Casio fx 3650P User Manual

fx-3650P  
fx-3950P  
User's Guide  
Guía del usuario  
E S  
ENGLISH  
E-1  
Safety Precautions  
Be sure to read the following safety precautions before using this calculator.  
Keep this manual handy for later reference.  
Caution  
This symbol is used to indicate information that can result in personal  
injury or material damage if ignored.  
Batteries  
• After removing the battery from the calculator, put it in a safe place  
where it will not get into the hands of small children and accidentally  
swallowed.  
• Keep batteries out of the reach of small children. If accidentally  
swallowed, consult with a physician immediately.  
• Never charge batteries, try to take batteries apart, or allow batteries to  
become shorted. Never expose batteries to direct heat or dispose of  
them by incineration.  
• Misuse of batteries can cause them to leak and damage nearby items,  
and can create the risk of fire and personal injury.  
• Always make sure that the battery’s positive k and negative l ends  
are facing correctly when you load it into the calculator.  
• Remove the battery if you do not plan to use the calculator for a long  
time (fx-3950P).  
• Use only the type of battery specified for this calculator in this manual.  
Disposing of the Calculator  
• Never dispose of the calculator by burning it. Doing so can cause  
certain components to suddenly burst, creating the risk of fire and  
personal injury.  
• 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.  
E-2  
• 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 these materials. Moreover,  
CASIO Computer Co., Ltd. shall not be liable for any claim of any kind  
whatsoever against the use of these materials by any other party.  
Handling Precautions  
• Be sure to press the 5 key before using the calculator for the first  
time.  
• Even if the calculator is operating normally, replace the battery at  
least once every three years.  
A dead battery can leak, causing damage to and malfunction of the  
calculator. Never leave a dead battery in the calculator.  
• The battery that comes with this unit discharges slightly during  
shipment and storage. Because of this, it may require replacement  
sooner than the normal expected battery life.  
• Low battery power can cause memory contents to become corrupted  
or lost completely. Always keep written records of all important data.  
• Avoid use and storage in areas subjected to temperature extremes.  
Very low temperatures can cause slow display response, total failure of  
the display, and shortening of battery life. Also avoid leaving the calculator  
in direct sunlight, near a window, near a heater or anywhere else it might  
be exposed to very high temperatures. Heat can cause discoloration or  
deformation of the calculator’s case, and damage to internal circuitry.  
• Avoid use and storage in areas subjected to large amounts of  
humidity and dust.  
Take care never to leave the calculator where it might be splashed by  
water or exposed to large amounts of humidity or dust. Such conditions  
can damage internal circuitry.  
• Never drop the calculator or otherwise subject it to strong impact.  
E-3  
• Never twist or bend the calculator.  
Avoid carrying the calculator in the pocket of your trousers or other tight-  
fitting clothing where it might be subjected to twisting or bending.  
• Never try to take the calculator apart.  
• Never press the keys of the calculator with a ballpoint pen or other  
pointed object.  
• Use a soft, dry cloth to clean the exterior of the calculator.  
If the calculator becomes very dirty, wipe it off with a cloth moistened in a  
weak solution of water and a mild neutral household detergent. Wring out  
all excess moisture before wiping the calculator. Never use thinner,  
benzene or other volatile agents to clean the calculator. Doing so can  
remove printed markings and can damage the case.  
E-4  
Contents  
Safety Precautions ....................................................... 2  
Handling Precautions .................................................. 3  
Before getting started... ............................................... 7  
k Key Markings ....................................................................................... 7  
k Modes .................................................................................................. 8  
k Input Capacity ...................................................................................... 9  
k Making Corrections During Input ......................................................... 9  
k Replay Function ................................................................................... 9  
k Error Locator ...................................................................................... 10  
k Exponential Display Formats ............................................................. 10  
k Initializing the Calculator (Reset Operation) ...................................... 11  
Basic Calculations ..................................................... 11  
k Arithmetic Calculations ...................................................................... 11  
k Fraction Operations ........................................................................... 12  
k Percentage Calculations .................................................................... 13  
k Degrees, Minutes, Seconds Calculations .......................................... 14  
k FIX, SCI, RND ................................................................................... 14  
Memory Calculations ................................................. 15  
k Answer Memory ................................................................................. 16  
k Consecutive Calculations .................................................................. 16  
k Independent Memory ......................................................................... 16  
k Variables ............................................................................................ 17  
Complex Number Calculations ................................. 17  
k Absolute Value and Argument Calculation ......................................... 18  
k Rectangular Form Polar Form Display .......................................... 18  
k Conjugate of a Complex Number ...................................................... 19  
Base-n Calculations ................................................... 19  
Scientific Function Calculations............................... 21  
k Trigonometric/Inverse Trigonometric Functions ................................. 21  
k Hyperbolic/Inverse Hyperbolic Functions .......................................... 22  
k Common and Natural Logarithms/Antilogarithms .............................. 22  
E-5  
k Square Roots, Cube Roots, Roots, Squares, Cubes, Reciprocals,  
Factorials, Random Numbers, π, and Permutation/Combination ....... 23  
k Angle Unit Conversion ....................................................................... 24  
k Coordinate Conversion (Pol (x, y), Rec (r, θ )) .................................. 24  
k Engineering Notation Calculations ..................................................... 25  
Statistical Calculations .............................................. 25  
Standard Deviation ................................................................................ 25  
Regression Calculations ........................................................................ 28  
Differential Calculations ............................................ 34  
Integration Calculations ............................................ 34  
Programming a Calculation ...................................... 35  
Storing a Program .................................................................................. 36  
k Editing a Program .............................................................................. 38  
Executing a Program ............................................................................. 38  
Deleting a Program ................................................................................ 40  
Useful Program Commands................................................................... 40  
k Program Command Menus ................................................................ 40  
k Unconditional Jump ........................................................................... 41  
k Conditional Jump Using a Relational Operator .................................. 42  
k Other Program Statements ................................................................ 42  
Statistical Data Memory and Program Memory....... 44  
k Statistical Data ................................................................................... 44  
k Programs ........................................................................................... 45  
Technical Information ................................................ 46  
k When you have a problem...... ........................................................... 46  
k Error Messages ................................................................................. 46  
k Order of Operations ........................................................................... 47  
k Stacks ................................................................................................ 49  
k Input Ranges ..................................................................................... 50  
Power Supply.............................................................. 52  
Specifications ............................................................. 54  
Practical Examples .................................................. A-1  
k Program Library ............................................................................... A-1  
E-6  
Before getting started...  
kKey Markings  
Many of the calculator’s keys are used to perform more than one function.  
The functions marked on the keyboard are color coded to help you find the  
one you need quickly and easily.  
M–  
M
A
DT CL  
Function  
M+  
Color  
Key Operation  
1
2
|
M–  
Orange  
Red  
A |  
Press A and then the key to perform  
the marked function.  
3
M
p |  
Press p and then the key to perform  
the marked function.  
4
5
DT  
CL  
Blue  
In the SD and REG Modes:  
|
Orange  
In the SD and REG Modes:  
A |  
Press A and then the key to perform  
the marked function.  
In blue  
brackets  
6
7
Orange  
In the CMPLX Mode:  
A D  
Press A and then the key to perform  
the marked function.  
In purple  
brackets  
A
Red  
p D  
Press p and then the key to  
specify variable A.  
In green  
brackets  
D
In the BASE Mode, press the key  
without pressing p.  
E-7  
kModes  
Before starting a calculation, you must first enter the correct mode as  
indicated in the table below.  
To perform this type of  
operation:  
Perform this  
key operation:  
To enter  
this mode:  
Basic arithmetic calculations  
Complex number calculations  
Standard deviation  
F 1  
COMP  
CMPLX  
SD  
F 2  
F F 1  
F F 2  
F F 3  
F F F 1  
F F F 2  
F F F 3  
Regression calculations  
Base-n calculations  
Program editing  
REG  
BASE  
PRGM  
RUN  
Program execution  
Program deletion  
PCL  
• Pressing the  
key more than three times displays additional setup  
F
screens. Setup screens are described where they are actually used to  
change the calculator setup.  
• In this manual, the name of the mode you need to enter in order to  
perform the calculations being described is indicated in the main title of  
each section.  
Example:  
CMPLX  
Complex Number Calculations  
Note!  
To return the calculation mode and setup to the initial defaults shown  
below, press A B 2(Mode) <.  
Calculation Mode:  
Angle Unit:  
COMP  
Deg  
Exponential Display Format:  
Norm 1  
Complex Number Display Format: a+bi  
Fraction Display Format:  
ab/c  
• Mode indicators appear in the upper part of the display, except for the  
BASE indicators, which appear in the exponent part of the display.  
E-8  
You cannot make changes to the angle unit or other display format (Disp)  
settings while the calculator is in the BASE Mode.  
• The COMP, CMPLX, SD, and REG modes can be used in combination  
with the angle unit settings.  
• Be sure to check the current calculation mode (SD, REG, COMP, CMPLX)  
and angle unit setting (Deg, Rad, Gra) before beginning a calculation.  
kInput Capacity  
• The memory area used for calculation input can hold 79 “steps.” One step  
is taken up each time you press a number key or arithmetic operator key  
( +, ,, -, \ ). A A or p key operation does not take up a step, so  
inputting A D, for example, takes up only one step.  
You can input up to 79 steps for a single calculation. Whenever you input  
the 73rd step of any calculation, the cursor changes from “_” to “k” to let  
you know memory is running low. If you need to input more than 79 steps,  
you should divide your calculation into two or more parts.  
• Pressing the g key recalls the last result obtained, which you can use in  
a subsequent calculation. See “Answer Memory” for more information  
about using the g key.  
kMaking Corrections During Input  
• Use e and r to move the cursor to the location you want.  
• Press [ to delete the number or function at the current cursor position.  
• Press A K to change to an insert cursor t. Inputting something while  
the insert cursor is on the display inserts the input at the insert cursor  
position.  
• Pressing A K, or < returns to the normal cursor from the insert cursor.  
kReplay Function  
• Every time you perform a calculation, the replay function stores the  
calculation formula and its result in replay memory. Pressing the [ key  
displays the formula and result of the calculation you last performed.  
Pressing [ again back steps sequentially (new-to-old) through past  
calculations.  
E-9  
• Pressing the e or r key while a replay memory calculation is on the  
display changes to the editing screen.  
• Pressing the e or r key immediately after you finish a calculation  
displays the editing screen for that calculation.  
• Pressing t does not clear replay memory, so you can recall the last  
calculation even after you press t.  
• Replay memory capacity is 128 bytes for storage of both expressions and  
results.  
• Replay memory is cleared by any of the following actions.  
When you press the 5 key  
When you initialize modes and settings by pressing A B 2 (or 3) <  
When you change from one calculation mode to another  
When you turn off the calculator.  
kError Locator  
• Pressing r or e after an error occurs displays the calculation with the  
cursor positioned at the location where the error occurred.  
kExponential Display Formats  
This calculator can display up to 10 digits. Larger values are automatically  
displayed using exponential notation. In the case of decimal values, you can  
select between two formats that determine at what point exponential  
notation is used.  
To change the exponential display format, press the F key a number of  
times until you reach the exponential display format setup screen shown  
below.  
F i x Sc i  
N
3
or  
m
1
2
• Press 3. On the format selection screen that appears, press 1 to select  
Norm 1 or 2 for Norm 2.  
E-10  
u Norm 1  
With Norm 1, exponential notation is automatically used for integer values  
with more than 10 digits and decimal values with more than two decimal  
places.  
u Norm 2  
With Norm 2, exponential notation is automatically used for integer values  
with more than 10 digits and decimal values with more than nine decimal  
places.  
• All of the examples in this manual show calculation results using the Norm  
1 format.  
kInitializing the Calculator (Reset Operation)  
• Performing the key operation below initializes the calculation mode and  
setup, and clears replay memory, variables, and all programs.  
A B 3(All) <  
COMP  
Basic Calculations  
kArithmetic Calculations  
Use the F key to enter the COMP Mode when you want to perform  
basic calculations.  
COMP............................................................................................ F 1  
Example 1: 3҂(5҂10–9) ҃ 1.5҂10–8  
3 - 5 e D 9 <  
Example 2: 5҂(9ѿ7) ҃ 80  
5 - R 9 + 7 T <  
You can skip all T operations before <.  
E-11  
kFraction Operations  
u Fraction Calculations  
• Values are displayed in decimal format automatically whenever the total  
number of digits of a fractional value (integer + numerator + denominator  
+ separator marks) exceeds 10.  
13  
15  
2
3
1
5
Example 1:  
ѿ
҃
2 C 3 + 1 C 5 <  
13 15.00  
1
4
2
3
11  
12  
Example 2: 3  
ѿ 1  
҃ 4  
3 C 1 C 4 +  
1 C 2 C 3 <  
4 11 12.00  
2 C 4 <  
2
4
1
2
Example 3:  
҃
1
2
Example 4:  
ѿ1.6 ҃ 2.1  
1 C 2 + 1.6 <  
• Results of calculations that mix fraction and decimal values are always  
decimal.  
u Decimal Fraction Conversion  
• Use the operation shown below to convert calculation results between  
decimal values and fraction values.  
• Note that conversion can take as long as two seconds to perform.  
3
4
Example 1: 2.75 ҃ 2  
(Decimal Fraction)  
2.75 <  
C
2.75  
2 3 4.00  
11 4.00  
11  
4
҃
A B  
1
2
Example 2:  
0.5 (Fraction Decimal)  
1 2.00  
0.500  
1 C 2 <  
C
1 2.00  
C
E-12  
u Mixed Fraction Improper Fraction Conversion  
2
3
5
3
Example: 1  
1 C 2 C 3 <  
A B  
1
1
2 3.00  
5 3.00  
2 3.00  
A B  
You can use the display setup (Disp) screen to specify the display format  
when a fraction calculation result is greater than one.  
To change the fraction display format, press the q key a number of times  
until you reach the setup screen shown below.  
Disp  
1
• Display the selection screen.  
1 (or 1 r in the CMPLX Mode)  
• Press the number key (1 or 2) that corresponds to the setting you want  
to use.  
1(ab/c): Mixed fraction  
2(d/c): Improper fraction  
• An error occurs if you try to input a mixed fraction while the d/c display  
format is selected.  
kPercentage Calculations  
Example 1: To calculate 12% of 1500 (180)  
Example 2: To calculate what percentage of 880 is 660 (75%)  
660 \ 880 A v  
1500 - 12 A v  
Example 3: To add 15% onto 2500 (2875)  
2500 - 15 A v +  
Example 4: To discount 3500 by 25% (2625)  
3500 - 25 A v ,  
Example 5: To discount the sum of 168, 98, and 734 by 20%  
(800)  
168 + 98 + 734 < g A j 1  
p 1 - 20 A v ,  
*
E-13  
* As shown here, if you want to use the current Answer Memory value in a  
mark up or discount calculation, you need to assign the Answer Memory  
value into a variable and then use the variable in the mark up/  
discount calculation. This is because the calculation performed when v is  
pressed stores a result to Answer Memory before the , key is pressed.  
Example 6: If 300 grams are added to a test sample originally weighing  
500 grams, what is the percentage increase in weight?  
(160%)  
300 + 500 A v  
Example 7: What is the percentage change when a value is increased  
from 40 to 46? How about to 48? (15%, 20%)  
46 , 40 A v  
e e e e e e 8 <  
kDegrees, Minutes, Seconds Calculations  
You can perform sexagesimal calculations using degrees (hours), minutes,  
and seconds, and convert between sexagesimal and decimal values.  
Example 1: To convert the decimal value 2.258 to a sexagesimal value  
and then back to a decimal value  
2.258  
2°15°28.8  
2.258  
2.258 <  
A O  
I
Example 2: To perform the following calculation: 12°34’56” ѿ 65°43’21”  
12 I 34 I 56 I  
78°18°17  
+ 65 I 43 I 21 I <  
kFIX, SCI, RND  
To change the settings for the number of decimal places, the number of  
significant digits, or the exponential display format, press the F key a  
number of times until you reach the setup screen shown below.  
F i x Sc i  
N
3
or  
m
1
2
E-14  
• Press the number key (1, 2, or 3) that corresponds to the setup item  
you want to change.  
1(Fix): Number of decimal places  
2(Sci): Number of significant digits  
3 (Norm): Exponential display format  
400.00  
Example 1: 200 7 14 ҃  
200 \ 7 - 14 <  
.....  
3
FIX  
(Fix)  
(Specifies three decimal places.)  
F
1
400.00000  
28.57100  
(Internal calculation continues using 12 digits.)  
200 \ 7 <  
400.00000  
- 14 <  
The following performs the same calculation using the specified number of  
decimal places.  
28.57100  
28.57100  
200 \ 7 <  
A Q  
(Internal rounding)  
399.99400  
- 14 <  
.....  
• Press F  
3(Norm) 1 to clear the Fix specification.  
Example 2: 1 3, displaying result with two significant digits (Sci 2)  
SCI  
.....  
(Sci)  
2
01  
×10  
F
2 1 \ 3 <  
3.3  
.....  
• Press F  
3(Norm) 1 to clear the Sci specification.  
COMP  
Memory Calculations  
Use the F key to enter the COMP Mode when you want to perform a  
calculation using memory.  
COMP............................................................................................ F 1  
E-15  
kAnswer Memory  
• Whenever you press < after inputting values or an expression, the  
calculated result automatically updates Answer Memory contents by  
storing the result.  
• In addition to <, Answer Memory contents are also updated with result  
whenever you press A v, |, A {, or A j followed by a letter (A  
through D, or M, X, or Y).  
You can recall Answer Memory contents by pressing g.  
• Answer Memory can store up to 12 digits for the mantissa and two digits  
for the exponent.  
• Answer Memory contents are not updated if the operation performed by  
any of the above key operations results in an error.  
kConsecutive Calculations  
You can use the calculation result that is currently on the display (and also  
stored in Answer Memory) as the first value of your next calculation. Note  
that pressing an operator key while a result is displayed causes the  
displayed value to change to Ans, indicating it is the value that is currently  
stored in Answer Memory.  
• The result of a calculation can also be used with a subsequent Type A  
function (x2, x3, x–1, x!, DRG'), +, –, ^(xy), x , , , nPr and nCr.  
kIndependent Memory  
• Values can be input directly into memory, added to memory, or subtracted  
from memory. Independent memory is convenient for calculating  
cumulative totals.  
• Independent memory uses the same memory area as variable M.  
To clear independent memory (M), input 0 A j 3.  
Example:  
23 ѿ 9 ҃ 32  
53 Ҁ 6 ҃ 47  
23 + 9 A j 3  
53 , 6 |  
Ҁ) 45 2 ҃ 90  
(Total) –11  
45 - 2 A {  
0 3  
E-16  
kVariables  
• There are seven variables (A through D, M, X and Y), which can be used  
to store data, constants, results, and other values.  
• Use the following operation to delete data assigned to a particular  
variable: 0 A j 1. This operation deletes the data assigned to  
variable A.  
• Perform the following key operation when you want to clear the values  
assigned to all of the variables.  
A B 1(Mcl) <  
Example: 193.2 23 ҃ 8.4  
193.2 A j 1 \ 23 <  
193.2 28 ҃ 6.9  
p 1 \ 28 <  
CMPLX  
Complex Number Calculations  
Use the F key to enter the CMPLX Mode when you want to perform  
calculations that include complex numbers.  
CMPLX .......................................................................................... F 2  
• The current angle unit setting (Deg, Rad, Gra) affects CMPLX Mode  
calculations.  
• Note that you can use variables A, B, C, and M only in the CMPLX Mode.  
You cannot use variables D, X, and Y.  
• The indicator “RI” in the upper right corner of a calculation result display  
indicates a complex number result. Press A r to toggle the display  
between the real part and imaginary part of the result.  
You can use the replay function in the CMPLX Mode. Since complex  
numbers are stored in replay memory in the CMPLX Mode, however, more  
memory than normal is used up.  
Example: (2ѿ3i)ѿ(4ѿ5i)҃ 6ѿ8i  
(Real part 6)  
2 + 3 i + 4 + 5 i <  
(Imaginary part 8i)  
A r  
E-17  
kAbsolute Value and Argument Calculation  
Supposing the imaginary number expressed by the rectangular form  
z = a + bi is represented as a point in the Gaussian plane, you can  
determine the absolute value (r) and argument () of the complex  
number. The polar form is rЄ.  
Example 1: To determine the absolute value (r) and argument () of  
3 + 4i (Angle unit: Deg)  
(r = 5, = 53.13010235°)  
Imaginary axis  
Real axis  
(r ҃ 5)  
A A R 3 + 4 i T <  
(҃ 53.13010235°)  
A a R 3 + 4 i T <  
• The complex number can also be input using the polar form rЄ.  
Example 2: 2 Є 45 ҃ 1 ѿ i  
(Angle unit: Deg)  
L 2 A Q 45 <  
A r  
kRectangular Form Polar Form Display  
You can use the operation described below to convert a rectangular form  
complex number to its polar form, and a polar form complex number to its  
rectangular form. Press A r to toggle the display between the absolute  
value (r) and argument ().  
Example: 1 ѿ i 1.414213562 Є 45  
(Angle unit: Deg)  
1 + i A Y < A r  
L 2 A Q 45 A Z < A r  
E-18  
You select rectangular form (a+bi) or polar form (rЄ) for display of  
complex number calculation results.  
.....  
F
1(Disp)  
1(a+bi):Rectangular form  
2(rЄ): Polar form (indicated by “rЄ” on the display)  
kConjugate of a Complex Number  
For any complex number z where z = a+bi, its conjugate (z) is z = abi.  
Example: To determine the conjugate of the complex number 1.23 + 2.34i  
(Result: 1.23 – 2.34i)  
A S R 1 l 23 + 2 l 34 i T <  
A r  
BASE  
Base-n Calculations  
Use the F key to enter the BASE Mode when you want to perform  
calculations using Base-n values.  
BASE ....................................................................................... F F 3  
• In addition to decimal values, calculations can be performed using binary,  
octal and hexadecimal values.  
You can specify the default number system to be applied to all input and  
displayed values, and the number system for individual values as you  
input them.  
You cannot use scientific functions in binary, octal, decimal, and  
hexadecimal calculations. You cannot input values that include decimal  
part and an exponent.  
• If you input a value that includes a decimal part, the unit automatically  
cuts off the decimal part.  
• Negative binary, octal, and hexadecimal values are produced by taking the  
two’s complement.  
You can use the following logical operators between values in Base-n  
calculations: and (logical product), or (logical sum), xor (exclusive or), xnor  
(exclusive nor), Not (bitwise complement), and Neg (negation).  
E-19  
• The following are the allowable ranges for each of the available number  
systems.  
Binary  
1000000000 Ϲ x Ϲ 1111111111  
0 Ϲ x Ϲ 0111111111  
Octal  
4000000000 Ϲ x Ϲ 7777777777  
0 Ϲ x Ϲ 3777777777  
Decimal  
–2147483648 Ϲ x Ϲ 2147483647  
Hexadecimal  
80000000 Ϲ x Ϲ  
FFFFFFFF  
0 Ϲ x Ϲ  
7FFFFFFF  
Example 1: To perform the following calculation and produce a binary  
result:  
101112 ѿ 110102 ҃1100012  
b
b
0.  
Binary mode:  
t b  
110001.  
10111 + 11010 <  
Example 2: To convert the value 2210 to its binary, octal, and hexadecimal  
equivalents.  
(101102 , 268 , 1616  
)
b
0.  
10110.  
26.  
Binary mode:  
t b  
b
o
l l l 1(d) 22 <  
Octal mode:  
o
h
H
16.  
Hexadecimal mode:  
Example 3: To convert the value 51310 to its binary equivalent.  
b
b
0.  
Binary mode:  
t b  
Ma t h ERROR  
l l l 1(d) 513 <  
You may not be able to convert a value from a number system whose  
calculation range is greater than the calculation range of the resulting  
number system.  
• The message “Math ERROR” indicates that the result has too many digits  
(overflow).  
E-20  
Example 4: To perform the following calculation and produce an octal  
result:  
76548 ÷ 1210 ҃ 5168  
o
o
0.  
Octal mode:  
t o  
l l l 4 (o) 7654 \  
l l l 1 (d) 12 <  
516.  
Example 5: To perform the following calculation and produce a  
hexadecimal and a decimal result:  
12016 or 11012 ҃ 12d16 ҃ 30110  
H
0.  
Hexadecimal mode:  
t h  
120 l 2(or)  
H
d
( )  
b
12d.  
301.  
l l l 3 1101 <  
Decimal mode:  
K
COMP  
Scientific Function Calculations  
Use the F key to enter the COMP Mode when you want to perform  
basic arithmetic calculations.  
COMP............................................................................................ F 1  
• Certain types of calculations may take a long time to complete.  
• Wait for the result to appear on the display before starting the next  
calculation.  
π = 3.14159265359  
kTrigonometric/Inverse Trigonometric Functions  
To change the default angle unit (degrees, radians, grads), press the F  
key a number of times until you reach the angle unit setup screen shown  
below.  
Deg Rad  
G
3
r a  
1
2
E-21  
• Press the number key (1, 2, or 3) that corresponds to the angle unit  
you want to use.  
π
(90° =  
radians = 100 grads)  
2
.....  
(
Example 1: sin 63°52o41ꢀ ꢁ 0.897859012  
q
1 Deg)  
S 63 I 52 I 41 I <  
π
.....  
(
Example 2: cos  
(
rad)0.5  
q
2 Rad)  
3
W R A x \ 3 T <  
2
π
Example 3: cosҀ1  
0.25 π (rad)  
(
(rad))  
q ..... 2 (Rad)  
2
4
A V R L 2 \ 2 T < g \ A x <  
Example 4: tanҀ1 0.741 36.53844577 °  
q
1 Deg)  
.....  
(
A g 0.741 <  
kHyperbolic/Inverse Hyperbolic Functions  
Example 1: sinh 3.6 18.28545536  
M S 3.6 <  
Example 2: sinhҀ1 30 4.094622224  
M A j 30 <  
kCommon and Natural Logarithms/Antilogarithms  
Example 1: log 1.23 0.089905111  
R 1.23 <  
Example 2: In 90 (= loge 90) = 4.49980967  
T 90 <  
ln e 1  
T p P <  
Example 3: e10 22026.46579  
Example 4: 101.5 31.6227766  
Example 5: (–2)4 16  
A U 10 <  
A Q 1.5 <  
R D 2 T W 4 <  
• Negative values included in a calculation must be enclosed in parentheses.  
For details, see “Order of Operations” on page 47 for more information.  
E-22  
kSquare Roots, Cube Roots, Roots, Squares,  
Cubes, Reciprocals, Factorials, Random Numbers,  
π, and Permutation/Combination  
Example 1: 2 ѿ 3 ҂ 5 5.287196909  
L 2 + L 3 - L 5 <  
3
Example 2: 5 ѿ 3 ȕ27 –1.290024053 A D 5 + A D D 27 <  
1
7
Example 3: 123 ( = 123(7)) 1.988647795  
7 A H 123 <  
123 + 30 K <  
12 N <  
Example 4: 123 ѿ 302 1023  
Example 5: 123 1728  
1
Example 6:  
12  
<
3
4
a , a T a  
R
1
3
1
4
ȕ
Example 7: 8! 40320  
8 A f <  
Example 8: To generate a random number between 0.000 and 0.999  
0.66400  
A M <  
(The above value is a sample only. Results differ each time.)  
Example 9: 3π 9.424777961  
3 A x <  
Example 10: To determine how many different 4-digit values can be  
produced using the numbers 1 through 7  
• Numbers cannot be duplicated within the same 4-digit value (1234 is  
allowed, but 1123 is not).  
(840)  
7 A m 4 <  
Example 11: To determine how many different 4-member groups can be  
organized in a group of 10 individuals (210)  
10 A n 4 <  
E-23  
kAngle Unit Conversion  
• Press A v to display the following menu.  
D
R
G
1 2 3  
• Pressing 1, 2, or 3 converts the displayed value to the corresponding  
angle unit.  
Example: To convert 4.25 radians to degrees  
.....  
q
1(Deg)  
( )  
r
4.25  
4.25 A v 2 R <  
243.5070629  
kCoordinate Conversion (Pol (x, y), Rec (r, θ ))  
u Rectangular Coordinates  
u Polar Coordinates  
• Calculation results are automatically assigned to variables X and Y.  
Example 1: To convert polar coordinates (r 2, 60°) to rectangular  
coordinates (x, y) (Angle unit: Deg)  
x 1  
A F 2 P 60 T <  
y 1.732050808  
0 y  
• Press 0 x to display the value of x, or 0 y to display the value of y.  
E-24  
Example 2: To convert rectangular coordinates (1, 3) to polar  
coordinates (r,) (Angle unit: Rad)  
r 2  
A f 1 P L 3 T <  
0 y  
θ 1.047197551  
• Press 0 x to display the value of r, or 0 y to display the value of .  
kEngineering Notation Calculations  
Example 1: To convert 56,088 meters to kilometers  
56.088 ҂103  
56088 < J  
(km)  
Example 2: To convert 0.08125 grams to milligrams  
81.25 ҂10–3  
0.08125 < J  
(mg)  
SD  
REG  
SD  
Statistical Calculations  
Standard Deviation  
Use the F key to enter the SD Mode when you want to perform  
statistical calculations using standard deviation.  
SD ........................................................................................... F F 1  
• Always start data input with A B 1(Scl) < to clear statistical memory.  
• Input data using the key sequence shown below.  
<x-data> S  
• Input data is used to calculate values for n, Σx, Σx2, o, σn and σn-1, which  
you can recall using the key operations noted nearby.  
To recall this type of value: Perform this key operation:  
Σx2  
Σx  
n
o
σn  
σn–1  
A U 1  
A U 2  
A U 3  
A X 1  
A X 2  
A X 3  
E-25  
Example: To calculate σnҀ1, σn, o, n, Σx, and Σx2 for the following data :  
55, 54, 51, 55, 53, 53, 54, 52  
In the SD Mode:  
A B 1(Scl) < (Stat clear)  
SD  
n=  
55 S  
1.  
Each time you press S to register your input,  
the number of data input up to that point is  
indicated on the display (n value).  
54 S 51 S 55 S  
53 S S 54 S 52 S  
Sample Standard Deviation (σnҀ1) = 1.407885953  
Population Standard Deviation (σn) = 1.316956719  
Arithmetic Mean (o) = 53.375  
A X 3 <  
A X 2 <  
A X 1 <  
A U 3 <  
A U 2 <  
A U 1 <  
Number of Data (n) = 8  
Sum of Values (Σx) = 427  
2
Sum of Squares of Values (Σx ) = 22805  
• After inputting data, you can perform the key operations that calculate  
statistical results (standard deviation, mean, etc.) in any order. You do not  
need to follow the order shown above.  
Data Input Precautions  
To input the same data twice: <x-data> S S  
To input multiple entries of the same data by specifying the “frequency”:  
<x-data> A G <frequency> S  
Example: To input the data 110 ten times  
110 A G 10 S  
• While inputting data or after inputting data is complete, you can use the  
[ and ] keys to scroll through data you have input. If you input multiple  
entries of the same data using A G to specify the data frequency  
(number of data items) as described above, scrolling through data shows  
both the data item and a separate screen for the data frequency (Freq).  
You can then edit the displayed data, if you want. Input the new value and  
then press the < key to replace the old value with the new one. This also  
means that if you want to perform some other operation (calculation, recall  
of statistical calculation results, etc.), you should always press the t key  
first to exit data display.  
• Pressing the S key instead of < after changing a value on the display  
registers the value you input as a new data item, and leaves the old value  
as it is.  
E-26  
You can delete a data value displayed using [ and ] by pressing A  
U. Deleting a data value causes all values following it to be shifted up.  
• Data values you register are normally stored in calculator memory. The  
message “Data Full” appears and you will not be able to input any more  
data if there is no memory left for data storage. If this happens, press the  
< key to display the screen shown below.  
Ed i t  
1
O
FF ESC  
2
Press 2 to exit data input without registering the value you just input.  
Press 1 if you want to register the value you just input, without saving it  
in memory. If you do this, however, you will not be able to display or edit  
any of the data you have input.  
• For information about the number of data items that can be stored in  
memory, see “Statistical Data Memory and Program Memory” on page 44.  
To delete data you have just input, press A U.  
• After inputting statistical data in the SD Mode or REG Mode, you will be  
unable to display or edit individual data items any longer after perform  
either the following operations.  
Changing to another mode  
Changing the regression type (Lin, Log, Exp, Pwr, Inv, Quad)  
u Arithmetic Mean  
u Standard Deviation  
All the data of a finite  
population is used to  
calculate the standard  
deviation for the population.  
Sample data for a  
population is used to  
estimate the standard  
deviation for the population.  
E-27  
REG  
Regression Calculations  
Use the F key to enter the REG Mode when you want to perform  
statistical calculations using regression.  
REG..........................................................................................F F 2  
• Entering the REG Mode displays screens like the ones shown below.  
r
L i n Log  
E
3
xp  
P r Inv  
Q
3
uad  
1
2
1w  
2
e
• Press the number key (1, 2, or 3) that corresponds to the type of  
regression you want to use.  
1 (Lin):  
Linear regression  
2 (Log): Logarithmic regression  
3 (Exp): Exponential regression  
r 1 (Pwr): Power regression  
r 2 (Inv):  
Inverse regression  
r 3 (Quad): Quadratic regression  
• Always start data input with A B 1(Scl) < to clear statistical memory.  
• Input data using the key sequence shown below.  
<x-data> P <y-data> S  
• The values produced by a regression calculation depend on the values  
input, and results can be recalled using the key operations shown in the  
table below.  
To recall this type of value: Perform this key operation:  
Σx2  
Σx  
n
A U 1  
A U 2  
A U 3  
Σy2  
Σy  
Σxy  
o
A U r 1  
A U r 2  
A U r 3  
A X 1  
xσn  
xσn-1  
p
A X 2  
A X 3  
A X r 1  
E-28  
To recall this type of value: Perform this key operation:  
yσn  
A X r 2  
yσn-1  
A X r 3  
Regression coefficient A  
Regression coefficient B  
A X r r 1  
A X r r 2  
Regression calculation other than quadratic regression  
Correlation coefficient r  
A X r r 3  
m
n
A X r r r 1  
A X r r r 2  
• The following table shows the key operations you should use to recall  
results in the case of quadratic regression.  
To recall this type of value: Perform this key operation:  
Σx3  
A U r r 1  
A U r r 2  
A U r r 3  
A X r r 3  
A X r r r 1  
A X r r r 2  
A X r r r 3  
Σx2y  
Σx4  
Regression coefficient C  
m
m
n
1
2
• The values in the above tables can be used inside of expressions the  
same way you use variables.  
u Linear Regression  
• The regression formula for linear regression is: y = A + Bx.  
Example: Atmospheric Pressure vs. Temperature  
Perform linear regression to determine the  
regression formula terms and correlation  
coefficient for the data nearby. Next, use  
the regression formula to estimate  
atmospheric pressure at 18°C and  
temperature at 1000 hPa. Finally, calculate  
the coefficient of determination (r2) and  
Atmospheric  
Pressure  
Temperature  
10°C  
15°C  
20°C  
25°C  
30°C  
1003 hPa  
1005 hPa  
1010 hPa  
1011 hPa  
1014 hPa  
sample covariance  
.
E-29  
In the REG Mode:  
(Lin)  
1
REG  
n=  
A B 1(Scl) <(Stat clear)  
10 P1003 S  
1.  
Each time you press S to register your input,  
the number of data input up to that point is  
indicated on the display (n value).  
15 P 1005 S  
20 P1010 S 25 P 1011 S  
30 P 1014 S  
Regression Coefficient A = 997.4  
A X r r 1 <  
A X r r 2 <  
Regression Coefficient B = 0.56  
Correlation Coefficient r = 0.982607368  
Atmospheric Pressure at 18°C = 1007.48  
Temperature at 1000 hPa = 4.642857143  
Coefficient of Determination = 0.965517241  
Sample Covariance = 35  
A X r r 3 <  
18 A X r r r 2 <  
1000 A X r r r 1 <  
A X r r 3 K <  
E A U r 3 ,  
A U 3 - A X 1 -  
A X r 1 F \  
E A U 3 , 1 F <  
u Logarithmic, Exponential, Power, and Inverse Regression  
• Use the same key operations as linear regression to recall results for  
these types of regression.  
• The following shows the regression formulas for each type of regression.  
Logarithmic Regression  
Exponential Regression  
Power Regression  
y A ѿ BؒIn x  
y A ؒe x (In y In A + Bx)  
B
·
y A ؒxB (In y In A + BIn x)  
y A ѿ Bؒ1/x  
Inverse Regression  
E-30  
u Quadratic Regression  
• The regression formula for quadratic regression is: y = A + Bx + Cx2.  
Example:  
Perform quadratic regression to determine the regression  
xi  
29  
50  
74  
103  
118  
yi  
1.6  
23.5  
38.0  
46.4  
48.0  
formula terms for the data nearby. Next, use the  
regression formula to estimate the values for n  
(estimated value of y) for xi = 16 and m (estimated value  
of x) for yi = 20.  
In the REG Mode:  
(Quad)  
r 3  
A B 1(Scl) < (Stat clear)  
29 P 1.6 S 50 P 23.5 S  
74 P 38.0 S 103 P 46.4 S  
118 P 48.0 S  
Regression Coefficient A = –35.59856934  
Regression Coefficient B = 1.495939413  
Regression Coefficient C = 6.71629667 × 10 –3  
n when xi is 16 = –13.38291067  
A X r r 1 <  
A X r r 2 <  
A X r r 3 <  
16 A X r r r 3 <  
20 A X r r r 1 <  
20 A X r r r 2 <  
m1 when yi is 20 = 47.14556728  
m2 when yi is 20 = 175.5872105  
• After inputting data, you can perform the key operations that calcutate  
statistical results (regression coefficients, n, m1, etc.) in any order. You do  
not need to follow the order shown above.  
Data Input Precautions  
<x-data>  
<y-data>  
S S  
To input the same data twice:  
To input multiple entries of the same data by specifying the “frequency”:  
<x-data> <y-data> <frequency>  
P
P
A G  
S
Example: To input the data X = 20, Y = 30 five times  
20 P 30 A G 5 S  
• Precautions when editing data input for standard deviation also apply for  
regression calculations.  
E-31  
1 Linear Regression y = A + Bx  
u Regression coefficient A  
u Regression coefficient B  
.
.
.
Σy B Σx  
n Σxy Σx Σy  
A =  
B =  
2
2
.
n
(
)
n Σx Σx  
u Correlation coefficient  
r
.
.
n Σxy Σx Σy  
r
=
2
2
2
2
.
.
(
)
(
)
{n Σx Σx }{n Σy Σy  
}
.
2 Logarithmic Regression y = A + B ln x  
u Regression coefficient A  
u Regression coefficient B  
.
.
.
Σy B Σln  
x
(
)y  
x
)
n Σ ln  
Σlnx Σy  
(
B =  
A =  
2
2
.
n
(
)
x
n Σ lnx Σln  
u Correlation coefficient  
r
.
.
(
)y  
x
n Σ ln  
)
Σlnx Σy  
r
=
2
2
2
2
.
.
(
(
)
x
(
)
{n Σ lnx Σln  
}{n Σy Σy  
}
3 Exponential Regression y = A e x (ln y = ln A + Bx)  
B
·
.
u Regression coefficient A  
u Regression coefficient B  
.
Σlny B Σx  
A = exp  
.
.
y
n Σxln Σx Σln  
y
B =  
(
)
2
2
.
n
(
)
n Σx Σx  
u Correlation coefficient  
r
.
.
y
n Σxln Σx Σln  
y
r
=
2
2
2
)
2
.
.
(
)
(
(
)
{n Σx Σx }{n Σ lny Σln  
y
}
B
.
4 Power Regression y = A x (ln y = ln A + Bln x)  
u Regression coefficient A  
u Regression coefficient B  
.
.
.
y
)
n Σln  
x
(
ln Σlnx Σln  
y
Σlny B Σln  
x
A = exp  
B =  
(
)
2
2
.
n
(
)
x
n Σ lnx Σln  
u Correlation coefficient  
r
.
.
y
2
n Σln  
x
ln Σlnx Σln  
y
r
=
2
)
2
)
2
)
y
.
.
(
(
)
(
(
{n Σ lnx Σln  
x
}{n Σ lny Σln  
}
E-32  
5 Inverse Regression y = A + Bؒ1/x  
u Regression coefficient A  
u Regression coefficient B  
–1  
.
Σy  
B Σx  
Sxy  
Sxx  
A =  
B =  
n
u Correlation coefficient  
r
Sxy  
r
=
.
Sxx Syy  
2
(
Σx–1  
n
)
(Σy)2  
Sxx  
Sxy  
=
=
Σ
Σ
(
(
x
–1)2 –  
Syy –  
Σy2  
=
,
n
–1  
.
Σx Σy  
x–1  
)
y
n
6 Quadratic Regression y = A + Bx + Cx2  
u Regression coefficient A  
2
Σy  
Σx  
Σx  
A =  
B  
C  
(
)
(
)
n
n
n
u Regression coefficient B  
2
B = (Sxy Sx2x2 Sx y Sxx2) ÷ {Sxx Sx2x2 – (Sxx2)2}  
.
.
.
u Regression coefficient C  
2
.
.
S
C
= Sx y  
S
xx Sxy  
xx2  
(Σx)2  
(Σx Σy)  
.
n
Sxx  
=
Σx2  
Σx3  
Σx2y  
,
Sxy  
=
Σxy  
n
2
2
(Σx Σx  
)
(
Σx2  
)
.
n
Sxx2  
Sx2y  
=
=
,
Sx2x2  
=
Σx4  
n
2
.
(Σx Σy)  
n
E-33  
COMP  
Differential Calculations  
The procedure described below obtains the derivative of a function.  
Use the F key to enter the COMP Mode when you want to perform a  
calculation involving differentials.  
COMP............................................................................................. F 1  
• Three inputs are required for the differential expression: the function of  
variable x, the point (a) at which the differential coefficient is calculated,  
and the change in x (x).  
A J expression P a P x T  
Example: To determine the derivative at point x = 2 for the function  
y = 3x2– 5x + 2, when the increase or decrease in x is x = 2 × 10-4  
(Result: 7 )  
A J 3 p x K , 5 p x + 2 P 2 P 2 e D 4 T <  
You can omit input of x, if you want. The calculator automatically  
substitutes an appropriate value for x if you do not input one.  
• Discontinuous points and extreme changes in the value of x can cause  
inaccurate results and errors.  
COMP  
Integration Calculations  
The procedure described below obtains the definite integral of a function.  
Use the F key to enter the COMP Mode when you want to perform  
integration calculations.  
COMP............................................................................................ F 1  
• The following four inputs are required for integration calculations:  
a function with the variable x; a and b, which define the integration range  
of the definite integral; and n, which is the number of partitions (equivalent  
to N = 2n) for integration using Simpson’s rule.  
d expression P a P b P n F  
Example: 15 (2x2 + 3x + 8) dx = 150.6666667 (Number of partitions n = 6)  
d 2 p x K + 3 p x + 8 P 1 P 5 P 6 T <  
E-34  
Note!  
You can specify an integer in the range of 1 to 9 as the number of  
partitions, or you can skip input of the number of partitions entirely, if you  
want.  
• Internal integration calculations may take considerable time to complete.  
• Display contents are cleared while an integration calculation is being  
performed internally.  
• The conditions described below can cause reduced calculation precision  
or slower calculation speed.  
Condition  
Countermeasure  
Minute shifts in the integration  
interval, which causes large  
change in the integration value  
Divide the integration interval,  
dividing sections that fluctuate  
widely into smaller intervals.  
Periodic functions, or positive and Separate positive and negative  
negative integration values  
depending on the interval  
parts, and add each together.  
PRGM  
RUN  
PCL  
Programming a Calculation  
• This section describes how to store a calculation program for instant recall  
whenever you need it.  
• The program storage area has about 360 bytes, which can be divided  
among up to four different programs named P1, P2, P3, and P4.  
To perform program calculation operations, press F F F, which  
displays the screen shown below. Next, press the number key that  
corresponds to the mode you want to select.  
P
PCL  
1RGM R2UN 3  
1 (PRGM) ....Edit Prog Mode for inputting and editing programs.  
2 (RUN) .......Mode for running programs.  
3 (PCL) ....... Clear Prog Mode for deleting programs.  
E-35  
PRGM  
Storing a Program  
Use the following procedure to specify the Edit Prog Mode and store a  
program in memory.  
Edit Prog............................................................................. F F F 1  
• Example: To create a program that uses Heron’s formula to calculate the  
area of a triangle based on the lengths of its three sides  
Formula: S = s (s – A)(s – B)(s – C)  
Note that: s = (A + B + C)  
.
/2  
1. Enter the Edit Prog Mode, which displays the screen shown below.  
If there is already a  
program in memory, its  
number appears on the  
display.  
PRGM  
g
PEd1i t23P4r o308  
Remaining capacity (bytes)  
2. Select the program number (P1 to P4) to which you want to assign the  
program.  
Ex.: 2 (Program P2)  
PRGM  
000  
Number of bytes used by program P2.  
3. Input the program.  
Program  
?A: ?B: ?C: (A + B + C) ÷ 2D^D × (D – A) × (D – B) × (D – C):  
Ans  
To input a colon (:), press <.  
To input “A”, press A j q.  
You can also input a variable name using the p key. To input “X” for  
example, press p x.  
E-36  
To input a question mark (?), right arrow (), colon (:), or output  
command (^), press A ?, and then use number keys 1 through  
4 to select the mark or command you want. See “Useful Program  
Commands” on page 40 for more information.  
4. Press t F F F 2 to exit program input.  
u Program Storage Notes  
• Use the syntax below to prompt for input of a value by the person running  
the program, which will be assigned to the variable whose name is  
indicated by the program.  
?<variable name>  
You can normally specify the variable names A, B, C, D, X, Y, and M  
(independent memory). In the CMPLX Mode, however, you can use only  
A, B, C, or M, because the other variables are used to store mode data.  
• Use a colon (:) to link statements into multi-statements. A “statement” can  
be a calculation expression or function (such as Fix 3 or Deg). Note that  
you do not need to include a colon (:) at the end of the program.  
• If you want execution of a program to pause at any point part way  
through, insert an output command (^) at the end of a statement instead  
of a colon (:). Note that you do not need to include an output command  
(^) at the end of the program.  
You can also specify a mode when inputting a program. The mode you  
specify is stored along with the program. You can specify different modes  
for programs P1, P2, P3, and P4. While the Edit Prog screen in step 1  
under “Storing a Program” (page 36) is on the display, use the F key to  
specify the mode you want. The following are the modes that you can  
specify for a program: COMP, CMPLX, SD*, REG*, BASE.  
* Data input for statistical calculations is always retained in memory, even  
after calculation is complete. Statistical data remaining in memory can  
cause calculation errors when you run a program that includes statistical  
calculations. Because of this, you should press A B 1(Scl) <  
before executing such a program, or you should include the Scl  
command at the beginning of the program to make sure that statistical  
data memory is cleared.  
• During program input, the cursor normally appears as a flashing underline  
mark (_). When there are eight bytes or less of memory remaining,  
however, the cursor changes to a flashing black box (k). If the remainder  
of the program you are inputting is larger than remaining memory  
E-37  
capacity, you will need to free up more memory capacity by deleting  
programs or statistical data you no longer need.  
• See page 44 for information about how bytes are counted and how  
memory is shared by statistical data.  
kEditing a Program  
• While a program’s contents are on the display in the Edit Prog Mode, you  
can use e and r to move the cursor to the location you want to edit.  
• Press [ to delete the function at the current cursor location.  
• Use the insert cursor (page 9) when you want to insert a new statement  
into a program.  
RUN  
Executing a Program  
The procedure in this section shows how to execute a program in the  
COMP Mode.  
Perform the following key operation to enter the COMP Mode.  
COMP.............................................................................................F 1  
• Example: To create a program that uses Heron’s formula to calculate the  
area of a triangle whose three sides measure A = 30, B = 40, C = 50  
1. Execute the program.  
(In the COMP Mode) > 2  
Specify the number of the program you want to execute.  
2. Input the values required for the calculation.  
A?  
B?  
C?  
30 <  
40 <  
50 <  
(Assigns the result of  
D = (A + B + C) ÷ 2 to  
variable D.)  
(A+B+C)Ö2 D  
60.  
Disp  
E-38  
3. Press < to resume program execution.  
The program number disappears after  
program execution is complete.  
Ans  
600.  
(Area)  
u Program Execution Notes  
• Pressing < after program execution finishes causes the same program  
to be executed again.  
You can also run a program from the Run Prog screen by using number  
keys 1 through 4 to specify a program number (P1 through P4). You  
can display the Run Prog screen by pressing t < from the Edit Prog  
screen after step 3 of the procedure under “Storing a Program” on page  
36.  
You can use the following keys on the currently displayed value while  
program execution is paused by the output command (^).  
J, I, C, r, F*  
* Note that you can use the F key to select the settings shown below  
only. Program execution is automatically cancelled if you try to select any  
other mode or setting.  
Deg, Rad, Gra, Fix, Sci, Norm, Dec, Hex, Bin, Oct  
To cancel further program execution, press t.  
u Errors During Program Execution  
• If an error message appears on the display during program execution,  
press the e or r key to automatically enter the Edit Prog Mode. The  
location of the error with the cursor located there will appear on the  
display at this time. Determine the cause of the error and edit the program  
as required.  
• Pressing the t key while an error message is on the display clears the  
message and terminates program execution.  
E-39  
PCL  
Deleting a Program  
Use the following procedure to specify the Clear Prog Mode and delete a  
program from memory.  
Clear Prog .......................................................................... F F F 3  
You can also enter the Clear Prog Mode by pressing [ while the Edit  
Prog screen is on the display.  
You can select programs individually by specifying a program number from  
P1 through P4.  
1. Enter the Clear Prog Mode, which displays the screen shown below.  
PRGM  
g
C
l ea r Pr o  
P–1234 247  
2. Select the program number (P1 to P4) of the program you want to delete.  
• Example: 1 (Program P1)  
• The number of the program you selected disappears from the upper part  
of the display, and remaining memory capacity increases by the size of the  
deleted program.  
• Note that the only way to delete all the programs in memory (P1 through  
P4) is to perform the reset operation (page 11).  
Useful Program Commands  
In addition to mathematical calculations, there are also a number of useful  
program commands you can use to perform loops and define conditions.  
kProgram Command Menus  
Press A ? to display a menu of available program commands.  
• The program command menu has three screens. Use the e and r keys  
to display the menu screen you want.  
To input one of the commands currently on the screen, press a number  
key from 1 through 5.  
E-40  
u Basic Commands  
?
1 2  
:
^
3 4  
1 (?) .......... Operator input command  
2 () ........ Assign to variable command  
3 (:) ........... Multi-statement separator code  
4 (^) ........ Output command  
u Conditional Jump Commands  
>
S
=
G
>
1 2 3 4 5  
1 (S) ........ Jump code (when condition is met)  
2 (=) .......... Relational operator  
3 (G) ......... Relational operator  
4 (>) .......... Relational operator  
5 (>) .......... Relational operator  
u Unconditional Jump Commands  
G
1o t o Lb l  
2
1 (Goto) .... Jump command  
2 (Lbl) ....... Label  
kUnconditional Jump  
• When the unconditional jump command (Goto n) is executed, processing  
jumps to the label (Lbl n) whose n value matches the n value of the  
unconditional jump command. You can specify an integer from 0 to 9 for n.  
You can also use the unconditional jump command and label to create an  
unconditional loop, which repeat a part of the program a specific number  
of times. To do this, put a label (such as Lbl 1, which is used in the  
example below) at the beginning of the part you want to repeat, and end  
the repeated part with an unconditional jump command (Goto 1, in the  
example).  
E-41  
• Example: Use Heron’s formula to perform a series of calculations to  
determine the area of triangles for which the length of side A is fixed, and  
the lengths of sides B and C are variable.  
Program  
?A: Lbl 1: ?B: ?C: (A + B + C) ÷ 2D^D × (D – A) × (D – B) ×  
(D – C):  
Ans^Goto 1  
kConditional Jump Using a Relational Operator  
You can use relational operators so program execution compares two  
values and then decides which processing should be performed based on  
the relationship between the two values.  
• Example: To create a program that calculates the total of a series of input  
values, with calculation being terminated whenever zero is input  
Program  
0B: Lbl 1: ?A: A = 0 S Goto 2: B + A B: Goto 1: Lbl 2: B  
1
2
Statement 1 Statement 2  
3
1 Assigns 0 to variable B.  
2 Assigns the input value to variable A.  
3 If A = 0 is true, Statement 1 (Goto 2) is executed. If false, execution  
advances to Statement 2 without executing Statement 1.  
u Relational Operator Notes  
• The relational operators you can use in a program are: =, G, >, >.  
• A relational operation that is true returns a value of 1, while a false  
relational operation returns a value of 0. For example, executing 3 = 3  
would return a result of 1, while 1 > 3 returns a result of 0.  
kOther Program Statements  
u F Key Settings  
The items shown below can be included as statements inside of a program.  
You can input one of these statements using the same procedure as you do  
for normal calculation. That is, press the F key to display a selection  
screen and then press the number key that corresponds to the setting you  
want.  
Deg, Rad, Gra, Fix, Sci, Norm, Dec, Hex, Bin, Oct  
• Example: Deg: Fix 3  
E-42  
u Inputting Statistical Data  
If you select the SD Mode or REG Mode before specifying a program  
number (P1 through P4), you can input statistical data as part of your  
program.  
• Input statistical data using the S key, just as you normally do (page 25).  
• In addition to values, you can also input calculation expressions as data.  
• Example 1: To determine o of the following data  
(o = 30.875)  
x
Frequency  
30  
27  
32  
2
1
5
(SD Mode) Scl: 30; 2 DT: 27 DT: 32; 5 DT: o  
*
* You do not need to specify the frequency when inputting a data item that  
has a single occurrence.  
• Example 2: To determine regression coefficients A, B, and C for the  
following data  
(A = 3, B = –2, C = 1)  
x
3
4
6
y
6
11  
27  
Frequency  
2
1
2
(REG (Quad) Mode) Scl: 3,6; 2 DT: 4,11 DT: 6,27; 2 DT: A^B^C  
*
**  
**A, B, and C are not variable names. They are regression coefficients.  
u Memory Calculations  
You can perform memory calculations in a program by inserting M+ and M–.  
• Example: ... : 2 × 3 M+ : ...  
u Percent Calculations  
You can perform percent calculations in a program by inserting %.  
• Example: ... : 250 + 280 % : ...  
Note that you cannot perform percent calculations like the following in a  
program: a × b%+, a × b%–.  
u Rnd  
You can round a value by using Rnd in a program.  
• Example: 1 ÷ 3 : Rnd: ...  
E-43  
Statistical Data Memory and  
Program Memory  
The following shows how the calculator uses memory for storage of  
statistical data and programs.  
(a) Statistical data only  
(256 bytes)  
Statistical  
(b) Shared between statistical data  
Data  
and programs (360 bytes)  
(c) Shared between program management  
and statistical data (24 bytes)  
Programs  
kStatistical Data  
• Each x-data or y-data (for regression calculations) item and each  
frequency value (other than 1) that you input uses up eight bytes of  
memory.  
Example: Inputting the following in the SD Mode uses 40 bytes of  
memory: 30 A G 2 S 27 A G 1 S 32 A G 5 S  
• The memory area indicated as (a) in the above illustration is exclusively  
for statistical data items. Since this area has 256 bytes, it can contain up  
to 32 individual (frequency = 1) x-data items (256 bytes Ö 8 bytes per  
data item = 32).  
• When memory area (a) becomes full, statistical data items are stored in  
the free space (space not being used for program storage) of memory  
area (b), if there is any. If there are no programs currently stored in  
memory, memory area (c) is also used to store statistical data items.  
Memory areas (a), (b), and (c) have a total capacity of 640 bytes, so there  
is enough total memory to store up to 80 individual (frequency = 1) x-data  
items (640 bytes Ö 8 bytes per data item = 80).  
E-44  
• Trying to input a data item that takes up more bytes than are currently  
available in memory area (b) causes the message “Data Full” to appear on  
the display. If this happens, you can press < 1 to select “EditOFF.”  
Though this will allow you to input more statistical data items (and free up  
memory area (b) for program storage), it also deletes the data items that  
are currently stored in memory areas (a) and (b). Also, the data items you  
input after pressing < 1 will not be saved. This means you will not be  
able to view or edit individual data items after you input them.  
To input new statistical data when editing is turned off (EditOFF), press  
A B 1(Scl) < to delete statistical data currently stored in memory  
and turn editing on (EditON). You will be able to input statistical data into  
the statistical data area (a) and the program memory area (b) that does  
not contain program data. You can also delete program data you no longer  
need to free up space for further statistical data input.  
kPrograms  
• Each function you input into program memory takes up either one byte or  
two bytes of memory, as shown below.  
• 1-byte Functions: sin, cos, log, (, ), :, ^, A, B, C, 1, 2, Fix 3 etc.  
• 2-byte Functions: Goto 1, Lbl 2 etc.  
• Pressing e or r while a program is on the display causes the cursor to  
jump one byte in the direction indicated by the arrow.  
• Inputting the first program while there are no other programs in memory  
causes 24 bytes of memory to be reserved automatically as a program  
management area (area (c) on page 44).  
• A newly input program is stored in free space (space not currently being  
used for program storage or statistical data storage) that is available in the  
program memory area (area (b) on page 44). All 360 bytes of the program  
memory area are available for program storage when there is no statistical  
data stored in the program memory area.  
E-45  
Technical Information  
kWhen you have a problem......  
If calculation results are not what you expect or if an error occurs, perform  
the following steps.  
1. Press A B 2(Mode) < to initialize all modes and settings.  
2. Check the formula you are working with to confirm it is correct.  
3. Enter the correct mode and try performing the calculation again.  
If the above steps do not correct the problem, press the 5 key. The  
calculator performs a self-check operation and deletes all data stored in  
memory if any abnormality is detected. Make sure you always keep written  
copies of all important data.  
kError Messages  
The calculator is locked up while an error message is on the display. Press  
t to clear the error, or press e or r to display the calculation and  
correct the problem. See “Error Locator” for details.  
Math ERROR  
• Causes  
• Calculation result is outside the allowable calculation range.  
• An attempt to perform a function calculation using a value that exceeds  
the allowable input range.  
• An attempt to perform an illogical operation (division by zero, etc.)  
• Action  
• Check your input values and make sure they are all within the allowable  
ranges. Pay special attention to values in any memory areas you are  
using.  
Stack ERROR  
• Cause  
• The capacity of the numeric stack or operator stack is exceeded.  
• Action  
• Simplify the calculation. The numeric stack has 10 levels and the  
operator stack has 24 levels.  
E-46  
• Divide your calculation into two or more separate parts.  
Syntax ERROR  
• Cause  
• A calculation formula or program formula contains an error.  
• There is a colon (:) or output command (^) at the end of the program.  
• Action  
• Press e or r to display the calculation with the cursor located at the  
location of the error and make required corrections.  
• Delete the colon (:) or output command (^) at the end of the program.  
Arg ERROR  
• Cause  
• Improper use of an argument  
• Action  
• Press e or r to display the location of the cause of the error and make  
required corrections.  
Go ERROR  
• Cause  
• A Goto n command does not have a corresponding Lbl n label.  
• Action  
• Correctly input an Lbl n label that corresponds to the existing Goto n  
command, or delete the Goto n command if it is not required.  
kOrder of Operations  
Calculations are performed in the following order of precedence.  
1Coordinate transformation: Pol (x, y), Rec (r, θ)  
Differentials: d/dx  
Integrations: dx  
2Type A functions:  
With these functions, the value is entered and then the function key is  
pressed.  
x3, x2, xҀ1, x!, ° ’ ”  
m m1 m2  
,
n
,
,
E-47  
Angle unit conversions (DRG')  
3Powers and roots: ^(xy), x  
4ab/c  
5Abbreviated multiplication format in front of π, e (natural logarithm base),  
memory name, or variable name: 2π, 3e, 5A, πA, etc.  
6Type B functions:  
With these functions, the function key is pressed and then the value is  
entered.  
3
,
, log, In, ex, 10x, sin, cos, tan, sinҀ1, cosҀ1, tanҀ1, sinh, cosh,  
tanh, sinhҀ1, coshҀ1, tanhҀ1, (Ҁ), d, h, b, o, Neg, Not, arg, Abs, Conjg  
7Abbreviated multiplication format in front of Type B functions: 2 3, Alog2,  
etc.  
8Permutation and combination: nPr, nCr  
9҂, Ö  
0ѿ, Ҁ  
!Ͼ, м  
@ϭ, G  
#and  
$xnor, xor, or  
• Operations of the same precedence are performed from right to left.  
exIn 120 ex{In( 120)}  
• Other operations are performed from left to right.  
• Operations enclosed in parentheses are performed first.  
• When a calculation contains an argument that is a negative number, the  
negative number must be enclosed within parentheses. The negative sign  
(–) is treated as a Type B function, so particular care is required when the  
calculation includes a high-priority Type A function, or power or root  
operations.  
Example: ( –2)4 = 16  
–24 = –16  
E-48  
kStacks  
This calculator uses memory areas, called “stacks,” to temporarily store  
values (numeric stack) and commands (command stack) according to their  
precedence during calculations. The numeric stack has 10 levels and the  
command stack has 24 levels. A stack error (Stack ERROR) occurs  
whenever you try to perform a calculation that is so complex that the  
capacity of a stack is exceeded.  
Example:  
1
2
3
4
5
1
2
3
4
5
6
7
Numeric Stack Command Stack  
1
2
3
4
5
4
1
2
3
4
5
6
7
҂
2
3
4
5
ѿ
҂
ѿ
• Calculations are performed in sequence according to “Order of  
Operations.” Commands and values are deleted from the stack as the  
calculation is performed.  
E-49  
k Input Ranges  
Internal digits: 12  
Accuracy*: As a rule, accuracy is ±1 at the 10th digit.  
Functions  
Input Range  
DEG  
RAD  
GRA  
DEG  
RAD  
GRA  
DEG  
RAD  
GRA  
0Ϲ xϹ4.499999999҂1010  
sinx  
0Ϲ xϹ785398163.3  
0Ϲ xϹ4.999999999҂1010  
0Ϲ xϹ4.500000008҂1010  
cosx  
0Ϲ xϹ785398164.9  
0Ϲ xϹ5.000000009҂1010  
Same as sinx, except when x= (2n-1) ҂ 90.  
Same as sinx, except when x= (2n-1) ҂ π/2.  
Same as sinx, except when x= (2n-1) ҂ 100.  
tanx  
sin–1x  
cos–1x  
tan–1x  
sinhx  
coshx  
sinh–1x  
cosh–1x  
tanhx  
tanh–1x  
logx/lnx  
10x  
0Ϲ xϹ1  
0Ϲ xϹ9.999999999҂1099  
0Ϲ xϹ230.2585092  
0Ϲ xϹ4.999999999҂1099  
1Ϲ x Ϲ4.999999999҂1099  
0Ϲ xϹ9.999999999҂1099  
0Ϲ xϹ9.999999999҂10–1  
0x Ϲ9.999999999҂1099  
–9.999999999҂1099Ϲ x Ϲ 99.99999999  
–9.999999999҂1099Ϲ x Ϲ 230.2585092  
0Ϲ x 1 ҂ 10100  
ex  
x
x2  
xꢀꢁ 1҂ 1050  
1/x  
xꢀꢁ 1҂ 10100 ; x G 0  
3
x
xꢀꢁ 1҂ 10100  
E-50  
Functions  
Input Range  
x!  
0Ϲ x Ϲ 69 (x is an integer)  
0Ϲ n 1҂1010, 0Ϲ r Ϲ n (n, r are integers)  
nPr  
1Ϲ {n!/(nr)!} 1҂10100  
0Ϲ n 1҂1010, 0Ϲ r Ϲ n (n, r are integers)  
1Ϲ [n!/{r!(nr)!}] 1҂10100  
nCr  
x, yϹ9.999999999҂1049  
(x2+y2) Ϲ9.999999999҂1099  
Pol (x, y)  
0Ϲ r Ϲ9.999999999҂1099  
θ: Same as sinx  
Rec(r, )  
a, b, c 1҂10100  
0 Ϲ b, c  
°’ ”  
xꢀꢁ1҂10100  
Decimal Sexagesimal Conversions  
0°0°0°Ϲ xϹ999999°59°  
xŒ0: –1҂10100ylogx100  
x҃0: yŒ0  
x0: y҃n,  
^(xy)  
m
2n+1  
(n, m are integers)  
However: –1҂10100 ylogxꢀꢁ100  
yŒ0: x G 0, –1҂101001/x logy100  
x
y
y҃0: xŒ0  
y0: x҃2nѿ1,  
1
n
(n G 0; n is an integer)  
However: –1҂10100 1/x logyꢀꢁ100  
Total of integer, numerator, and denominator must be 10  
digits or less (including division marks).  
b
a /c  
xꢀꢁ 1҂1050  
yꢀꢁ 1҂1050  
SD  
(REG)  
nꢀꢁ 1҂10100  
xn, yn, o, p : n G 0  
xn1, yn1, A, B, r : n G 0, 1  
E-51  
* For a single calculation, calculation error is ±1 at the 10th digit. (In the  
case of exponential display, calculation error is ±1 at the last significant  
digit.) Errors are cumulative in the case of consecutive calculations, which  
can also cause them to become large. (This is also true of internal  
consecutive calculations that are performed in the case of ^(xy), x y , x!,  
3
, nPr, nCr, etc.)  
In the vicinity of a function’s singular point and point of inflection, errors  
are cumulative and may become large.  
Power Supply  
The type of battery you should use depends on the model number of your  
calculator.  
fx-3650P  
The TWO WAY POWER system actually has two power supplies: a solar  
cell and a G13 Type (LR44) button battery. Normally, calculators equipped  
with a solar cell alone can operate only when relatively bright light is  
present. The TWO WAY POWER system, however, lets you continue to use  
the calculator as long as there is enough light to read the display.  
• Replacing the Battery  
Either of the following symptoms indicates battery power is low, and that  
the battery should be replaced.  
• Display figures are dim and difficult to read in areas where there is little  
light available.  
• Nothing appears on the display when you press the 5 key.  
E-52  
• To replace the battery  
1 Remove the six screws that hold the back  
cover in place and then remove the back  
cover.  
Screw  
Screw  
2 Remove the old battery.  
3 Wipe off the sides of new battery with a dry,  
soft cloth. Load it into the unit with the  
positive  
side facing up (so you can see it).  
k
4 Replace the back cover and secure it in place  
with the six screws.  
5 Press 5 to turn power on. Be sure not to  
skip this step.  
fx-3950P  
This calculator is powered by single G13 Type (LR44) button battery.  
• 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.  
• To replace the battery  
1 Press A i to turn off power.  
Screw  
2 Remove the screw that holds the battery  
cover in place and then remove the battery  
cover.  
3 Remove the old battery.  
4 Wipe off the sides of new battery with a dry,  
soft cloth. Load it into the unit with the positive  
side facing up (so you can see it).  
k
5 Replace the battery cover and secure it in  
place with the screw.  
6 Press 5 to turn power on.  
E-53  
Auto Power Off  
Calculator power automatically turns off if you do not perform any operation  
for about six minutes. When this happens, press 5 to turn power back on.  
Specifications  
Power Supply:  
fx-3950P: Single G13 Type button battery (LR44)  
fx-3650P: Solar cell and a single G13 Type button battery (LR44)  
Battery Life:  
fx-3950P: Approximately 9,000 hours continuous display of flashing  
cursor.  
Approximately 3 years when left with power turned off.  
fx-3650P: Approximately 3 years (1 hour use per day).  
Dimensions: 11.8 (H) ҂ 80 (W) ҂ 159 (D) mm  
7/16Љ (H) ҂ 31/8Љ (W) ҂ 61/4Љ (D)  
Weight:  
100 g (3.5 oz) including battery  
Power Consumption: 0.0002 W  
Operating Temperature: 0°C to 40°C (32°F to 104°F)  
E-54  
Practical Examples/Ejemplos prácticos  
kProgram Library  
kBiblioteca de programas  
Problem: Quadratic Equation  
Create a program that solves the quadratic equation ax2 + bx + c = 0 for x,  
when values are provided for a, b, and c.  
Problema: Ecuación cuadrática  
Crear un programa que resuelva la ecuación cuadrática ax2 + bx + c = 0  
para x, cuando se proporcionan valores para a, b y c.  
x = (–b ± b2 – 4ac)/2a (b2 – 4ac > 0)  
Program  
Press F F F 1 to display the Edit Prog screen. Input a value from 1 to  
4 to select a program number (P1 through P4), and then input the program  
below.  
Programa  
Presione F F F 1 para visualizar la pantalla Edit Prog. Ingrese un  
valor de 1 a 4 para seleccionar un número de programa (P1 a P4), y luego  
ingrese el programa siguiente.  
Lbl 0: ? A: ? B: ? C: Bx2 – 4AC D: D = 0 S Goto 1: D > 0 S  
Goto 2: Goto 0: Lbl 2: (– B – D) ÷ (2A) X: X ^Lbl 1: (– B + D) ÷ (2A)  
X: X  
A-1  
Program Execution / Ejecución de programa  
Display / Presentación Operation / Operación  
> 1 (Example: Program P1)  
(Ejemplo: Programa P1)  
A?  
B?  
C?  
2 <  
D 7 <  
6 <  
<
X = 1.5  
(Value appears in line 2 of display.)  
(El valor aparece en la línea 2 de la  
presentación.)  
X = 2  
(Value appears in line 2 of display.)  
(El valor aparece en la línea 2 de la  
presentación.)  
A-2  
Problem: Solution of a Triangle when Two Sides and Their Angle are  
Known  
Problema: Solución de un triángulo cuando se conocen dos lados y su  
ángulo.  
Create a program that calculates the remaining side and two angles of a  
triangle when the length of two sides (a, b) and the angle they form (γ ) are  
known.  
Crear un programa que calcule el lado restante y dos ángulos de un  
triángulo, cuando se conocen la longitud de los dos lados (a y b) y el  
ángulo que forman (γ ).  
1
S = bc sin  
α
γ
2
b2  
+
2
c2  
bc  
a2  
b
a
cos  
α
=
S
β
α
c
65°41' 23"  
41  
32  
S = 597.8321153  
40.30827888  
67°58' 1.54"  
46°20' 35.46"  
Program  
Press F F F 1 to display the Edit Prog screen. Input a value from 1 to  
4 to select a program number (P1 through P4), and then input the program  
below.  
Programa  
Presione F F F 1 para visualizar la pantalla Edit Prog. Ingrese un  
valor de 1 a 4 para seleccionar un número de programa (P1 a P4), y luego  
ingrese el programa siguiente.  
Deg: ? A: ? B: ? D: A × B × sin D ÷ 2^ Ans X:  
( A x2 + B x2 –  
cos D × 2 × A × B) C^ sin–1 (X × 2 ÷ B ÷ C) Y: Y > 90 S Bx2 + Cx2 >  
Ax2 S Y – 90 Y: 90 > Y S Ax2 > Bx2 + Cx2 S Y + 90 Y: Y^ 180 – Y –  
D
A-3  
Program Execution / Ejecución de programa  
Display / Presentación Operation / Operación  
> 2 (Example: Program P2)  
(Ejemplo: Programa P2)  
A?  
B?  
D?  
32 <  
41 <  
65 I 41 I 23 I <  
597.8321153 (Area)/(Area)  
<
<
40.30827888 (Length of side c)  
(Longitud de lado c)  
46.34318362 (Angle α)/(Angulo α) A O  
46°20°35.46  
<
67.96709416 (Angle β)/(Angulo β ) A O  
67°58°1.54  
Note  
• The conditional jump in the latter part of the program performs a process  
that determines whether angle α is an acute angle or an obtuse angle.  
First it checks whether the sum of the squares of side b and side c, which  
form angle α, is greater than or less than the square of side a. That way it  
can tell if angle α is an acute angle or an obtuse angle. Next, it uses the  
1
2
formula S = –– bc sin α to determine whether the result matches the  
value calculated for α. If it does not match, it changes the value of α to  
an acute angle if it is currently an obtuse angle, or to an obtuse angle if it  
is currently an acute angle.  
Nota  
• El salto condicional en la parte posterior del programa realiza un proceso  
que determina si un ángulo α es un ángulo agudo o un ángulo obtuso.  
Primero verifica si la suma de los cuadrados del lado b y lado c, que  
forman el ángulo α, es mayor o menor que el cuadrado del lado a. De  
esta manera puede indicar si un ángulo α es un ángulo agudo o un  
1
2
–– bc sen α  
ángulo obtuso. Luego, utiliza la fórmula S =  
para determinar  
si el resultado coincide con el valor calculado para α. Si no coincide,  
cambia el valor de α a un ángulo agudo si actualmente es un ángulo  
obtuso, o a un ángulo obtuso si actualmente es un ángulo agudo.  
A-4  
CASIO COMPUTER CO., LTD.  
6-2, Hon-machi 1-chome  
Shibuya-ku, Tokyo 151-8543, Japan  
SA0207-C Printed in China  
RCA 500003-001V01  

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