} and everything after it is executed.
Lbl 1 : ? → A : A > 0 S '(A) ^ Goto 1
=, ≠, >, >, <, < (Relational Operators)
Syntax
Function
Example
{expression} {relational operator} {expression}
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 S, and when structuring the {conditional expression} of
If statements and While statements.
See the entries for S (page 47), If statement (page 48), and While statement
(page 49).
E-47
Note
These commands evaluate the expressions on either side, and return 1 if true and 0 if false,
and store the result in Ans.
A Control Structure Commands/If Statement g
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
Function
Example 1
Example 2
If {conditional expression} : Then {expression*} : Else {expression*} : IfEnd :
{statement} : ...
• 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.
? → A : If A < 10 : Then 10A ^ Else 9A ^ IfEnd : Ans×1.05
? → A : If A > 0 : Then A × 10 → A : IfEnd : Ans×1.05
A Control Structure Commands/For Statement g
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.
For~To~Next
Syntax
Function
Example
For {expression (starting value)} → {variable (control variable)} To {expression
(ending value)} : {statement} : ... {statement} : Next : ....
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.
2
For 1 → A To 10 : A → B : B ^ Next
E-48
For~To~Step~Next
Syntax
Function
Example
For {expression (starting value)} → {variable (control variable)} To {expression
(ending value)} Step {expression (step)} : {statement} : ... {statement} :
Next : ....
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.
2
For 1 → A To 10 Step 0.5 : A → B : B ^ Next
A Control Structure Commands/While Statement g
While~WhileEnd
Syntax
Function
Example
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.
2
? → A : While A < 10 : A ^ 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.
A Program Control Commands g
Break
Syntax
Function
Example
.. : {Then ; Else ; S } Break : ..
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.
? → A : While A > 0 : If A > 2 : Then Break : IfEnd : WhileEnd : A ^
A Setup Commands
These commands function the same way as the calculator’s various setup settings. For
more information, see “Calculator Setup” on page 6.
Important!
With some setup commands, the settings you configure remain in effect even after you
finish running the program.
E-49
Angle Unit Commands
Deg, Rad, Gra
Syntax
Operation
Function
(COMP, CMPLX, SD, REG)
.. : Deg : ..
.. : Rad : ..
.. : Gra : ..
!,(SETUP)b(Deg)
!,(SETUP)c(Rad)
!,(SETUP)d(Gra)
These commands specify the angle unit setting.
Display Format Command
Fix
Syntax
Operation
Function
(COMP, CMPLX, SD, REG)
.. : Fix {n} : .. (n = an integer from 0 to 9)
!,(SETUP)eb(Fix)a to j
This command fixes the number of decimal places (from 0 to 9) for output of
calculation results.
Sci
Syntax
Operation
Function
(COMP, CMPLX, SD, REG)
.. : Sci {n} : .. (n = an integer from 0 to 9)
!,(SETUP)ec(Sci)a to j
This command fixes the number of significant digits (from 1 to 10) for output
of calculation results.
Pressing !,(SETUP)ec(Sci) and then a specifies 10 significant
digits.
Norm
Syntax
Operation
Function
(COMP, CMPLX, SD, REG)
.. : Norm {1 ; 2} : ..
!,(SETUP)ed(Norm)b or c
This command specifies either Norm1 or Norm2 for output of calculation
results.
Statistical Frequency Command
FreqOn, FreqOff
Syntax
Operation
Function
(SD, REG)
.. : FreqOn : ..
.. : FreqOff : ..
!,(SETUP)db(FreqOn)
!,(SETUP)dc(FreqOff)
This command turns statistical frequency on (FreqOn) or off (FreqOff).
E-50
A Clear Commands
ClrMemory
Syntax
Operation
Function
(COMP, CMPLX, BASE)
.. : ClrMemory : ..
!j(CLR)b(Mem)
This command clears all variables to zero.
Note
To clear a specific variable, use 0 → {variable}.
ClrStat
Syntax
Operation
Function
(SD, REG)
.. : ClrStat : ..
!j(CLR)b(Stat)
This command clears all statistical sample data currently in memory.
A Independent Memory Commands
M+, M–
Syntax
Operation
Function
(COMP, CMPLX, BASE)
.. : {expression} M+ : .. / .. : {expression} M– : ..
l/!l(M–)
M+ adds the value of the expression to independent memory, while M–
subtracts it.
A Rounding (Rnd) Command
Rnd(
Syntax
Operation
Function
(COMP, CMPLX, SD, REG)
.. : {expression} : Rnd(Ans : ..
!a(Rnd)
This command rounds a calculation result in accordance with the number of
digits specified by the display format.
A Number Base Commands
Dec, Hex, Bin, Oct
Syntax
Operation
Function
(BASE)
.. : Dec : .. / .. : Hex : .. / .. : Bin : .. / .. : Oct : ..
x(DEC)/M(HEX)/l(BIN)/I(OCT)
These commands specify the number base for base-n calculations.
E-51
A Statistical Data Input Command
DT
Syntax
(SD, REG)
.. : {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
Important!
To input a semicolon (;) in the above syntax, press !,(;). To input a comma (,), press
,.
Operation
Function
l(Inputs DT.)
Use this command to input one set of sample data. The DT command
functions the same way as the l key (DT key) in the SD Mode and REG
Mode.
A 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 (!w(Re⇔Im)) while a complex number calculation result is
displayed
• Reset (!j(CLR)d(All)w)
• Setup information clear (!j(CLR)c(Setup) w)
E-52
Appendix
k 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
1
Parenthetical Functions
Pol(, Rec(, ∫(, d/dx(, sin(, cos(, tan(, sin–1(, cos–1(,
tan–1(, sinh(, cosh(, tanh(, sinh–1(, cosh–1(,
tanh–1(, log(, ln(, e^(, 10^(, '(, 3'(, arg(, Abs(,
Conjg(, Not(, Neg(, Rnd(
2
Functions Preceded by Values
x2, x3, x–1, x!, ° ´ ˝, °, r, g
Power, Power Root
Percent
^(, x'(
%
3
Fractions
a b/c
4
Prefix Symbols
(–) (minus sign)
d, h, b, o (number base symbol)
5
Statistical Estimated Value
Calculations
m, n, m1, m2
6
Omitted Multiplication Sign
Multiplication sign can be omitted immediately
before π, e, variables (2π, 5A, πA, 2i, etc.),
parenthetical functions (2'(3), Asin(30), etc.)
and prefix symbols (except for the minus sign).
7
Permutation, Combination
nPr, nCr
Complex Number Symbol
∠
8
Multiplication, Division
×, ÷
9
Addition, Subtraction
+, −
10
Relational Operators
=, ≠, >, <, >, <
11
Logical Product
and
12
Logical Sum, Exclusive Logical
Sum, Exclusive Negative
Logical Sum
or, xor, xnor
Note
• If a calculation contains a negative value, you may need to enclose the negative value in
2
parentheses. If you want to square the value –2, for example, you need to input: (–2) . This is
2
because x is a function preceded by a value (Priority 2, above), whose priority is greater than
the negative sign, which is a prefix symbol (Priority 4).
-cxw
2
–2 = –4
(-c)xw
E-53
2
(–2) = 4
• As shown in the examples below, multiplication where the sign is omitted is given higher priority
than signed multiplication and division.
1
= 0.159154943
2π
1
1÷2×π=
π = 1.570796327
2
1 ÷ 2π =
k 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.
Calculation Range
±1×10–99 to ±9.999999999×1099 or 0
Internal Calculation
15 digits
Precision
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.
A Function Calculation Input Ranges and Precision
Functions
sinx
cosx
tanx
sin–1x
cos–1x
tan–1x
sinhx
coshx
Input Range
DEG
0 < | x | < 9×109
RAD
0 < | x | < 157079632.7
GRA
0 < | x | < 1×1010
DEG
Same as sinx, except when | x | = (2n–1)×90.
RAD
Same as sinx, except when | x | = (2n–1)×π/2.
GRA
Same as sinx, except when | x | = (2n–1)×100.
0<|x|<1
0 < | x | < 9.999999999×1099
0 < | x | < 230.2585092
sinh–1x
0 < | x | < 4.999999999×1099
cosh–1x
1 < x < 4.999999999×1099
tanhx
0 < | x | < 9.999999999×1099
tanh–1x
0 < | x | < 9.999999999×10–1
logx/lnx
0 < x < 9.999999999×1099
10x
–9.999999999×1099 < x < 99.99999999
ex
–9.999999999×1099 < x < 230.2585092
E-54
Functions
Input Range
'
x
0 < x < 1×10100
x2
1/x
3
'
x
x!
| x | < 1×10
50
100
| x | < 1×10
;xG0
100
| x | < 1×10
0 < x < 69 (x is an integer)
nPr
0 < n < 1×1010, 0 < r < n (n, r are integers)
1 < {n!/(n–r)!} < 1×10100
nCr
0 < n < 1×1010, 0 < r < n (n, r are integers)
1 < n!/r! < 1×10100 or 1 < n!/(n–r)! < 1×10100
Pol(x, y)
Rec(r, θ )
°’ ”
| x |, | y | < 9.999999999×1099
x2+y2 < 9.999999999×1099
0 < r < 9.999999999×1099
θ : Same as sinx
| a |, b, c < 1×10100
0 < b, c
| x | < 1×10100
Decimal ↔ Sexagesimal Conversions
0°0´0˝ < | x | < 9999999°59´59˝
^(xy)
x'
y
x > 0: –1×10100 < ylog x < 100
x = 0: y > 0 m
x < 0: y = n, 2n+1 (m, n are integers)
However: –1×10100 < ylog | x | < 100
y > 0: x G 0, –1×10100 < 1/x logy < 100
y = 0: x > 0
2n+1
y < 0: x = 2n+1, m (m G 0; m, n are integers)
However: –1×10100 < 1/xlog | y | < 100
a b/c
Total of integer, numerator, and denominator must be 10 digits or less (including
separtor symbols).
• ^(xy), x'
y, 3', x!, nPr, nCr type functions require consecutive internal calculation, which can
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.
k 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.
E-55
Mat h ERROR
Sample Error Message
A 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 d or e 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 10.
• Pressing A 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.
A 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
• 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).
Action
• 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 54.
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.
Syntax ERROR
Cause
The calculation has a format problem.
Action
Check the syntax and make the required corrections.
Argument ERROR
Cause
The calculation has a problem with how an argument being used.
Action
Check how arguments are being used and make the required corrections.
E-56
Time Out Error
Cause
The current differential or integration calculation ends without the ending
condition being fulfilled.
Action
Differential or integration calculation: Try increasing the tol value. Note that
this also decreases solution precision.
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 29.
Go ERROR
Cause
A program (that you created in the PRGM Mode) has a “Goto n” command
without a corresponding “Lbl n” label.
Action
Either add a “Lbl n” for the “Goto n” command, or delete the applicable “Goto
n” command.
k 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.
1 Check the calculation expression to make sure it does not include 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 restore normal operation, press the p key. The calculator will perform
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.
4 If step 3 does not restore normal operation, initialize all modes and settings by pressing
!j(CLR)c(Setup)w.
Power Requirements
A Replacing the Battery
Dim figures on the display of the calculator indicate that battery power is low. Continued
use of the calculator when the battery is low can result in improper operation. Replace the
battery as soon as possible when display figures become dim. Even if the calculator is
operating normally, replace the battery at least once every three years.
Important!
Removing the battery will cause all of the calculator’s memory contents to be deleted.
E-57
1. Press 1A(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.
Screw
2. Remove the cover as shown in the illustration and replace the
battery, taking care that its plus (+) and minus (–) ends are facing
correctly.
3. Replace the cover.
4. Initialize the calculator: O19(CLR)3(All)w(Yes)
• Do not skip the above step!
A 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 p key to turn the calculator back on.
Specifications
Power Requirements:
Solar Cell: Built into front of calculator (fixed)
Button Battery: LR44 (GPA76) × 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: 11.1 (H) × 80 (W) × 162 (D) mm
3
1
3
/8" (H) × 3 /8" (W) × 6 /8" (D)
Approximate Weight: 95 g (3.4 oz) including the battery
Bundled Accessories: Hard Case
E-58
Manufacturer:
CASIO COMPUTER CO., LTD.
6-2, Hon-machi 1-chome
Shibuya-ku, Tokyo 151-8543, Japan
Responsible within the European Union:
CASIO EUROPE GmbH
Casio-Platz 1
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
SA1303-A
Printed in China
© 2013 CASIO COMPUTER CO., LTD.
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