Casio fx-3600P User Manual

This is the English part of the original user manual of the Casio fx-3600P.
Scanned, transformed to ASCII via OCR and copied to HTML by F. Seebass, February 2008

#

# CASIO fx-3600P

## Scientific Calculator

## Operation Manual

Dear customer.
Thank you very much for purchasing our scientific calculator.
This high-performance, pocket-size calculator employs true algebraic logic (judging the precedence of operations) and allows the use of up to 18 nesting parentheses at six levels. Its major features are 61 functions, seven memory registers, regression analysis, integrals, and up to 38 programmable steps for repeated calculation.
This booklet will familiarize you with the many ways this highly capable unit can serve you.
* Special care should be taken not to damage the unit by bending or dropping. For example, do not carry it in your hip pocket.

# Index

- 0 Internal registers (user registers)
- 1 Nomenclature
  - (1) Power switch
  - (2) Display
    - Auto power-off
  - (3) Inverse key (symbolized by )
  - (4) Mode key (symbolized by )
  - (5) Numeral and decimal point keys
  - (6) Exponent/Pi entry key
  - (7) (R -> P) Addition/Rectangular -> polar key
  - (8) (P -> R) Subtraction/Polar -> rectangular key
  - (9) Multiplication/Power key
  - (10) Division/Root key
  - (11) Equal/Percent key
  - (12) Open parenthesis/Square root/Regression analysis data input key
  - (13) Close parenthesis/Factorial/Regression analysis estimator key
  - (14) (x <-> y) Constant memory entry/Register exchange key
  - (15) (x <-> K) Constant memory recall/Register exchange key
  - (16) (M in) Independent memory recall/Independent memory entry key
  - (17) (M-) Memory plus (minus) key
  - (18) Sign change/Square key
  - (19) Sexagesimal/Decimal conversion key
  - (20) Sine/Arc sine key
  - (21) Cosine/Arc cosine key
  - (22) Tangent/Arc tangent key
  - (23) Hyperbeltaste
  - (24) Common logarithm/Antilogarithm key
  - (25) Natural logarithm/Exponential key
  - (26) ( <- ) Engineering Key
  - (27) (1/x) Fraction entry/Reciprocal key
  - (28) (KAC, ON) All clear key
  - (29) Clear key
  - (30) (P1/P2) Program number key
  - (31) (ENT, HLT, DATA, DEL) RUN/ENT/HLT/Data entry/delete key
- 2 Battery Maintenance
- 3 Before Using the Calculator
  - 3.1 Precedence of operations and precedence levels
  - 3.2 Correction
  - 3.3 Calculation range and scientific notation
  - 3.4 Overflow or error check
- 4 Normal Calculations
  - 4.1 Four basic calculations
  - 4.2 Assignment for the number of fractional digits and the number of significant digits
  - 4.3 Constant calculations
  - 4.4 Memory calculations using the independent memory
  - 4.5 Memory calculations using 6 constant memories
  - 4.6 Fraction calculations
  - 4.7 Percentage calculations
- 5 Function Calculations
  - 5.1 Degree-Minute-Second <-> Decimal conversion
  - 5.2 Trigonometric/Inverse trigonometric functions
  - 5.3 Hyperbolic/Inverse hyperbolic functions
  - 5.4 Common & Natural logarithms/Exponentiations (Antilogarithms, Exponentials, Powers and Roots)
  - 5.5 Square roots, Squares, Reciprocals, Factorials & Random numbers
  - 5.6 Rectangular to polar co-ordinates conversion
  - 5.7 Polar to Rectangular co-ordinates conversion
  - 5.8 Applications
    - 5.8.1 Decibel (dB) conversion
    - 5.8.2 Parabolic movement
    - 5.8.3 Cycle of a conical pendulum
    - 5.8.4 Triangle
    - 5.8.5 Pro-rating
    - 5.8.6 Time calculations
- 6 Statistical Calculations
  - 6.1 Standard deviation
  - 6.2 Regression analysis
    - 6.2.1 Linear regression
    - 6.2.2 Logarithmic regression
    - 6.2.3 Exponential regression
    - 6.2.4 Power regression
- 7 Programmed Calculations
  - 7.1 How to store and execute programs
  - 7.2 Program step
  - 7.3 How to erase a program
  - 7.4 Jump instructions
  - 7.5 Applications
    - Permutation and combination:
    - Calculate the area of triangle when the lengths of the three sides are given:
    - Sort sales slips by item code and add up the total of each item (for five items):
    - Calculation for loan-repayment (Equally divided monthly repayment)
- 8 Integrals
  - 8.1 Defining function f (x)
  - 8.2 Execution of integral
  - 8.3 Example
  - 8.4 Remarks for execution of integrals
- 9 Specifications
  - Basic features
  - Programmable features:
  - Decimal point:
  - Read-out:
  - Power consumption:
  - Power source:
  - Ambient temperature range:
  - Dimensions:
  - Weight:

# 0 Internal registers (user registers)

X-register
Y (L1)-register

- Used in arithmetic and functional calculations.

L2-register
L3-register
L4-register
L5-register
L6-register

- Used in calculations with nesting parentheses and for judging the precedence of addition/subtraction and multiplication/division.

M-register

- Independent memory register (, , , ).

K1 (x2) register
K2 (x) register
K3 (n) register
K4 (y2) register
K5 (y) register
K6 (xy) register

- Constant memory registers (, , - ).
- For storing intermediate results (x2, x, n etc.) of statistical calculations.

# 1 Nomenclature

(click to enlarge)

## (1) Power switch

Move the switch to the right to activate the calculator and "ON" is displayed. Even when power is off, the contents is held in independent memory and constant memory registers, and the programs are not lost.

## (2) Display

The display shows input data, intermediate results and results of operation. The mantissa section displays up to 10 digits (9 for negative numbers). The exponent section displays up to ±99. The fraction and angle in the sexagesimal scale are displayed as follows:

456

12

23

is displayed

4561223.

12°34'56,77" is displayed

12°34°56.7

"E" (error check, see here) may be displayed in the position of the mantissa's least significant digit. "DEG", "RAD" or "GRA" (angular unit), "INV" (when the key has been pressed), "M" (when data is stored in independent memory), "K" (during calculation with constants), "SD" (during calculation of standard deviation), "LR" (during calculation of regression analysis), and/or "dx" (during execution of integral), as well as "LRN" and "ENT" will be displayed to indicate the operating mode.

### Auto power-off

If the calculator is left with the power switch at the "ON" position (except while programmed calculation), the auto power-off function automatically turns off the power in approximately 6 minutes, thereby saving battery life. Power is resumed either by pressing the key or by re-operating the ON-OFF switch.
(Even when power is off, the contents of memories and written programs as well as the angular unit and operating mode are not lost)

## (3) Inverse key (symbolized by )

Activates the functions printed in brown on the keyboard.
When the key is pressed, "INV" appears on the display and the subsequent pressing of makes "INV" disappear.

## (4) Mode key (symbolized by )

To put the calculator into the desired operating mode or select a specific angular unit, press first, then , , ... or .

- :

Manual and programmed calculations can be executed.

- :

"LRN" is displayed. Programs can be written.

- :

"dx" is displayed. Integral can be carried out.

- :

"LR" is displayed. Calculation of regression analysis can be executed.

- :

"SD" is displayed. Calculation of standard deviation can be executed.

*To carry out manual or programmed calculation, select the RUN mode (press ( and ).

- :

"DEG" is displayed, indicating that "degrees" is selected as the unit of angle.

- :

"RAD" is displayed, indicating that "radians" is selected as the unit of angle.

- :

"GRA" is displayed, indicating that "gradient" is selected as the unit of angle.

(Note: 90 degrees = /2 radians = 100 gradients)

- :

"Fix" assignment (assignment for the number of fractional digits). Specify the number of digits of the fractional part after pressing and .(Example: (three fractional digits are effective))

- :

"Scientific" assignment (assignment for the number of significant digits). Specify the number of significant digits after pressing and . (Example: )

- :

"Normal" assignment. Press in this sequence to release the "fix" or "scientific" assignment.

* To clear programs, press this key, following the key. ( denotes this "program clear" sequence.)
* Once power is off, the "fix" and "scientific" assignments will be released but the
operating mode ("LRN", "dx", "LR" or "SD") and the angular unit ("DEG",
"RAD" or "GRA") will be kept.

## (5) -, Numeral and decimal point keys

Enters numerals. For decimal places, use the key in its logical sequence.

* Varying functions will be designated when you press and a numeral key, as summarized below.

- (RND):

Cutting off internal data
The internal data (held in the Y-register) will be cut off so as to be equal to the displayed data.

- (RAN#):

Random number generation
A random number between 0.000 and 0.999 will be generated.

* Use following sequences in calculation of standard deviation and in regression analysis. For more details, refer to the chapter 6 "STATISTICAL CALCULATIONS".

- ():

Calculation of (average of x)

- (xn):

Calculation of xn (population standard deviation of x)

- (xn-1):

Calculation of xn-1 (sample standard deviation of x)

- ():

Calculation of (average of y)

- (yn):

Calculation of yn (population standard deviation of y)

- (yn-1):

Calculation of yn-1 (sample standard deviation of y)

- (A):

Calculation of A (constant terms in regression equations)

- (B):

Calculation of B (regression coefficients)

- (r):

Calculation of r (correlation coefficients)

* Different functions will be designated when you press , then a numeral key as summarized below.

- (x2):

Calculation of x2 (square sum of x)

- (x):

Calculation of x (total sum of x)

- ( n ):

Calculation of n (number of data)

- (y2):

Calculation of y2 (square sum of y)

- (y):

Calculation of y (total sum of y)

- (xy):

Calculation of xy (inner product)

* use (x>0), (x<=M) and (RTN) only for writing programs (in "LRN" mode).

- (x>0):

Conditional jump
"Return to the first step of the program when the contents of the X-register (display) is positive and otherwise go to the next step."

- (x<=M):

Conditional jump
"Return to the first step of the program when the contents of the X-register is equal to or smaller than those of the M-register (independent memory) and otherwise go to the next step."

- (RTN):

Unconditional jump ("Return")
Press these keys to return to the first step of the program unconditionally.

## (6) () Exponent/Pi entry key

- Enters the exponent of ten up to ±99. To enter 2.34 x 1056, for example, press in sequence (symbolized by ).
- Enters circular constant in 10 digits (3.141592654) when pressed after , , , or a function command key (symbolized by ).

## (7) (R -> P) Addition/Rectangular -> polar key

- Enters summands.
- Performs rectangular to polar co-ordinates conversion when pressed after the key.

## (8) (P -> R) Subtraction/Polar -> rectangular key

- Enters minuend.
- Performs polar to rectangular co-ordinates conversion when pressed after the key.

## (9) (xy) Multiplication/Power key

- Enters multiplicand.
- Raises the base x to the yth power when pressed after the key.

## (10) (x1/y) Division/Root key

- Enters dividend.
- Calculates the yth root of x when pressed after the key.

## (11) (%) Equal/Percent key

- Obtains answer.
- Perform regular percentages, add-ons, discounts, ratios and increase/decrease values when pressed after the key.

## (12) (, xD, yD) Open parenthesis/Square root/Regression analysis data input key

- Opens the parentheses. Nesting of up to 18 parentheses at six levels is allowed.
- Extracts the square root of the displayed number when pressed after the key. (In this manual this sequence is represented by . Other sequences described below are also represented in the same way.)
- Enters data (x) in regression analysis ("LR" mode).

## (13) (x!, , ) Close parenthesis/Factorial/Regression analysis estimator key

- Closes the parentheses.
- Obtains the factorial of the displayed number when pressed after the key.
- Obtains an estimator of regression in regression analysis ("LR" mode). will be obtained if you press it immediately after data entry and if you press it following after data entry.

## (14) (x <-> y) Constant memory entry/Register exchange key

- Enters numbers into each constant memory, through operation of ENTRY (to ).
Example:
To enter 12.3 into constant memory 3:
- Exchanges the displayed number (X-register) with the content of the working register (y-register) when pressed after the key.

## (15) (x <-> K) Constant memory recall/Register exchange key

- Recalls the contents in each constant memory without clearing, through operation of (to ).
Example:
To recall the contents of constant memory 5:
- Exchanges the displayed number (X-register) with the contents of a constant memory (K-register) when pressed after the key.
Example:
To exchange the contents of constant memory 2 with the displayed number:

## (16) (M in) Independent memory recall/Independent memory entry key

- Recalls the contents of the independent memoy (M-register) without clearing.
- Puts the displayed number in the independent memory when pressed after the key. Old data held in the memory will be automatically erased.

## (17) (M-) Memory plus (minus) key

- Adds the displayed number to the contents of the independent memory, and obtains answer in 4 basic calculations/xy/ x1/y and automatically adds it to the contents of the memory.
- Subtracts the displayed number from the contents of the independent memory, and obtains answer in 4 basic calculations/xy/ x1/y and automatically subtracts it from the contents of the memory when pressed after the key.

## (18) (x2) Sign change/Square key

- Changes the sign of the displayed number from plus to minus and vice versa.
- Obtains the square of the displayed number when pressed after the key.

## (19) ( <- ) Sexagesimal/Decimal conversion key

- Converts the sexagesimal figure to decimal notation.
- Converts the decimal notation to sexagesimal notation when pressed after the key.

## (20) (sin-1) Sine/Arc sine key

- Obtains the sine of the displayed angle.
- Obtains the angle when pressed after the key.

## (21) (cos-1) Cosine/Arc cosine key

- Obtains the cosine of the displayed angle.
- Obtains the angle when pressed after the key.

## (22) (tan-1) Tangent/Arc tangent key

- Obtains the tangent of the displayed angle.
- Obtains the angle when pressed after the key.

## (23) Hyperbolic key

- Obtains the hyperbolic functions in combination with the , or key.
- Obtains the inverse hyperbolic functions in combination with the , or key when pressed after the key.

## (24) (10x) Common logarithm/Antilogarithm key

- Obtains the common logarithm (base 10) of the displayed number.
- Calculates the xth power of 10 when pressed after the key.

## (25) (ex) Natural logarithm/Exponential key

- Obtains the natural logarithm (base e) of the displayed number.
- Calculates the xth power of e (2.718281828) when pressed after the key.

## (26) ( <- ) Engineering Key

- Allows the displayed number to be shown with exponents of ten that are multiples of three (e.g., 103, 10-6, 109).
Example:

12 3456

12.3456

12 3456

12.3456

12.3456 00

0.0123456 03

12345.6 -03

0.0000123456 06

12345600 -06

0.0000000123456 09

12345600 -06

0.0000000123456 09

0.0000123456 06

0.0123456 03

## (27) (1/x) Fraction entry/Reciprocal key

- Enters fractions for fraction calculations. To enter the fraction 1-2/3, for example, in sequence.
- Obtains the reciprocal of the displayed number when pressed after the key.

## (28) (KAC, ON) All clear key

- Clears the entire machine except the independent and constant memories, and also releases overflow or error check.
- Clears contents of all constant memories when pressed after the key.
- It also overrides the auto power-off function.

## (29) Clear key

Clears entry for correction.

## (30) (P2) Program number key

This calculator is capable of holding two programs of up to 38 steps in total. P1 will be designated if you press this key and P2 if you press it after the key.
A sequence must be designated for executing a programmed calculation.

## (31) (ENT, HLT, DATA, DEL) RUN/ENT/HLT/Data entry/delete key

> - When a program is being written, depression of this key writes a halt instruction.
> In the programmed operation mode, depression of this key restarts execution which has been temporarily suspended.

- :

When "LRN" is displayed (i.e. during program loading), depression of this key writes a halt instruction for data entry.

- :

When "LRN" is displayed, depression of this sequence writes a halt instruction for the display of a result.

- :

When execution is at a halt during programmed operation, depression of this key restarts execution.

> - When "LR" or "SD" is displayed, this key works as a data entry/deletion key.

- :

In the SD mode, operate in the sequence of a data and .
In the LR mode, operate in the sequence of x data , y data, and .

- :

To delete the data which has just been imput, press this sequence instead of in the above sequences.

# 2 Battery Maintenance

One lithium battery (Typ: CR2025) gives approximately 1300 hours continuous operation.
When battery power decreases, the whole display darkens. Battery should be then be renewed. Be sure to switch OFF the power before changing.

1) Side open the battery compartment lid on the back of the unit.
2) Remove dead battery and insert new battery with the plus terminal (flat side) on top.
3) Replace the battery compartment lid.
4) Press in sequence.

* Before inserting the new battery, be sure to thoroughly wipe it off with a dry cloth to maintain good contacts.
* Never leave dead battery in the battery compartment.
* Remove the battery when not using for an extended period.
* It is recommended that battery be replaced every 2 years to prevent the chance of malfunctions due to battery leakage.
* Keep the batteries away from children. If swollowed consult your doctor immediately.

# 3 Before Using the Calculator

Select the SD mode (press ) for standard diviation, the LR mode (press ) for regression analysis, the dx mode () for carrying out integral, and the RUN mode () for ordinary arithmetic and functional calculations.
Select the LRN mode () to write a program.
Whatever angular unit is displayed does not matter in calculation which does not use angular data.

## 3.1 Precedence of operations and precedence levels

- This calculator automatically evaluates precedence of operations and executes in the proper sequence thus determined. The precedence of operations is as follows.
(1) Functions
(2) xy, x1/y
(3) Multiplication and division
(4) Addition and subtraktion
Operations of the same precedence will be carried out in the order of input. An expression enclosed with a pair of parentheses will be given the highest precedence level.
- Internal registers L1 to L6 are used to retain intermediate results of operations, including expressions enclosed with parentheses, which have low precedence levels. Therefore, intermediate results of up to six levels may be retained.
- Up to three nested parentheses will be given the same precedence level. As a result, parentheses can be nested up to 18 pairs.

* How to evaluate precedence levels (an example of 4 levels and 5 pairs of nested parentheses)

Expression: 2 x [{(3+4x {(5+4)3}) 5} +9] =

Entry operation:

Contents of registers when entry has proceeded to A

x | 4
L1 | ( ( 5 +
L2 | 4 x
L3 | ( ( ( 3 +
L4 | 2 x
L5 |
L6 |

## 3.2 Correction

- If you are aware of data entry error before pressing a command key, press and re-input the correct data.
- In a series of calculations, you can correct a wrong intermediate result of a functional calculation or within nested parentheses: press and calculate the correct value, then resume the interrupted sequence of calculations.
- If you have pressed , , , , or by mistake, you may press the correct key immediately. Note that, though the correct operation overrides the wrong one designated first, the precedence of operation of the first command retains effective.

## 3.3 Calculation range and scientific notation

-9.99999999x1099

-109 | -1 | -10-2

-10-99

0

10-99

10-2 | 1 | 109

9.999999999x1099

| Normal display
| Scientific notation

When the answer exceeds the normal display capacity, it is automatically shown by scientific notation, 10-digit mantissa and exponents of 10 up to ±99.

(1) The minus (-) sign for mantissa
(2) The mantissa
(3) The minus (-) sign for exponent
(4) The exponent of ten

The whole display is read: -1,23456789 x 10-99

* Entry can be made in scientific notation by using the key after entering the mantissa.

Example | Operation | Read-out
--- | --- | ---

-1.23456789 x 10-3
(= -0.00123456789)

1 2 3 4 5 6 7 8 9

-1.23456789

-1.23456789 00

3

-1.23456789 -03

## 3.4 Overflow or error check

Overflow or error is indicated by the "E." or "C." sign and stops further calculations.

Overflow or error occurs:

1. When an answer, whether intermediate or final, or accumulated total in the independent memory is more than 1 x 10100 ("E." sign appears).
2. When function caculations are performed with a number exceeding the input range ("E." sign appears).
3. When unreasonable operations are performed in statistical calculations ("E." sign appears).
   Ex.: You attempt to obtain or n without any input data (n = 0).
4. When the total number of levels of explicitly and/or implicitly (with addition-subtraction versus multiplication-division including xy und x1/y) nested parentheses exceeds six, or more than 18 pairs of parentheses are used.
   Ex.: You have pressed the key 18 times continuously before designating the sequence .

To release these overflow checks:

1., 2., 3.: | Press the key.
4.: | Press the key. Or press the key, and the intermediate result just before the overflow occurs is displayed and the subsequent calculation is possible.

# 4 Normal Calculations

* Set the function mode to "RUN" by pressing .
* Calculations can be performed in the same sequence as the written formula (true algebraic logic).
* Nesting of up to 18 parenthesis at six levels is allowed.

## 4.1 Four basic calculations

* Parenthesis calculations can not be performed with the function mode at "LR".

Example | Operation | Read-Out
--- | --- | ---
23 + 4.5 - 53 = -25.5 |

23 4 5 53

-25.5

56 x (-12) (-2.5) = 268.8 |

56 12 2 5

268.8

2 3 x (1 x 1020) = 6.666666667x1019 |

2 3 1 20

6.666666667 19

7 x 8- 4 x 5 (= 56 - 20 ) = 36 |

7 8 4 5

36.

1 + 2 - 3 x 4 5 + 6 = 6.6 |

1 2 3 4 5 6

6.6

6

4 x 5

= 0.3

4 5 6

0.3

* The number of depression of the key can be displayed: |
2 x { 7 + 6 x (5 + 4) } = 122 |

2

[01 0.

7 6

[02 0.

5 4

122.

( 2 + 3 ) x 4 = 20 |

2 3 4

20.

3 + 4 x 5

5

= ( 3 + 4 x 5 ) 5 = 4.6

3 4 5 5

4.6

* It is unnecessary to press the key before the key: |
10 - { 7 x (3 + 6 ) } = - 53 |

10 7 3 6

-53.

Another operation:
10 7 3 6

## 4.2 Assignment for the number of fractional digits and the number of significant digits

* To designate the number of fractional digits, press n in sequence.
* To designate the number of significant digits, press n.
* The "FIX" and/or "SCI" assignment will not be released until another assignment is made or is pressed. (Power-off and auto power-off release the assignment.)
* Even when "FIX" and/or "SCI" is assigned, internal data use 11-digit mantissa. Press in the sequence to make the internal and displayed data equal.
* Press and the data will be converted to representation with the exponent of which is a multiple of three.

Example | Operation | Read-Out
--- | --- | ---

100 6 = 16.66666666...

100 6

16.66666667

(Specifies four fractional digits)

16.6667

(Releases assignment)

16.66666667

(Specifies five significant digits)

1.6667 01

16.66666667

* When an assignment for the number of digits is made, the data displayed is rounded up or down lowest digit position in the specified range but internal data remain unchanged in the registers. The assignment can be made at any time before or in the middle of calculation.

Example | Operation | Read-Out
--- | --- | ---

200 7 x 14 = 400

0.000

200

28.571

(Continues calculation with internal data consisting of 11 digits.)

14

400.000

To perform the same calculation with internal rounding

Example | Operation | Read-Out
--- | --- | ---

200 7

28.571

(Internal rounding)

14

399.994

(Releases assignment)

399.994

123m x 456 = 56088m

123 456

56088.

= 56.088km

56.088 03

7.8g 96 = 0.08125g

7 8 96

0.08125

= 81.25mg

81.25 -03

## 4.3 Constant calculations

* The "K" sign appears when a number is set as a constant.

Example | Operation | Read-Out
--- | --- | ---

3 + 2.3= 5.3

2 3 3

5.3

6 + 2.3= 8.3

6

8.3

Example | Operation | Read-Out
--- | --- | ---

7 - 5.6 = 1.4

5 6 7

1.4

-4.5 - 5.6 = -10.1

4.5

-10.1

Example | Operation | Read-Out
--- | --- | ---

2.3 x 12 = 27.6

12 2 3

27.6

(-9) x 12 = -108

9

-108.

Example | Operation | Read-Out
--- | --- | ---

74 2.5 = 29.6

2.5 74

29.6

85.2 2.5 = 34.08

85 2

34.08

Example | Operation | Read-Out
--- | --- | ---

17 + 17 + 17 + 17 = 68

17

34.

51.

68.

Example | Operation | Read-Out
--- | --- | ---

1.72 = 2.89

1.7

2.89

1.73 = 4.913

4.913

1.74 = 8.3521

8.3521

Example | Operation | Read-Out
--- | --- | ---

3 x 6 x 4 = 72

3 6

18.

3 x 6 x (-5) = -90

4

72.

5

-90.

Example | Operation | Read-Out
--- | --- | ---

56

4 x (2 + 3)

= 2.8

4 2 3

20.

56

2.8

23

4 x (2 + 3)

= 2.8

23

1.15

## 4.4 Memory calculations using the independent memory

* When a new number is entered into the independent memory by the key, the previous number stored is automatically cleared and the number is put in the independent memory.
* The "M" sign appears when a number is stored in the independent memory.
* The contents accumulated into the independent memory are preserved even after the power switch is turned off.
To clear the contents press or in sequence.

Example | Operation | Read-Out
--- | --- | ---

53 + 6 = | 59 |
23 - 8 = | 15 |
56 x 2 = | 112 |
+ ) 99 4 = | 24 | .75

| 210 | .75

53 6

59.

23 8

15.

56 2

112.

99 4

24.75

210.75

7 + 7 - 7 +
(2 x 3) + (2 x 3) + (2 x 3) - (2 x 3) = 19

7 2 3

19.

12 x 3 = 36

3 12

36.

- ) 45 x 3 = 135

45

135.

78 x 3 = 234

78

234.

135

135.

## 4.5 Memory calculations using 6 constant memories

* When a new number is entered into a constant memory by operating ENTRY (to ), the previous number stored is automatically cleared and the new number is put in the constant memory
* The contents stored in the constant memories are preserved even after the power switch is turned off.
To clear the contents press (to ) or (to ) in sequence.

Example | Operation | Read-Out
--- | --- | ---

193.2 23 = 8.4

193 2 23

8.4

193.2 28 = 6.9

28

6.9

193.2 42 = 4.6

42

4.6

* Another operations by using the independent memory:
193 2 23 , 28 , 42

Example | Operation | Read-Out
--- | --- | ---

9 x 6 + 3

(7 - 2) x 8

= 1.425

9 6 3

57.

7 2 8

40.

1.425

* Calculations in constant memory registers can also be performed by using the , , and keys.

7 x 8 x 9 = | 504
4 x 5 x 6 = | 120
3 x 6 x 9 = | 162

14 19 24 | 786 (Total)

| Operation | Read-Out
--- | --- | ---

7 8
9

504.

4 5
6

120.

3 6
9

162.

14.

19.

24.

786.

12 x (2.3 + 3.4) - 5 = 63.4 |

12 2 3 3 4 5

63.4

30 x (2.3 + 3.4+ 4.5) - 15 x 4.5 = 238.5 |

30 4 5 15

238.5

To exchange the displayed number (4.5) with the contents of constant memory 1 press .

## 4.6 Fraction calculations

* The display capacity of a fraction, whether entry or result, is limited to a max. 3 digits for each integer, numerator or denominator part and at the same time to a max. 8 digits in the sum of each part. When an answer exceeds the above capacity, it is automatically converted to the decimal scale.
* A fraction can be transferred to the independent memory and the constant memories.
* A fraction answer can be converted to the decimal scale by pressing the key. However, a decimal answer cannot be converted to the fraction scale.

Example | Operation | Read-Out
--- | --- | ---

4

5

6

x (3

1

4

+1

2

3

) 7

8

9

= 3

7

568

4 5 6
3 1 4
1 2 3
7 8 9

37568.

(= 3.012323944)

3.012323944

Example | Operation | Read-Out
--- | --- | ---

2

4

5

+

3

4

`-`1

1

2

= 2

1

20

2 4 5 3 4

31120.

3.55

1 1 2

2120.

(1.5 x 107) - {(2.5 x 106) x

3

100

} = 14925000

1.5 7 2 5 6 3 100

14925000.

* During a fraction calculation, a figure is reduced to the lowest terms by pressing a function command key (, , , ) or the key if the figure is reducible.

3

456

78

= 8

11

13

(Reduction)

3 456 78

345678.
81113.

12

45

`-`

32

56

= -

32

105

12 45
32 56

415.
-32105.

* The answer in a calculation performed between a fraction and a decimal is displayed as a decimal.

41

52

x 78.9 = 62.20961538

41 52
78 9

4152.
62.20961538

## 4.7 Percentage calculations

Example | Operation | Read-Out
--- | --- | ---

12% of 1500: 180

1500 12

180.

Percentage of 660 against 880: 75%

660 880

75.

15% add-on of 2500: 2875

2500 15

2875.

25% discount of 3500: 2625

3500 25

2625.

300cc is added to a solution of 500cc. What is the percent of the new volume to the initial one?

300 500

160.

(%)

If you made $80 last week and $100 this week, what is the percent increase?

100 80

25.

(%)

Example | Operation | Read-Out
--- | --- | ---

12% of 1200: 144

1200 12

144.

18% of 1200: 216

18

216.

23% of 1200: 276

23

276.

Example | Operation | Read-Out
--- | --- | ---

26% of 2200: 572

26 2200

572.

26% of 3300: 858

3300

858.

26% of 3800: 988

3800

988.

Example | Operation | Read-Out
--- | --- | ---

Percentage of 30 against 192: 15.625%

192 30

15.625

Percentage of 156 against 192: 81.25%

156

81.25

Example | Operation | Read-Out
--- | --- | ---

600 grams was added to 1200 grams. What percent is the total to the initial weight? 150%

1200 600

150.

510 grams was added to 1200 grams. What percent is the total to the initial weight? 142.5%

510

142.5

Example | Operation | Read-Out
--- | --- | ---

How many percent down is 138 grams to 150 grams?
Down 8%

150 138

-8.

How many percent down is 129 grams to 150 grams?
Down 14%

129

-14.

# 5 Function Calculations

* Scientific function keys can be utilized as subroutines of four basic calculations (including patenthesis calculations).
* In some scientific functions, the display disappears momentarily while complicated formulas are being processed. So do not enter numerals or press a function key until the previous answer is displayed.
* For each input range of the scientific functions, refer here.

## 5.1 Degree-Minute-Second <-> Decimal conversion

The key converts the sexagesimal figure (degree, minute and second) to decimal notation. Operation of converts the decimal notation to the sexagesimal notation.

Example | Operation | Read-Out
--- | --- | ---

14°25'36" = 14.42666667°

14

14.

25

14.41666667

36

14.42666667

14°25°36.

## 5.2 Trigonometric/Inverse trigonometric functions

Example | Operation | Read-Out
--- | --- | ---

sin (

6

rad) = 0.5

"RAD" () 6

0.5

Example | Operation | Read-Out
--- | --- | ---

cos 63°52'41" = 0.440283084

"DEG" ()
63 52 41

63.87805555

0.440283084

Example | Operation | Read-Out
--- | --- | ---

tan (-35 gra) = -0.61280078

"GRA" () 35

-0.61280078

Example | Operation | Read-Out
--- | --- | ---

2 x sin 45° x cos 65° =
0.597672477

"DEG" 2 45 65

0.597672477

Example | Operation | Read-Out
--- | --- | ---

sin-1

1

2

= 30°

"DEG" 1 2

30.

Example | Operation | Read-Out
--- | --- | ---

cos-1

2

= 0.785398163 rad

"RAD" 2 2

0.785398163

Example | Operation | Read-Out
--- | --- | ---

tan-1(0.6104) = 31.39989118

"DEG" 6104

31.39989118

31°23°59.61

Example | Operation | Read-Out
--- | --- | ---

sin-10.8 - cos-10.9 = 27°17'17.41"

"DEG" 8 9

27.28816959

27°17°17.41

## 5.3 Hyperbolic/Inverse hyperbolic functions

Example | Operation | Read-Out
--- | --- | ---

sinh 3.6 = 18.28545536

3 6

18.28545536

Example | Operation | Read-Out
--- | --- | ---

tanh 2.5 = 0.986614298

2 5

0.986614298

Example | Operation | Read-Out
--- | --- | ---

cosh 1.5 - sinh 1.5 = 0.223130
= e-1.5

1 5

2.352409615

0.22313016

-1.5

Example | Operation | Read-Out
--- | --- | ---

sinh-130 = 4.094622224

30

4.094622224

Example | Operation | Read-Out
--- | --- | ---

cosh-1

20

15

= 0.795365461

20 15

0.795365461

Example | Operation | Read-Out
--- | --- | ---

Wenn tanh 4x gleich 0.88 beträgt

x =

tanh-1 0.88

4

= 0.343941914

88 4

0.343941914

Example | Operation | Read-Out
--- | --- | ---

sinh-12 x cosh-11.5 = 1.389388923

2 1 5

1.389388923

## 5.4 Common & Natural logarithms/Exponentiations (Antilogarithms, Exponentials, Powers and Roots)

Example | Operation | Read-Out
--- | --- | ---

log 1.23 (= log101.23) = 0.089905111

1 23

0.089905111

Example | Operation | Read-Out
--- | --- | ---

ln 90 (=loge 90) = 4.49980967

90

4.49980967

Example | Operation | Read-Out
--- | --- | ---

log 456 ln 456 = 0.434294481

456

0.434294481

Example | Operation | Read-Out
--- | --- | ---

101.23 = 16.98243652

1 23

16.98243652

Example | Operation | Read-Out
--- | --- | ---

e4.5 = 90.0171313

4 5

90.0171313

Example | Operation | Read-Out
--- | --- | ---

100.4 + 5 e-3 = 2.760821773

4 5 3

2.760821773

Example | Operation | Read-Out
--- | --- | ---

5.62.3 = 52.58143837

5 6 2 3

52.58143837

Example | Operation | Read-Out
--- | --- | ---

1231/7(= ) = 1.988647795

123 7

1.988647795

Example | Operation | Read-Out
--- | --- | ---

(78 - 23)-12 = 1.30511183-21

78 23 12

1.30511183 -21

Example | Operation | Read-Out
--- | --- | ---

312+ e10 = 553467.4658

3 12 10

553467.4658

Example | Operation | Read-Out
--- | --- | ---

log sin 40° + log cos 35° = -0.27856798

"DEG" 40 35

-0.27856798

(The antilogarithm: 0.526540784)

0.526540784

Example | Operation | Read-Out
--- | --- | ---
151/5+251/6+351/7 = 5.090557037 |

15 5 25 6 35 7

5.090557037

* xy and x1/y can be registered as a constant.

Example | Operation | Read-Out
--- | --- | ---

42.5 = 32

2 5 4

32.

0.162.5 = 0.01024

16

0.01024

92.5 = 243

9

243.

## 5.5 Square roots, Squares, Reciprocals, Factorials & Random numbers

Example | Operation | Read-Out
--- | --- | ---

+ x = 5.287196908

2 3 5

5.287196908

Example | Operation | Read-Out
--- | --- | ---

123 + 302 = 1023

123 30

1023.

Example | Operation | Read-Out
--- | --- | ---

1 |

= 12

1

3

-

1

4

3 4

12.

Example | Operation | Read-Out
--- | --- | ---

8! (= 1 x 2 x 3 x...x 7 x 8) = 40320

8

40320.

Example | Operation | Read-Out
--- | --- | ---

Generate a random number between 0.000 and .999.

0.570

(Example)

## 5.6 Rectangular to polar co-ordinates conversion

Formula: r = , ß = tan-1(y/x) (-180° < ß<= 180°)

Example:
Find the length r and angle ß in radian when the point P is shown as x = 1 und y = in the rectangular co-ordinates.

Operation | Read-Out
--- | ---

"RAD" (5) 1 3

2.

(r)

1.047197551

(ß)

## 5.7 Polar to Rectangular co-ordinates conversion

Formula: x = r cos ß, y = r sin ß

Example:
Obtain the values of x and y when the point P is shown as ß = 60° and length r = 2 in the polar co-ordinates.

Operation | Read-Out
--- | ---

"DEG" (4) 2 60

1.

(x)

1.732050808

(y)

## 5.8 Applications

### 5.8.1 Decibel (dB) conversion

Example:
How many dB of amplifier gain is in an amp with 5mW of input power and 43W of output power?

Formula: dB = 10 x log10 (P2/P1)

P1: Input power (W)
P2: Output power (W)

Operation | Read-Out
--- | ---

10 435 3

39.34498451

### 5.8.2 Parabolic movement

Example:
Obtain the height of a ball 3 seconds after throwing it at a 50° angle and at an initial velocity of 30 m/sec. (not calculating air resistance).

Formula: h = V0 t sin ß-

1

2

g t2

h: Height of ball at T seconds after thrown (m)
V0: Initial velocity (m/sec.)
t : Time (sec.)
ß: Throwing angle to level surface
g : Gravitational acceleration (9.8 m/sec.2)

Operation | Read-Out
--- | ---

"DEG" () 30 3 50 1 2 9 8 3

24.84399988

(m)

### 5.8.3 Cycle of a conical pendulum

Example:
How many seconds is the cycle of a conical pendulum with a cord length of 30 cm and maximum swing angle of 90°.

Formula: T = |

T: Cycle (sec.)
l: Cord length (m)
ß: Maximum cord swing angle
g: Gravitational acceleration (9.8 m/sec.2)

Operation | Read-Out
--- | ---

"DEG" ()
2 3 90 2 9 8

0.924421332

(sek.)

### 5.8.4 Triangle

Example:
Calculate the interior angle (ß) and area (S) of the triangle when the lengths of three sides (a, b and c) are given.
a: 18 m, h: 21 m, c: 12 m

Formula: cos ß =

a2 + b2 - c2

2ab

S =

1

2

ab sin ß

Operation | Read-Out
--- | ---

"DEG" ()
18
21
12

34°46°19.

(ß)

2

107.7888561

(m2)

### 5.8.5 Pro-rating

Division | Sales amount/$ | %
--- | --- | ---
A | 84 | 22.4
B | 153 | 40.8
C | 138 | 36.8
Summe | 375 | 100.0

Operation | Read-Out
--- | ---

84 153 138

375.

100 84

M K 22.4

153

M K 40.8

138

M K 36.8

M K 100.

### 5.8.6 Time calculations

`1 hr. 27 min. 58 sec.`
`1 hr. 35 min. 16 sec.`
`+) 1 hr. 41 min. 12 sec.`
`------------------------`
`4 hr. 44 min. 26 sec.`

Average: 1 hr. 34 min. 48.67 sec.

Operation | Read-Out
--- | ---

1 27 58
1 35 16
1 41 12

4°44°26.

3

1°34°48.67

# 6 Statistical Calculations

* Be sure to press in sequence prior to starting a statistical calculation.

## 6.1 Standard deviation

* Set the function mode to "SD" by pressing .
Example: Find n-1, n, , x und x2 based on the data 55, 54, 51, 55, 53, 53, 54, 52.

Operation | Read-Out
--- | ---

"SD" 55 54 51 55 53 54 52

52.

(Sample standard deviation)

1.407885953

(Population standard deviation)

1.316956719

(Arithmetic mean)

53.375

(Number of data)

8.

(Sum of value)

427.

(Sum of square value)

22805.

Calculate the unbiased variance and the deviation between each data item and the average.

Operation | Read-Out |

(Subsequently)

1.982142857

(Unbiased variance)

55

1.625

(55 - )

54

0.625

(54 - )

51

-2.375

(51 -)

... | ... |

Note: The sample standard deviation n-1 is defined as:

the population standard deviation n is defined as:

and the arithmetical mean is defined as:

x

n

* Pressing , , , , or key need not be done sequentially.

Example:
Find n, and n-1 based on data: 1,2, -0,9, -1,5, 2,7, -0,6, 0,5, 0,5, 0,5, 0,5, 1,3, 1,3, 1,3, 0,8, 0,8, 0,8, 0,8, 0,8.

| Operation | Read-Out

"SD"
1 2 9

-0.9

1) (Mistake)

2 5

-2.5

1') (To correct)

0.

1 5

-1.5

2 7

2.7

2) (Mistake)

2.7

3) (Mistake)

1 6

-1.6

3') (To correct)

-1.6

6

-0.6

2') (To correct)

2 7

2.7

5

0.5

4

0.5

4) (Mistake)

1 4

1.4

4') (To correct)

0.

1 3 3

1.3

8

0.8

5) (Mistake)

6

0.8

5') (To correct)

8 6

0.8

8 5

0.8

17.

0.635294117

0.95390066

## 6.2 Regression analysis

* Set the function mode to "LR" by pressing .

### 6.2.1 Linear regression

Formula:

Example:
Results from measuring the length and temperature of a steel bar.

Temperature/°C | Length/mm
--- | ---
10 15 20 25 30 | 1003 1005 1010 1008 1014

Find the term (A), regression coefficient (B), correlation coefficient (r) and estimated values (, ) using the above figures as a basis.

| Operation | Read-Out |

"LR" 10

10.

1003

1003.

15 1005

1005.

20 1010

1010.

25 1008

1008

30 1014

1014.

998.

(A)

0.5

(B)

0.919018277

(r)

(When the temp. is 18 °C)

18

1007

(mm)

(When the length is 1000mm)

1000

4.

(°C)

Note: x2, x,n, y2, y, xy, , xn,xn-1, , yn, yn-1, A, B and r are respectively obtained by pressing a numeral key ( to ) after the or key.

* Correction of data entry

Example:

xi | 2 | 3 | 2 | 3 | 2 | 4
yi | 3 | 4 | 4 | 5 | 5 | 5

| Operation | Read-Out

2 3

3.

1) (Mistake)

4

4.

1') (To correct)

0.

3

3.

4

4.

2) (Mistake)

3

3.

2') (To correct)

2

2.

4

4.

3) (Mistake)

1

1.

5

5.

3') (To correct)

5.

3 5

5.

2

2.

4) (Mistake)

4

4.

4

4.

5) (Mistake)

6

6.

5') (To correct)

6.

4 5

5.

4') (To correct)

2 4

4.

2 5

5.

These ways of correction can also be applied to logarithmic, exponential or power regression.

### 6.2.2 Logarithmic regression

Formula: y = A + B · lnx

* Input data items are the logarithm of x (lnx), and y which is the same as in linear regression.
* Operation for calculating and correction regression coefficients are basically the same as in linear regression. Operate the sequence x to obtain estimator and y for estimator . Note that lnx, (lnx)2 and lnx·y are obtained instead of x, x2 and xy respectively.

Example:

xi | 29 | 50 | 74 | 103 | 118
yi | 1.6 | 23.5 | 38.0 | 46.4 | 48.9

Find A, B. r, and using the avove figures as a basis.

| Operation | Read-Out |

"LR" 29

3.36729583

16

1.6

50 23 5

23.5

74 38

38.

103 46 4

46.4

118 48 9

48.9

-111.128397

(A)

34.02014743

(B)

0.994013945

(r)

(When xi is 80)

80

37.94879479

()

(When yi is 73)

73

224.1541318

()

### 6.2.3 Exponential regression

Formula: y = A · eB·x

* Input data items are the logarithm of y (lny) and x which is the same as in linear regression
* Operation for correction is basically the same as in linear regression. Operate to obtain coefficient A, x for estimator , and y for estimator . Note that lny, (lny)2 and x·lny are obtained instead of y, y2 and xy.

Example:

xi | 6.9 | 12.9 | 19.8 | 26.7 | 35.1
yi | 21.4 | 15.7 | 12.1 | 8.5 | 5.2

Find A, B, r, and using the above figures as a basis.

| Operation | Read-Out |

"LR" 6 9

6.9

21 4

3.063390922

12 9 15 7

2.753660712

19 8 12 1

2.493205453

26 7 8 5

2.140066164

35 1 5 2

1.648658626

30.49758743

(A)

-0.0492037

(B)

-0.99724735

(r)

(When xi is 16)

16

13.87915739

()

(Wenn yi is 20)

20

8.57486805

()

### 6.2.4 Power regression

Formula: y = A · xB

* Input data items are lnx and lny.
* Operation for correction is basically the same as in linear regression. Operate to obtain coefficient A, x for estimator , and y for estimator . Note that lnx, (lnx)2, lny, (lny)2 and lnx·lny are obtained instead of x, x2, y, y2 and xy respectively.

Example:

xi | 28 | 30 | 33 | 35 | 38
yi | 2410 | 3033 | 3895 | 4491 | 5717

Find A, B, r, and using the above figures as a basis.

| Operation | Read-Out |

"LR" 28

3.33220451

2410

7.787382026

30 3033

8.017307508

33 3895

8.267448958

35 4491

8.409830673

38 5717

8.651199471

0.238801299

(A)

2.771865947

(B)

0.998906243

(r)

(When xi is 40)

40

6587.67582

()

(When yi is 1000)

1000

20.26225439

()

# 7 Programmed Calculations

* This calculator has a program memory of 38 steps. Up to two programmed procedures of calculation may be stored in the memory.
* To store a program (mathematical procedure) in the calculator, execute ordinary (i.e. manual) calculation in the LRN mode (press ) only once.
* Now the calculator has memorized the program. Input data and press the key, and the calculator exexutes the program with the data. This is very convinient for repeating calculations with varying sets of data.

## 7.1 How to store and execute programs

Example 1:

Calculate the surface areas (S) of regular octahedrons whose ridges are respectively 10, 7 and 15 cm long.

Formula: S = 2 - a2

Ridge length (a)/cm | Surface area/cm2
--- | ---
10 | (346.41)
7 | (169.74)
15 | (779.42)

Values enclosed with parentheses are to be obtained.

The following sequence of key operations realizes a mathematical procedure of the above formula.

2 3 | 10 |  | => S
| ^ |  |

Value of a (data)

Operate the above sequence in the LRN mode (). Note that must be pressed prior to data entry (the value of a in this case).

| Operation | Read-Out |

(Select LRN mode)

LRN . 0. P1 P2

LRN lit, P1 P2 blinking.

(Designate program No.)

LRN . 0. P1 .

Select a program number, P1 or P2

2

LRN . 2. P1 .

LRN . 2. P1 .

3

LRN . 3. P1 .

LRN . 1.732050808 P1 .

The mathematical procedure is stored in P1.

LRN . 3.464101615 P1 .

(Input data)

10

LRN . 10.ENT P1.

LRN . 100. P1 .

LRN . 346.4101615 P1 .

S for a = 10

Excution of the program stored: |  |

(Select RUN mode)

. 346.4101615 .

LRN disappears

(Designates program No.)

. 3.464101615 ENT P1.

7

. 169.7409791 .

S for a = 7

15

. 779.4228634 .

S for a = 15

Example 2:

Calculate the length l of the arc and the length a of the chord of a sector with radius and radii making an angle of ß°.

l =

rß

180

a =

2r sin

ß

2

Radius (r)/cm | Angle of radii (ß) | Arc length (l)/cm | Cord length (a)/cm
--- | --- | --- | ---
10 | 60° | (10.47) | (10)
12 | 42°34' | (8.91) | (8.71)
15 | 36° | (9.42) | (9.27)

* The values enclosed with parentheses are to be obtained.

| Operation | Read-Out |

(Select LRN mode)

LRN . 0. P1 P2

LRN lit, P1 P2 blinking.

(Designate program No.)

LRN . 0. P2.

10

LRN DEG . 10.ENT P2.

r => to K1 register

60

LRN DEG . 60.ENT P2.

ß => to K2 register

180

LRN DEG . 10.47197551 P2.

HLT for displaying result (l)

2

LRN DEG . 10. P2.

K1 x 2, K2 2
sin(ß/2) x K1

Execution of the program stored: |  |

(Select RUN mode)

DEG . 10. .

LRN disappears

(Designate progam No.)

DEG . 10. ENT P2.

(Input r)

12

DEG . 12. ENT P2.

(Input ß)

42 34

DEG . 8.915141819 P2.

Result (l)

(Subsequently)

DEG . 8.711524731 .

Result (a)

15 36

DEG . 9.424777961 P2.

Result (l)

(Subsequently)

DEG . 9.270509832 .

Result (a)

## 7.2 Program step

- The program is stored (written) in the calculator as shown below.

No. of steps | Program
--- | ---
P1
1 | 2
2 | x
3 | 3
4 | INV
5 | x
6 | ENT
7 | INX x2
8 | =
P2
9 | MODE 4
10 | ENT
11 | Kin 1
12 | x
13 | ENT
14 | Kin 2
15 | x
16 |
17 |
18 | 1
19 | 8
20 | 0
21 | =
22 | INV HLT
23 | 2
24 | Kin x 1
25 | Kin 2
26 | Kout 2
27 | sin
28 | Kin x 1
29 | Kout 1
30 |
31 |
... | ...
36 |
37 |
38 |

- The program capacity is 38 steps. The program may be divided into two areas (P1 and P2) and each can be used independently of the other.
- An error results ("E" displayed) when there is an attempt to write the 39th step. No subsequent steps can be written. In this case, press to release the error check.
- After the program is started, instruction steps are executed one after another and execution does not stop. But it is needed to halt execution for inputting a data or reading a result. This is accomplished by and .
When the end of a program is reached, execution stops automatically and the state is displayed. So, HLT may be absent.
- Each function comprises a step of program. The depression of keys in a certain sequence produces a single program step if it generates a single function.
1) Functions generated by the depression of a single key:
Example: Numeral value, +/-, +, -, x, , =, [(, )], sin, log, ENT, ...
2) Functions generated by the depression of a two-key sequence:
Example: INV x2, INV , hyp sin, INV sin-1, INV X <-> Y, INV x y, INV R -> P, Kin 2, INV RAN#, ...
3) Functions generated by the depression of a three-key sequence:
Example: INV X <-> K 5, INV hyp sin-1, MODE 8 3 (Assignment for the number of significant digits), Kin x 3 (Multiplication with contents of K3 register), ...
- If you have misoperated when writing a program (i.e. in the LRN mode), press the sequence of and perform the correct operation.
- The depression of a data entry key (, - ) followed by , , , or will not be written in if such a sequence immediately follows the depression of . Note that one of the functions which does not follow a numeric data will be written in as a step.
Example:

## 7.3 How to erase a program

An old program will be automatically overwritten by a new program if the same program number is assigned to them.
To erase a program for making corrections or erase all 38 steps, operate the following sequence.

- To erase program P1 or P2:

| (oder )
^ |
Selects the LRN mode

- To erase both P1 and P2:

## 7.4 Jump instructions

There are two types of jump instructions as follows.
1. Unconditional return to the first step of program: RTN
Write the sequence of at the end of a program to execute it repeatedly.

Example: Let us use the unconditional return instruction in the regular octahedron program explained on page 30. (In this case, the formula must be modified to S = a2 x 2.)

Operation:

| 10 | 2 3 |
| ^ |  | ^

Value of a | Return instruction

Step No. | Instruction step
--- | ---
1 | ENT
2 | INV x2
3 | x
4 | 2
5 | x
6 | 3
7 | INV
8 | =
9 | INV RTN

| Operation | Read-Out |

(Select RUN mode)

0.

(Designate program No.)

0. ENT P1

(For a = 7)

7

169.7409791 ENT P1

Result S
for a = 7

(For a = 15)

15

779.4228634 ENT P1

Result S
for a = 15

* If a program includes an RTN instruction but neither ENT nor HLT, the program will, once started, not stop in an endless loop. To stop the program in such a case, press .

2. Return to the first step of program depending on the condition of the contents of the X-register (display):
x > 0, x <= M

- x > 0: Return to the first step of program if the contents of the X-register is greater than zero and go to the next step otherwise.
- x <= M: Return to the first step of program if the contents of the X-register is equal to or smaller than the contents of the M-register and otherwise go to the next step.

Example: Find the maximum of 456, 852, 321, 753, 369, 741, 684 and 643.

Step No. | Instruction step
--- | ---
1 | ENT
2 | INX x <=M
3 | INV Min
4 | INV RTN

| Operation | Read-Out |

0.

Memory cleared

(Designate P2)

0. ENT P1

(Input data ...)

456

456. ENT P2

852

852. ENT P2

321

321. ENT P2

753

753. ENT P2

369

369. ENT P2

741

741. ENT P2

684

684. ENT P2

643

643. ENT P2

852. ENT P2

Maximum displayed

## 7.5 Applications

### Permutation and combination:

Calculate nPr and nCr for (n = 10: r = 4) and (n = 25: r = 5).

nPr=

n!

(n-r)!

, nCr=

n!

r!(n-r)!

Programming:

|  | 10 |  | 4 |
^ |  | ^ |  | ^ |

"LRN" displayed
(Value of n)
(Value of r)

... 5040 (Permutation)

| 10 |  | 4 |
| ^ |  | ^ |

(Value of n) | (Value of r)

... 210 (Combination)

Operation:

| 25 5 | 6375600 (Permutation)
| 25 5 | 53130 (Combination)

### Calculate the area of triangle when the lengths of the three sides are given:

s =

a + b + c

2

S = |

How large is S, when a = 18, b = 22 and c = 31?
How large is S, when a = 9.7, b = 13.4 und c = 6.5?

Programming:

^ "LRN" displayed | 18 22 31 |
| 2 |
|  | 194.2702692 (Area S)
Operation: |  |
| 9 7 13 4 6 5 | 29.61549594 (Area S)

### Sort sales slips by item code and add up the total of each item (for five items):

Code | Amount
3 | 2870
2 | 1960
5 | 3850
5 | 1250
1 | 2500
2 | 2310
3 | 1850
5 | 4370
3 | 5360
1 | 2220
2 | 1450
4 | 6120
1 | 3100

=>

Code | Amount
1 | 7820
2 | 5720
3 | 10080
4 | 6120
5 | 9470

Programming:

^
"LRN" displayed

5
4
3
2
1

(A)
(B)
(C)
(D)
(E)
(F)
(G)
(G)

(A) Sets to input the code numbers into independent memory (M) and the amount to K the constant memory (K6).
(B) Adds amount to K5 (still on display) temporarily and compares the code number (stored in M) with "5". If code number is 5, then amount is kept in K5 and returns to first line. If code number is less than 5, proceeds to the next line.
(C) Subtracts the amount (stored in K6) from K5 and adds to K4 temporarily. Compares the code number with "4": if 4, then returns to first line, if less than 4 proceeds to next.
(D), (E) Repeats same thing for code numbers 3 and 2.
(F) Subtracts the amount (stored in K6) from K2 and adds to K1. Returns to first step.
(G) Displays each amount accumulated per code number (contents of K1 through K5).

Operation: |  |
| 3 2870 2 1960 5 3850 5 1250 1 2500 2 2310 3 1850 5 4370 3 5360 1 2220 2 1450 4 6120 1 3100 |
| ........... 7820 (Amount of code No. 1) .................... 5720 (Amount of code No. 2) ....................10080 (Amount of code No. 3) .................... 6120 (Amount of code No. 4) .................... 9470 (Amount of code No. 5) |

### Calculation for loan-repayment (Equally divided monthly repayment)

Formula: P = PV

i

1 - (1 + i)-n

P: | Amount of monthly repayment |
PV: | Amount of loan | (Kin 1)
i: | Monthly interest | (Kin 2)
n: | Number of times of repayment | (Kin 3)

* The amount of repayment will be calculated in units of dollar by counting 50 cents or more as 1 dollar and disregarding the rest.

1) We borrow $30,000 at an annual interest of 7,65% for 10 years. What is the amount of monthly repayment?
2) We borrow $5,000 at an annual interest of 5,05% for 10 years. What is the amount of monthly repayment?

Programing: |
^ "LRN" displayed | 30000 7 65 12 2 10 12 1 1 ......358 (Amount of monthly repayment)
Operation: |
| 5000 5 05 5 ......94 (Amount of monthly repayment)

# 8 Integrals

* To carry out integrals, (1) define (write) function f(x) during the "LRN" mode, then (2) designate the interval of integral during the "dx" mode.

We calculate area ab f(x) dx.

* The approximation method used for integrating the function written in P1 or P2 is the Simpson's rule. This method requires to devide the interval of integral into equal parts. If the number of divisions is not specified, the calculator determines it by itself according to the form of the function. To specify it, designate n (an integer of 1 to 9) which meets N = 2n where N is the number of divisions.

## 8.1 Defining function f (x)

1. Select the "LRN" mode (press ).
2. Designate a program number (press or ).
3. Press .
* This is needed, as the first program step, to assign variable x of the function f(x) to the M-register.
4. Write the expression of function f(x) by true algebraic logic. Use to represent variable x. Write at the end.
   Example: For

f( x ) =

1

x2 + 1

write the sequence of 1, , [(, MR, INV x2, +, 1, )], =.
5. Press to select "dx" mode.

Note: For a function f (x) whose variable x cannot take the zero value, input an appropriate number in between steps 1) and 2) above.
Do not use constant registers, , and during expressions a function (step 4).

## 8.2 Execution of integral

1. Select the "dx" mode (press ).
2. Designate the program number assigned to the function, f (x). (Press or ).
3. Press a sequence of n to specify division number N (this will be displayed). This step may be skipped.
4. Designate the interval of integral, [ a , b ]. (Press a b .)
   * In seconds or minutes the result will be displayed in a floating point representation.

At this time the memory registers contain the following data.

K1-Register (Press ) ...... a
K2-Register (Press ) ...... b
K3-Register (Press ) ...... N (= 2n)
K4-Register (Press ) ...... f (a)
K5-Register (Press ) ...... f (b)
K6-Register (Press ) ...... abf (x)dx
M-Register (Press )................. a

## 8.3 Example

For f(x) = 2x2 + 3x + 4, calculate 25 f (x)dx and 28 f (x)dx.

| Operation | Read-Out |

(Select "LRN" mode)

LRN . 0. P1P2

(Designate program No.)

LRN . 0. P1 .

LRN . 0. P1 .

(Write f(x)) 2 3 4 |

(Select "dx" mode)

dx . 4. P1 .

(Designate program No.)

dx . 0. ENT P1 .

(Input n)

2

dx . 4. ENT P1 .

N displayed

(Input a and b)

2 5

dx . 1.215000000 02 .

Result displayed in about 4 seconds:
25 f(x)dx

(Designate program No.)

dx . 0. ENT P1 .

(Input a and b)

2 8

dx . 4.500000000 02 .

Result displayed in about 6 seconds:
28 f(x)dx

dx . 2. .

a

dx . 8. .

b

dx . 8. .

N

dx . 18. .

f(a)

dx . 156. .

f(b)

dx . 450. .

ab f(x)dx

## 8.4 Remarks for execution of integrals

- If you press during execution of integral (nothing is displayed), the execution will be aborted and the state selected by the depression of entered.
- If no function f (x) is defined (written in), the calculator will carry out integral for f (x) = x.
- It is normal to set the angular mode to "RAD" when executing integral of trigonometrics.
- Integral approximated by the Simpson's rule may take much execution time to raise the accuracy of result. Error may be large even when much execution time has been consumed. If the number of significant digits of result is smaller than one, error termination occurs ("E" displayed).
  In such cases, dividing the integral interval will reduce execution time and raise accuracy:

1. If the result varies greatly when the integral interval is moved slightly: Divide the interval into sections and sum up the results obtained in the sections.
2. For a periodic function or if the value of integral becomes positive or negative depending on the interval:
   Calculate for each period or separately for the sections where the result of integral is positive from where the result is negative, and sum up the results obtained.
3. If long execution time is due to the form of the function defined:
   Divide the function, if possible, into terms, execute integral for each term separately, and sum up the results.

# 9 Specifications

## Basic features

- Basic operations: 4 basic calculations, constants for `+`/`-`/ x / / x y,x1/y, and parenthesis calculations.
- Built-in functions: trigonometric/inverse trigonometric functions (with angle in degrees, radians or gradients), hyperbolic functions, logarithmic/exponential functions, reciprocals, factorials, square roots, powers, roots, decimal `<->` sexagesimal conversion, conversion of co-ordinate system (R`->`P, P`->`R), random number, , and percentages.
- Statistical functions: standard deviation, linear regression, logarithmic regression, exponential regression, and power regression.
- Integrals: Simpson's rule.
- Memory: 1 independent memory and 6 constant memories.
- Capacity:
  Entry/basic functions: 10 digit mantissa, or 10 digit mantissa plus 2 digit exponent up to 10±99.
  Fraction calculations: Max. 3 digit mantissa for each integer, numerator or denominator and at the same time max. 8 digit mantissa for the sum of each part.

Scientific functions | Input range | Output accuracy
--- | --- | ---
sinx/cosx/tanx | |x| < 1440° (8 rad, 1600 gra) | ± 1 in the 10. digit
sin-1x/cos-1x | |x| <= 1 | "
tan-1x | |x| < 1 x 10100 | "
sinhx/coshx/tanhx | -227 <= x <= 230 | "
sinh-1x | |x| < 1 x 10100 | "
cosh-1x | 1 <= x < 1 x 10100 | "
tanh-1x | |x| < 1 | "
log x/ln x | 0 < x <= 1 x 10100 | "
ex | -227 <= x<= 230 | "
10x | |x| < 100 | "
x y | |x| < 1 x 10100 with x < 0 => y : integer x = 0 => y > 0 | "
x1/y | |x| < 1 x 10100, y 0 | "
| 0 <= x < 1 x 10100 | "
x2 | |x| < 1 x 1050 | "
1/x | |x| < 1 x 10100(x 0) | "
x! | 0 <= x <= 69 (x: natural number) | "
POL `->`REC | |r| < 1 x 10100 |ß| < 1440° (8 Bogenmaß, 1600 Neugrad) | "
REC `->`POL | |x| < 1 x 10100 |y| < 1 x 10100 | "
° ' " | up to second | "
| 10 digits | "

## Programmable features:

- Total number of steps: up to 38 (1 step performs a function).
- Jump: Unconditional jump (RTN), conditional jump (x > 0, x <= M).
- Numbers of programs storable: up to 2 (P1 and P2).

## Decimal point:

Full floating with underflow.

## Read-out:

Liquid crystal display.

## Power consumption:

0.00043 W.

## Power source:

One lithium battery (Type: CR2025).
The unit gives approximately 1300 hours continues operation on type CR2025.

## Ambient temperature range:

0°C - 40°C (32°F - 104°F).

## Dimensions:

8,7mm (H) x 71,5mm (W) x 134mm (D) (3/8"H x 2-7/8"W x 5-1/4"D)

## Weight:

64 g (2.3 oz) including battery.