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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. Last change Aug 25 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)

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 ([M in][M+][M-][MR]).
K1 (Sigmax2) register
K2 (Sigmax) register
K3 (n) register
K4 (Sigmay2) register
K5 (Sigmay) register
K6 (Sigmaxy) register
  • Constant memory registers ([K in][K out][1][6]).
  • For storing intermediate results (Sigmax2Sigmax, n etc.) of statistical calculations.

1 Nomenclature

Abbildung des Casio fx-3600P (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

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
                   456Winkel12Winkel23.
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 [INV] 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 "Integral ueberdx" (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 [AC] 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 [INV])

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

(4) Mode key (symbolized by [MODE])

To put the calculator into the desired operating mode or select a specific angular unit, press [MODE] first, then [.][1], ... or [9].
 
  • [MODE][.]:
Manual and programmed calculations can be executed.
  • [MODE][0]
"LRN" is displayed. Programs can be written.
  • [MODE][1]
"Integral ueberdx" is displayed. Integral can be carried out.
  • [MODE][2]:
"LR"  is displayed. Calculation of regression analysis can be executed.
  • [MODE][3]:
"SD" is displayed. Calculation of standard deviation can be executed.
*To carry out manual or programmed calculation, select the RUN mode (press  ([MODE] and [.]).
 
  • [MODE][4]:
"DEG" is displayed, indicating that "degrees" is selected as the unit of angle.
  • [MODE][5]:
"RAD" is displayed, indicating that "radians" is selected as the unit of angle.
  • [MODE][6]:
"GRA" is displayed, indicating that "gradient" is selected as the unit of angle.
(Note: 90 degrees =  Pi/2  radians = 100 gradients)
 
  • [MODE][7]:
"Fix" assignment (assignment for the number of fractional digits). Specify the number of digits of the fractional part after pressing  [MODE] and [7].(Example: [MODE][7][3] (three fractional digits are effective))
  • [MODE][8]:
"Scientific" assignment (assignment for the number of significant digits). Specify the number of significant digits after pressing [MODE] and [8]. (Example: [MODE][8][4])
  • [MODE][9]:
"Normal" assignment. Press in this sequence to release the "fix" or "scientific" assignment.

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

(5) [0]-[9][.] 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 [INV] and a numeral  key, as summarized below.
 
  • [INV][0](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.
  • [INV][.](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".

  • [INV][1](x quer):
Calculation of x quer(average of x)
  • [INV][2](xsigman):
Calculation of xsigman (population standard deviation of  x)
  • [INV][3](xsigman-1):
Calculation of xsigman-1 (sample standard deviation of  x)
  • [INV][4](y quer):
Calculation of y quer(average of  y)
  • [INV][5](ysigman):
Calculation of ysigman (population standard deviation of y)
  • [INV][6](ysigman-1):
Calculation of ysigman-1 (sample standard deviation of  y)
  • [INV][7](A):
Calculation of A (constant terms in regression equations)
  • [INV][8](B):
Calculation of B (regression coefficients)
  • [INV][9](r):
Calculation of r (correlation coefficients)

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

  • [Kout][1](Sigmax2):
Calculation of Sigmax2 (square sum of x)
  • [Kout][2](Sigmax):
Calculation of Sigmax (total sum of x)
  • [Kout][3]( n ):
Calculation of n (number of data)
  • [Kout][4](Sigmay2):
Calculation of Sigmay2 (square sum of y)
  • [Kout][5](Sigmay):
Calculation of Sigmay (total sum of y)
  • [Kout][6](Sigmaxy):
Calculation of Sigmaxy (inner product)

* use [INV][7](x>0), [INV][8](x<=M) and [INV][9](RTN) only for writing programs (in "LRN" mode).

  • [INV][7](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."
  • [INV][8](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."
  • [INV][9](RTN):
Unconditional jump ("Return")
Press these keys to return to the first step of the program unconditionally.

(6) [EXP] (Pi) Exponent/Pi entry key

(7) [+] (R -> P) Addition/Rectangular -> polar key

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

(9) [x] (xy) Multiplication/Power key

(10) [/] (x1/y) Division/Root key

(11) [=] (%) Equal/Percent key

(12) [[(...)] (Wurzel aus, xD, yD) Open parenthesis/Square root/Regression analysis data input key

(13) [...)]] (x!x-Dachy-Dach) Close parenthesis/Factorial/Regression analysis estimator key

(14) [Kin] (x <-> y) Constant memory entry/Register exchange key

(15) [Kout] (x <-> K) Constant memory recall/Register exchange key

(16) [MR] (M in) Independent memory recall/Independent memory entry key

(17) [M+] (M-) Memory plus (minus) key

(18) [+/-] (x2) Sign change/Square key

(19) [° '  ''] ( <- ) Sexagesimal/Decimal conversion key

(20) [sin] (sin-1) Sine/Arc sine key

(21) [cos] (cos-1) Cosine/Arc cosine key

(22) [tan] (tan-1) Tangent/Arc tangent key

(23) [hyp] Hyperbolic key

(24) [log] (10x) Common logarithm/Antilogarithm key

(25) [ln] (ex) Natural logarithm/Exponential key

(26) [ENG] ( <- ) Engineering Key

12 [.]3456
12.3456      
12 [.]3456
12.3456     
[ENG]
12.3456   00
[INV][<-ENG]
0.0123456  03
[ENG]
12345.6  -03
[INV][<-ENG]
0.0000123456  06
[ENG]
12345600  -06
[INV][<-ENG]
0.0000000123456  09
[ENG]
12345600  -06
[INV][<-ENG]
0.0000000123456  09


[ENG]
0.0000123456  06


[ENG]
0.0123456  03

(27) [a b/c] (1/x) Fraction entry/Reciprocal key

(28) [AC] (KAC, ON) All clear key

(29) [C] Clear key

Clears entry for correction.

(30) [P1] (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 [INV] key.
A sequence must be designated for executing a programmed calculation.

(31) [RUN] (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.
      • [ENT]:
    When "LRN" is displayed (i.e. during program loading), depression of this key writes a halt instruction for data entry.
      • [INV][HLT]:
    When "LRN" is displayed, depression of this sequence writes a halt instruction for the display of a result.
      • [RUN]:
    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.
      • [DATA]:
    In the SD mode, operate in the sequence of a data and [DATA].
    In the LR mode, operate in the sequence of x data [Xd,Yd], y data, and [DATA].
      • [INV][DEL]:
    To delete the data which has just been imput, press this sequence instead of [DATA] 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 [MODE][0][INV][PCL][MODE][.][INV][KAC][INV][Min][MODE][4] 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 [MODE][3]) for standard diviation, the LR mode (press [MODE][2]) for regression analysis, the Integral ueberdx mode ([MODE][1]) for carrying out integral, and the RUN mode ([MODE][.]) for ordinary arithmetic and functional calculations.
    Select the LRN mode ([MODE][0]) 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

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

    Expression: 2 x [{(3+4x {(5+4)geteilt durch3}) geteilt durch5} +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

    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.

    Komponenten in der Anzeige

    (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 [EXP] key after entering the mantissa.

    Example Operation Read-out
    -1.23456789 x 10-3
    (= -0.00123456789)
    [.]2 3 4 5 6 7 8 9 [+/-]
    -1.23456789    

    [EXP]
    -1.23456789  00

    [+/-]
    -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 x queror sigman 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 [2][+][3][x].
    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 [MODE][.].
    * 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 [.][-]53 [=]
    -25.5
    56 x (-12) /(-2.5) = 268.8


    56 [x]12 [+/-][/][.][+/-][=]
    268.8 
    /3 x (1 x 1020) = 6.666666667x1019


    [/][x][EXP]20 [=]
    6.666666667  19
    7 x 8- 4 x 5 (= 56 - 20 ) = 36


    [x][-][x][=]
    36. 
    1 + 2 - 3 x 4 /5 + 6 = 6.6


    [+][-][x][/][+][=]
    6.6

    6

     4 x 5
     = 0.3


    [x][/][INV][x <-> y][=]
    0.3



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

    [x][[(...)]
    [01                    0.

    [+][x][[(...)]
    [02                    0.

    5 [+][...)]][...)]][=]
    122.



    ( 2 + 3 ) x 4 = 20


    [[(...)][+] 3 [...)]][x] 4 [=]
    20.



    3 + 4 x 5

    5
     = ( 3 + 4 x 5 ) geteilt durch 5 = 4.6



    [[(...)] 3 [+] 4 [x] 5 [...)]] [/] 5 [=]
    4.6



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


    10 [-][[(...)][x][[(...)][+][=]
    -53. 
    Another operation:
    10 [-][[(...)][x][[(...)][+][...)]][...)]][=]

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

    * To designate the number of fractional digits, press [MODE][7]n in sequence.
    * To designate the number of significant digits, press [MODE][8]n.
    * The "FIX" and/or "SCI" assignment will not be released until another assignment is made or [MODE][9] 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 [INV][RND] to make the internal and displayed data equal.
    * Press [ENG] and the data will be converted to representation with the exponent of which is a multiple of three.  

    Example Operation Read-Out
    100 geteilt durch6 = 16.66666666... 100 [/]6 [=]
    16.66666667 
    (Specifies four fractional digits) [MODE][7][4]
    16.6667 
    (Releases assignment) [MODE][9]
    16.66666667 
    (Specifies five significant digits) [MODE][8][5]
    1.6667  01

    [MODE][9]
    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 geteilt durch7 x 14 = 400 [MODE][7][3]
    0.000

    200 [/][7][=]
    28.571
    (Continues calculation with internal data consisting of 11 digits.) [x]14 [=]
    400.000

    To perform the same calculation with internal rounding

    Example Operation Read-Out

    200 [/][=]
    28.571
    (Internal rounding) [INV][RND][x]14 [=]
    399.994
    (Releases assignment) [MODE][9]
    399.994
    123m x 456 = 56088m 123 [x]456 [=]
    56088. 
    = 56.088km [ENG]
    56.088  03
    7.8g geteilt durch96 = 0.08125g [.][/]96 [=]
    0.08125 
    = 81.25mg [ENG]
    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 
    [.][+][+][=]
                       5.3
    6 + 2.3= 8.3 [=]
                       8.3


    Example Operation Read-Out
    7 - 5.6  = 1.4 [.][-][-][=]
                        1.4
    -4.5 - 5.6 = -10.1 4.5 [+/-][=]
                    -10.1


    Example Operation Read-Out
    2.3 x 12 = 27.6 12 [x][x][.][=]
                     27.6
    (-9) x 12 = -108 [+/-][=]
                   -108.


    Example Operation Read-Out
    74 geteilt durch2.5 = 29.6 2.5 [/][/]74 [=]
                     29.6
    85.2 geteilt durch2.5 = 34.08 85 [.][=]
                   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 [x][x][=]
                     2.89
    1.73 = 4.913 [=]
                    4.913
    1.74 = 8.3521 [=]
                 8.3521


    Example Operation Read-Out
    3 x 6 x 4 = 72 [x][x][x]
                       18.
    3 x 6 x (-5) = -90  4 [=]
                       72.

    [+/-][=]
                     -90.


    Example Operation Read-Out
    56 

    4 x (2 + 3)
     = 2.8 
    [x][[(...)][+][...)]][/][/]
                       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 [Min] 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 [0][INV][Min] or [AC][INV][Min] in sequence.  

    Example Operation Read-Out
     53 + 6 = 59
    23 - 8 = 15
    56 x  2 = 112
    + )  99 /  4 = 24 .75


    210 .75
    53 [+][=][INV][Min]
                          59.
    23 [-][M+]
                          15.
    56 [x][M+]
                        112.
    99 [/][M+]
                      24.75
    [MR]
                    210.75


       
    7 + 7 - 7 +
    (2 x 3) + (2 x 3) + (2 x 3) - (2 x 3) = 19
     7 [INV][Min][M+][INV][M-]2 3 [M+][M+][M+][INV][M-][MR]
                          19.


       
            12 x 3 =   36 [x][x]12 [=][INV][Min]
                       36.
    - )    45 x 3 =  135 45 [INV][M-]
                     135.
            78 x 3 =  234 78 [M+]
                     234.

                           135
    [MR]
                     135.

    4.5 Memory calculations using 6 constant memories

    * When a new number is entered into a constant memory by operating ENTRY [Kin][1] (to [6]), 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 [0][Kin][1] (to [6]) or [AC][Kin][1] (to [6]) in sequence.  

    Example Operation Read-Out
    193.2 geteilt durch23 = 8.4 193 [.][Kin][1][/]23 [=]
    8.4
    193.2 geteilt durch28 = 6.9 [Kout][1][/]28 [=]
    6.9
    193.2 geteilt durch42 = 4.6 [Kout][1][/]42 [=]
    4.6
    * Another operations by using the independent memory:
    193 [.][INV][Min][/]23 [=][MR][/]28 [=][MR][/]42 [=]
     

    Example Operation Read-Out
    9 x 6 + 3 

    (7 - 2) x 8
    = 1.425
    [x][+][=][Kin][1]
    57.

    [[(...)][-][...)]][x]8 [=][Kin][2]
    40.

    [Kout][1][/][Kout][2][=]
    1.425


    * Calculations in constant memory registers can also be performed by using the [+][-][x] 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

    [Kin][1][x]8 [Kin][2][x]
    [Kin][3][=][INV][Min]
                          504.

    [Kin][+][1][x][Kin][+][2][x]
    [Kin][+][3][=][M+]
                         120.

    [Kin][+][1][x][Kin][+][2][x]
    [Kin][+][3][=][M+]
                         162.

    [Kout][1]
                           14.

    [Kout][2]
                           19.

    [Kout][3]
                           24.

    [MR]
                        786.
     


    12 x (2.3 + 3.4) - 5 = 63.4

    12 [x][[(...)]2 [.][+][.][...)]][Kin][1][-][=]
    63.4
    30 x (2.3 + 3.4+ 4.5) - 15 x 4.5 = 238.5

     30 [x][.][Kin][+][1][INV][x<->K][1][-]15 [x][Kout][1]
    238.5
    To exchange the displayed number (4.5) with the contents of  constant memory 1 press [INV][x<->K][1].

    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 [a b/c] key. However, a decimal answer cannot be converted to the fraction scale.  

    Example Operation Read-Out
    4
    6
    x (3
    4
    +1
    3
    ) 7
    9
    = 3
    7

    568
    [a b/c][a b/c][x]
    [[(...)][a b/c][a b/c][+]
    [a b/c][a b/c][...)]][/]
    [a b/c][a b/c][=]
     3Winkel7Winkel568.
    (= 3.012323944) [a b/c]
    3.012323944


    Example Operation Read-Out
    2
    5
     + 
    4
     -1
    2
    = 2
    1

    20
    [a b/c][a b/c][+][a b/c][-]
    3Winkel11Winkel20.

    [a b/c]
    3.55

    [a b/c][a b/c][=]
    2Winkel1Winkel20.


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

    100
    } = 14925000
     
    1.5 [EXP][-][.][EXP][x][a b/c]100 [=]
    14925000.


    * During a fraction calculation, a figure is reduced to the lowest terms by pressing a function command key ([+][-][x][/]) or the [=] key if the figure is reducible.

    3 456 
    78
     =  8 11 
    13
     (Reduction)
    [a b/c]456 [a b/c]78 
    [=]
     3Winkel456Winkel78.
    8Winkel11Winkel13.


    12 
    45
    - 32 
    56
     = - 32 
    105
    12 [a b/c]45 [-]
    32 [a b/c]56 [=]
    4Winkel15.
    -32Winkel105.


    * 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 [a b/c]52 [x]
    78 [.][=]
    41Winkel52.
    62.20961538

    4.7 Percentage calculations

    Example Operation Read-Out
    12% of 1500: 180 1500 [x]12 [INV][%]
    180.
    Percentage of 660 against 880: 75% 660 [/]880 [INV][%]
    75.
    15% add-on of 2500: 2875 2500 [x]15 [INV][%][+]
    2875.
    25% discount of 3500: 2625 3500 [x]25 [INV][%][-]
     2625.
    300cc is added to a solution of 500cc. What is the percent of the new volume to the initial one? 300 [+]500 [INV][%]  
     160.
    (%)
    If you made $80 last week and $100 this week, what is the percent increase? 100 [-]80 [INV][%]  
    25.
    (%)


    Example Operation Read-Out
    12% of 1200: 144 1200 [x][x]12 [INV][%]
                     144.
    18% of 1200: 216 18 [INV][%]
                     216.
    23% of 1200: 276 23 [INV][%]
                     276.


    Example Operation Read-Out
    26% of 2200: 572 26 [x][x]2200 [INV][%]
                     572.
    26% of 3300: 858 3300 [INV][%]
                     858.
    26% of 3800: 988 3800 [INV][%]
                     988.


    Example Operation Read-Out
    Percentage of 30 against 192: 15.625% 192 [/][/]30 [INV][%]
                  15.625
    Percentage of 156 against 192: 81.25% 156 [INV][%]
                    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 [INV][%]
                      150.
    510 grams was added to 1200 grams. What percent is the total to the initial weight? 142.5% 510 [INV][%]
                    142.5


    Example Operation Read-Out
    How many percent down is 138 grams to 150 grams?
    Down 8% 
    150 [-][-]138 [INV][%]
                         -8.
    How many percent down is 129 grams to 150 grams?
    Down 14%
    129 [INV][%]
                       -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 [INV][<- ° ' ] 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

    [INV][<- ° ' ]
    14°25°36.

    5.2 Trigonometric/Inverse trigonometric functions

    Example Operation Read-Out
    sin ( Pi 
    6
    rad) = 0.5
    "RAD" ([MODE][5][pi][/][=][sin]
    0.5


    Example Operation Read-Out
    cos 63°52'41" = 0.440283084 "DEG" ([MODE][4]
    63 [° '  '']52 [° '  '']41[° '  '']
     63.87805555

    [cos]
    0.440283084


    Example Operation Read-Out
    tan (-35 gra) = -0.61280078 "GRA" ([MODE][6]) 35 [+/-][tan]
    -0.61280078


    Example Operation Read-Out
    2 x sin 45° x cos 65° = 
     0.597672477
    "DEG" 2 [x]45 [sin][x]65[cos][=]
    0.597672477


    Example Operation Read-Out
    sin-1
    2
     = 30°
    "DEG" 1 [a b/c][INV][sin]
    30.


    Example Operation Read-Out
    cos-1 Wurzel aus 2
    2
     =  0.785398163 rad
    "RAD" 2 [INV][sqrt][/][=][INV][acos]
    0.785398163


    Example Operation Read-Out
    tan-1(0.6104) =  31.39989118 "DEG" [.]6104 [INV][atan]
    31.39989118

    [INV][<- ° ' ]
    31°23°59.61


    Example Operation Read-Out
    sin-10.8 - cos-10.9 =  27°17'17.41" "DEG" [.][INV][asin][-][.][INV][acos][=]
    27.28816959

    [INV][<- ° ' ]
    27°17°17.41

    5.3 Hyperbolic/Inverse hyperbolic functions

    Example Operation Read-Out
    sinh 3.6 =  18.28545536 [.][hyp][sin]
    18.28545536


    Example Operation Read-Out
    tanh 2.5 = 0.986614298 [.][hyp][tan]
    0.986614298


    Example Operation Read-Out
    cosh 1.5 - sinh 1.5 = 0.223130 
                                 = e-1.5
    [.][INV][Min][hyp][cos][-]
             2.352409615

    [MR][hyp][sin][=]
               0.22313016

    [ln]
                            -1.5


    Example Operation Read-Out
    sinh-130 =  4.094622224 
    30 [INV][hyp][asin]
    4.094622224


    Example Operation Read-Out
    cosh-1 20 
    15
     = 0.795365461
    20 [a b/c]15 [INV][hyp][acos]
    0.795365461


    Example Operation Read-Out
    Wenn tanh 4x gleich 0.88 beträgt 
    x =  tanh-1 0.88 
    4
     = 0.343941914
    [.]88 [INV][hyp][atan][/][=]
    0.343941914


    Example Operation Read-Out
    sinh-12 x cosh-11.5 =  1.389388923 [INV][hyp][asin][x]1 [.][INV][hyp][acos][=]
    1.389388923

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

    Example Operation Read-Out
    log 1.23 (= log101.23) =  0.089905111 [.]23 [log]
    0.089905111


    Example Operation Read-Out
    ln 90 (=loge 90) = 4.49980967 90 [ln]
    4.49980967


    Example Operation Read-Out
    log 456 ln 456 = 0.434294481 456 [INV][Min][log][/][MR][ln][=]
    0.434294481


    Example Operation Read-Out
    101.23 = 16.98243652 [.]23 [INV][10^x]
    16.98243652


    Example Operation Read-Out
    e4.5 = 90.0171313 [.][INV][e^x]
    90.0171313


    Example Operation Read-Out
    100.4 + 5 e-3 = 2.760821773 [.][INV][10^x][+][x][+/-][INV][e^x][=]
    2.760821773


    Example Operation Read-Out
    5.62.3  = 52.58143837 5 [.]6 [INV][x^y][.][=]
    52.58143837


    Example Operation Read-Out
    1231/7(= 7. Wurzel aus 123)  = 1.988647795 123 [INV][x^1/y][=]
    1.988647795


    Example Operation Read-Out
    (78 - 23)-12 = 1.30511183-21 [[(...)]78 [-]23 [...)]][INV][x^y]12 [+/-][=]
    1.30511183 -21


    Example Operation Read-Out
    312+ e10 = 553467.4658  3 [INV][x^y]12 [+]10 [INV][e^x][=]
    553467.4658


    Example Operation Read-Out
    log sin 40° + log cos 35° =  -0.27856798 "DEG" 40 [sin][log][+]35 [cos][log][=]
    -0.27856798
    (The antilogarithm: 0.526540784) [INV][10^x]
    0.526540784


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

    15 [INV][x^1/y][+]25 [INV][x^1/y][+]35 [INV][x^1/y][=]
    5.090557037


    * xy and x1/y can be registered as a constant.
      
    Example Operation Read-Out
    42.5 = 32 [.]5 [INV][x^y][INV][x^y]4 [=]
                          32.
    0.162.5 = 0.01024 [.]16 [=]
                  0.01024
    92.5 = 243 [=]
                        243.

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

    Example Operation Read-Out
    Wurzel aus 2Wurzel aus 3Wurzel aus 5= 5.287196908 [INV][sqrt][+][INV][sqrt][x][INV][sqrt][=]
    5.287196908


    Example Operation Read-Out
    123 + 302 = 1023 123 [+]30 [INV][x^2][=]
    1023.


    Example Operation Read-Out
    1

     = 12


    3
     - 

    4

    [INV][1/x][-][INV][1/x][=][INV][1/x]
    12.


    Example Operation Read-Out
    8! (= 1 x 2 x 3 x...x 7 x 8) = 40320 [INV][x!]
    40320.


    Example Operation Read-Out
    Generate a random number between 0.000 and .999.
    [INV][RAN#]
    0.570
    (Example)

    5.6 Rectangular to polar co-ordinates conversion

    Formula: rWurzel aus x^2 plus y^2ß = tan-1(y/x)  (-180° < ß<= 180°)

    Polarkoordinaten

    Example:
    Find the length r and angle ß in radian when the point P is shown as x = 1 und y = Wurzel aus 3 in the rectangular co-ordinates.

    Operation Read-Out
    "RAD" ([MODE]5)     1  [INV][R<->P][INV][sqrt][=]

    2.
    (r)
    [INV][x <-> y]

    1.047197551
    (ß)

    5.7 Polar to Rectangular co-ordinates conversion

    Formula: x = r cos ßy = r sin ß

    Polarkoordinaten

    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" ([MODE]4) 2 [INV][P<->R]60 [=]

    1.
    (x)
    [INV][x <-> y]

    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 [x][[(...)]43[/][EXP][+/-][...)]][log][=]
    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-

    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" ([MODE][4]) 30 [x][x]50 [sin][-][a b/c]2 [x][.][x]3 [INV][x^2][=]

    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 = 
    Pendelformel

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

    Operation Read-Out
    "DEG" ([MODE][4])
    [x][pi][x][[(...)][.][x][[(...)]90 [/][...)]][cos][/][.][...)]][INV][sqrt][=]

    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 = 

    2
    ab sin ß
     
    Operation Read-Out
    "DEG" ([MODE][4])
    18 [Kin][1][INV][x^2][+]
    21 [Kin][2][INV][x^2][-]
    12 [INV][x^2][=]
    [/][[(...)][Kout][1][x][Kout][2][x]
    [INV][Min][2][...)]][=][INV][cos][INV][<- ° ' ]

    34°46°19.
    (ß)
    [sin][x][MR][/][=]

    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 [=][INV][Min]
    M K                 22.4
    153 [M+]
    M K                 40.8
    138 [M+]
    M K                 36.8
    [MR]
    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
    [° '  '']27 [° '  '']58 [° '  ''][+]
    [° '  '']35 [° '  '']16 [° '  ''][+]
    [° '  '']41 [° '  '']12 [° '  ''][=][INV][<- ° ' ]
    4°44°26.
    [/][=][INV][<- ° ' ]
    1°34°48.67

    6 Statistical Calculations

    * Be sure to press [INV][KAC] in sequence prior to starting a statistical calculation.

    6.1 Standard deviation

    * Set the function mode to "SD" by pressing [MODE][3].
    Example: Find sigman-1sigmanx querSigmax und  Sigmax2 based on the data 55, 54, 51, 55, 53, 53, 54, 52.
      
    Operation Read-Out
    "SD" [INV][KAC]55 [DATA]54 [DATA]51 [DATA]55 [DATA]53 [DATA][DATA]54 [DATA]52 [DATA]
    52.
    (Sample standard deviation) [INV][x_sigma_n-1]
    1.407885953
    (Population standard deviation) [INV][x_sigma_n]
    1.316956719
    (Arithmetic mean) [INV][x quer]
    53.375 
    (Number of data) [Kout][n]
    8.
     (Sum of value) [Kout][Sigma x]
    427. 
    (Sum of square value) [Kout][Sigma x^2]
    22805.

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

    Operation Read-Out
    (Subsequently) [INV][x_sigma_n-1][INV][x^2]
    1.982142857
    (Unbiased variance)
    [INV][x quer][-][-]55 [=]
    1.625
    (55 - x quer)
    54 [=]
    0.625
    (54 - x quer)
     51 [=]
    -2.375 
    (51 -x quer)
    ...  ...

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

    Stichproben-Standardabweichung

    the population standard deviation sigman is defined as:

    Grundgesamtheits-Standardabweichung

    and the arithmetical mean x quer is defined as:
     
    Sigmax

    n

    * Pressing [x_sigma_n-1][x_sigma_n][x quer][n][Sigma x] or [Sigma x^2] key need not be done sequentially.

    Example:
    Find nx quer and sigman-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" [INV][KAC]
    [.]2 [DATA][.][+/-][DATA]
    -0.9
    1) (Mistake) [.][+/-]
    -2.5
    1') (To correct) [C]
    0.

    [.][+/-][DATA]
    -1.5

    [.][DATA]
    2.7
    2) (Mistake) [DATA]
    2.7
    3) (Mistake) [.][+/-][DATA]
    -1.6
    3') (To correct) [INV][DEL]
    -1.6

    [.][+/-][DATA]
    -0.6
    2') (To correct) [.][INV][DEL]
    2.7

    [.][x]
    0.5

     4 [DATA]
    0.5
    4) (Mistake) [.][x]
    1.4
    4') (To correct) [AC]
    0.

    [.][x][DATA]
    1.3

    [.][x]
    0.8
    5) (Mistake) [DATA]
    0.8
    5') (To correct) [.][x][INV][DEL]
    0.8

    [.][x][DATA]
    0.8

    [Kout][n]
    17.

    [INV][x quer]
    0.635294117

    [INV][x_sigma_n-1]
    0.95390066

    6.2 Regression analysis

    * Set the function mode to "LR" by pressing [MODE][2].

    6.2.1 Linear regression

    Formula:

    y=A+Bx
     

    B
     

    A
     

    r
     

    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 (x-Dachy-Dach) using the above figures as a basis.


    Operation Read-Out

    "LR" [INV][KAC]10 [Xd,Yd]
    10.


    1003 [DATA]
    1003.


    15 [Xd,Yd]1005 [DATA]
    1005.


    20 [Xd,Yd]1010 [DATA]
    1010.


    25 [Xd,Yd]1008 [DATA]
    1008


    30 [Xd,Yd]1014 [DATA]
    1014.


    [INV][A]
    998.
    (A)

    [INV][B]
    0.5
    (B)

    [INV][r]
    0.919018277
    (r)
    (When the temp. is 18 °C) 18 [y Dach]
    1007
    (mm)
    (When the length is 1000mm) 1000 [INV][x Dach]
    4.
    (°C)

    Note: Sigmax2Sigmax,nSigmay2SigmaySigmaxyx quer, xsigman,xsigman-1y quer, ysigman, ysigman-1, A, B and r are respectively obtained by pressing a numeral key ([1] to [9]) after the [Kout] or [INV] key.

    * Correction of data entry

    Example:
     
    xi 2 3 2 3 2 4
    yi 3 4 4 5 5 5
     


    Operation Read-Out

    [INV][KAC][Xd,Yd][DATA]
    3.
    1) (Mistake) 4
    4.
    1') (To correct) [C]
    0.

    [Xd,Yd]
    3.

    [DATA]
    4.
    2) (Mistake) [Xd,Yd]
    3.
    2') (To correct) [Xd,Yd]
    2.

    [DATA]
    4.
    3) (Mistake) [Xd,Yd]
    1.

    [DATA]
    5.
    3') (To correct) [INV][DEL]
    5.

    [Xd,Yd][DATA]
    5.

    [Xd,Yd]
    2.
    4) (Mistake) [DATA]
    4.

    [Xd,Yd]
    4.
    5) (Mistake) [DATA]
    6.
    5') (To correct) [INV][DEL]
    6.

    [Xd,Yd][DATA]
    5.
    4') (To correct) [Xd,Yd][INV][DEL]
    4.

    [Xd,Yd][DATA]
    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 [ln][y Dach] to obtain estimator y-Dach and y [INV][x Dach][INV][e^x] for estimator x-Dach. Note that SigmalnxSigma(lnx)2 and Sigmalnx·y are obtained instead of SigmaxSigmax2 and Sigmaxy respectively.

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

    Find A, B. r, x-Dach and y-Dach using the avove figures as a basis.


    Operation Read-Out

    "LR" [INV][KAC]29 [ln][Xd,Yd]
    3.36729583


    1[.][DATA]
    1.6


    50 [ln][Xd,Yd]23 [.][DATA]
    23.5


    74 [ln][Xd,Yd]38 [DATA]
    38.


    103 [ln][Xd,Yd]46 [.][DATA]
    46.4


    118 [ln][Xd,Yd]48 [.][DATA]
    48.9


    [INV][A]
    -111.128397
    (A)

    [INV][B]
    34.02014743
    (B)

    [INV][r]
    0.994013945
    (r)
    (When xi is 80) 80 [ln][y Dach]
    37.94879479
    (y-Dach)
    (When yi is 73) 73 [INV][x Dach][INV][e^x]
    224.1541318
    (x-Dach)

    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 [INV][A][INV][e^x] to obtain coefficient A, x [y Dach][INV][e^x] for estimator y-Dach, and y [ln][INV][x Dach] for estimator x-Dach. Note that SigmalnySigma(lny)2 and Sigmax·lny are obtained instead of SigmaySigmay2 and Sigmaxy.

    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, x-Dach and y-Dach using the above figures as a basis.


    Operation Read-Out

    "LR" [INV][KAC][.][Xd,Yd]
    6.9


    21 [.][ln][DATA]
    3.063390922


    12 [.][Xd,Yd]15 [.][ln][DATA]
    2.753660712


    19 [.][Xd,Yd]12 [.][ln][DATA]
    2.493205453


    26 [.][Xd,Yd][.][ln][DATA]
    2.140066164


    35 [.][Xd,Yd][.][ln][DATA]
    1.648658626


    [INV][A][INV][e^x]
    30.49758743
    (A)

    [INV][B]
    -0.0492037
    (B)

    [INV][r]
    -0.99724735
    (r)
    (When xi is 16) 16 [y Dach][INV][e^x]
    13.87915739
    (y-Dach)
    (Wenn yi is 20) 20 [ln][INV][x Dach]
    8.57486805
    (x-Dach)

    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 [INV][A][INV][e^x] to obtain coefficient A, x [ln][y Dach][INV][e^x] for estimator y-Dach, and y[ln][INV][x Dach][INV][e^x] for estimator x-Dach. Note that Sigmalnx, Sigma(lnx)2SigmalnySigma(lny)2 and Sigmalnx·lny are obtained instead of SigmaxSigmax2SigmaySigmay2 and Sigmaxy respectively.

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

    Find A, B, r, x-Dach and y-Dach using the above figures as a basis.


    Operation Read-Out

    "LR" [INV][KAC]28 [ln][Xd,Yd]
    3.33220451


    2410 [ln][DATA]
    7.787382026


    30 [ln][Xd,Yd]3033 [ln][DATA]
    8.017307508


    33 [ln][Xd,Yd]3895 [ln][DATA]
    8.267448958


    35 [ln][Xd,Yd]4491 [ln][DATA]
    8.409830673


    38 [ln][Xd,Yd]5717 [ln][DATA]
    8.651199471


    [INV][A][INV][e^x]
    0.238801299
    (A)

    [INV][B]
    2.771865947
    (B)

    [INV][r]
    0.998906243
    (r)
    (When xi is 40) 40 [ln][y Dach][INV][e^x]
    6587.67582
    (y-Dach)
    (When yi is 1000) 1000 [ln][INV][x Dach][INV][e^x]
    20.26225439
    (x-Dach)

    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 [MODE][0]) only once.
    * Now the calculator has memorized the program. Input data and press the [RUN] 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 - Wurzel aus 3a2

    Oktaeder
     
     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.

    [x][INV][sqrt][x] 10 [INV][x^2][=]   => S

    ^

    Value of a (data)

    Operate the above sequence in the LRN mode ([MODE][0]). Note that [ENT] must be pressed prior to data entry (the value of a in this case).


    Operation Read-Out
    (Select LRN mode) [MODE][0]
    LRN                       .
    0.    P1 P2
    LRN lit, P1 P2 blinking. 
    (Designate program No.) [P1]
    LRN                       .
    0.       P1    .
    Select a program number, P1 or P2

    2
    LRN                       .
    2.       P1    .


    [x]
    LRN                       .
    2.       P1    .


    3
    LRN                      .
    3.       P1    .


    [INV][sqrt]
    LRN                       .
    1.732050808       P1    .
    The mathematical procedure is stored in P1.

    [x]
    LRN                       .
    3.464101615       P1    .

    (Input data) [ENT]10
    LRN                       .
    10.ENT P1.


    [INV][x^2]
    LRN                       .
    100.       P1    .


    [=]
    LRN                       .
    346.4101615       P1    .
    S for a = 10
    Excution of the program stored:


    (Select RUN mode) [MODE][.]
                           .
    346.4101615            .
    LRN disappears
    (Designates program No.) [P1]
                           .
    3.464101615  ENT P1.


    7 [RUN]
                           .
    169.7409791           .
    S for a = 7

    [P1]15 [RUN]
                           .
    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 = Pirß

    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) [MODE][0]
    LRN                       .
    0.    P1 P2
    LRN lit, P1 P2 blinking.
    (Designate program No.) [INV][P2]
    LRN                       .
    0.            P2.


    [MODE][4][ENT]10
    LRN        DEG            .
    10.ENT      P2.
    r => to K1 register

    [Kin][1][x][ENT]60 
    LRN        DEG           .
    60.ENT      P2.
    ß => to K2 register

    [Kin][2][x][pi][/]180 [=][INV][HLT]
    LRN        DEG            .
    10.47197551            P2.
    HLT for displaying result (l)

    [Kin][x][1][Kin][/][2]
    [Kout][2][sin][Kin][x][1]
    [Kout][1]
    LRN        DEG           .
    10.            P2.
    K1 x 2, K2 geteilt durch2
    sin(ß/2) x K1
    Execution of the program stored:
     
    (Select RUN mode) [MODE][.]
        DEG           .
    10.             .
    LRN disappears
    (Designate progam No.) [INV][P2]
    DEG        .
    10. ENT     P2.

    (Input r) 12 [RUN]
      DEG        .
    12.  ENT     P2.

    (Input ß) 42 [° '  '']34 [° '  ''][RUN]
    DEG        .
    8.915141819             P2.
    Result (l)
    (Subsequently) [RUN]
    DEG        .
    8.711524731            .
    Result (a)

    [INV][P2]15 [RUN]36 [RUN]
    DEG        .
    9.424777961             P2.
    Result (l)
    (Subsequently) [RUN]
    DEG        .
    9.270509832            .
    Result (a)

    7.2 Program step


    No. of steps
    Program
    P1
    1 2
    2 x
    3 3
    4 INV Wurzel aus
    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 Pi
    17 geteilt durch
    18 1
    19 8
    20 0
    21 =
    22 INV HLT
    23 2
    24 Kin x 1
    25 Kin geteilt durch2
    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 [AC] 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 [ENT] and [INV][HLT]
    • 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, geteilt durch, =, [(, )], sin, log, ENT, ... 
      2) Functions generated by the depression of a two-key sequence:
      Example: INV x2,  INV Wurzel aus, 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 [INV][PCL] and perform the correct operation.
    • The depression of a data entry key ([.][0][9]) followed by [EXP][+/-][a b/c][° '  '']or [C] will not be written in if such a sequence immediately follows the depression of [ENT]. Note that one of the functions which does not follow a numeric data will be written in as a step.
    • Example:  

      Programm-Aufzeichnung

    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.

    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 [INV][RTN] 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 2Wurzel aus 3.)
     
    Operation:
    [MODE] [0] [P1]
    [ENT] 10 [INV][x^2][x][x]3[INV][sqrt][=] [INV][RTN]

    ^
    ^
    Value of a Return instruction

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



     
    Program with RTN


    Operation Read-Out
    (Select RUN mode) [MODE][.]
    0. 

    (Designate program No.) [P1]
    0. ENT P1

    (For a = 7) [RUN]
    169.7409791 ENT P1
    Result S 
    for a = 7
    (For a = 15) 15 [RUN]
    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 [AC].

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

    Example: Find the maximum of 456, 852, 321, 753, 369, 741, 684 and 643.
     
    [MODE][0][INV][P2]
    [ENT][INV][x<=M][INV]
    [Min][INV][RTN]
    Step No. Instruction step
    1 ENT
    2 INX x <=M
    3 INV Min
    4 INV RTN
    Programm mit Zustandstest


    Operation Read-Out

    [MODE][.][AC][INV][Min]
    0. 
    Memory cleared
    (Designate P2) [INV][P2]
    0. ENT P1

    (Input data ...) 456 [RUN]
    456. ENT   P2


    852 [RUN]
    852. ENT    P2


    321 [RUN]
    321. ENT    P2


    753 [RUN]
    753. ENT    P2


    369 [RUN]
    369. ENT    P2


    741 [RUN]
    741. ENT    P2


    684 [RUN]
    684. ENT    P2


    643 [RUN]
    643. ENT    P2


    [MR]
    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:
     
               [MODE][0]          
    [P1][ENT] 10 [Kin][1][ENT] 4 [Kin][2]
    ^
    ^
    ^
    "LRN" displayed
    (Value of n)
    (Value of r)
    [Kout][1][INV][x!][/][[(...)][Kout][1][-][Kout][2][...)]][INV][x!][=]... 5040 (Permutation)
     
    [INV][P2][ENT] 10 [Kin][1][ENT] 4 [Kin][2]

    ^
    ^
    (Value of n) (Value of r)
    [Kout][1][INV][x!][/][Kout][2][INV][x!][/][[(...)][Kout][1][-][Kout][2][...)]][INV][x!][=]... 210 (Combination)

    Operation:
     
    [MODE][.] [P1]25 [RUN][RUN]    6375600 (Permutation)

    [INV][P2]25 [RUN][RUN]       53130 (Combination)

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

    Dreieck
    s =  a + b + c 

    2
    S =  Wurzel aus (s(s-a)(s-b)(s-c))

    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:
     
    [MODE][0]

    "LRN" displayed
    [P1]
    [ENT]18 [Kin][1][+]
    [ENT]22 [Kin][2][+]
    [ENT]31 [Kin][3]


    [=][/][=][Kin][4]

    [x][[(...)][Kout][4][-][Kout][1][...)]]
    [x][[(...)][Kout][4][-][Kout][2][...)]]
    [x][[(...)][Kout][4][-][Kout][3][...)]]


    [=][INV][sqrt] 194.2702692
    (Area S)
    Operation:

    [MODE][.] [P1]
      9 [.][RUN]
    13 [.][RUN]
      6 [.][RUN]
    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:
     
    [MODE][0]

    "LRN" displayed
    [P1][ENT][INV][Min][ENT][Kin][6]
    [Kin][+][5][INV][x<=M]
    [Kout][6][Kin][-][5][Kin][+][4]4 [INV][x<=M]
    [Kout][6][Kin][-][4][Kin][+][3]3 [INV][x<=M]
    [Kout][6][Kin][-][3][Kin][+][2]2 [INV][x<=M]
    [Kout][6][Kin][-][2][Kin][+][1]1 [INV][RTN]
    [INV][P2][Kout][1][INV][HLT][Kout][2][INV][HLT]
    [Kout][3][INV][HLT][Kout][4][INV][HLT][Kout][5]
    (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:

    [MODE][.] [INV][KAC][P1]
    [RUN]2870 [RUN][RUN]1960 [RUN]5 [RUN]3850 [RUN][RUN]1250 [RUN]
    1 [RUN]2500 [RUN][RUN]2310 [RUN]3 [RUN]1850 [RUN][RUN]4370 [RUN]
    [RUN]5360 [RUN][RUN]2220 [RUN]2 [RUN]1450 [RUN][RUN]6120 [RUN]
    [RUN]3100 [RUN]


    [INV][P2]...........  7820 (Amount of code No. 1) 
    [RUN]....................  5720 (Amount of code No. 2) 
    [RUN]....................10080 (Amount of code No. 3) 
    [RUN]....................  6120 (Amount of code No. 4) 
    [RUN]....................  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:
    [MODE][0]

    "LRN" displayed
    [P1][ENT]30000 [Kin][1]
    [ENT][.]65 [/]12 [EXP][=][Kin][2]
    [ENT]10 [x]12 [=][Kin][3]
    [Kout][1][x][Kout][2][/][[(...)]1 [-][[(...)][+][Kout][2][...)]]
    [INV][x^y][Kout][3][+/-][...)]]
    [=][MODE][7][0]......358 (Amount of monthly repayment)
    Operation:
    [MODE][1] [P1]5000 [RUN][.]05 [RUN][RUN]......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 "Integral ueberdx" mode.



    We calculate area Integral ueberab 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 [MODE][0]).
    2. Designate a program number (press [P1] or [INV][P2]).
    3. Press [INV][Min].
    4. * This is needed, as the first program step, to assign variable x of the function f(x) to the M-register.
    5. Write the expression of function f(x) by true algebraic logic. Use [MR] to represent variable x. Write [=] at the end.
      Example: For
    6. f( x ) =  1

      x2 + 1
      write the sequence of 1, geteilt durch, [(, MR, INV x2, +, 1, )], =.
    7. Press [MODE][1] to select "Integral ueberdx" 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, [KAC][ENT] and [HLT] during expressions a function (step 4).

    8.2 Execution of integral

    1. Select the "Integral ueberdx" mode (press [MODE][1]).
    2. Designate the program number assigned to the function, f (x). (Press [P1] or [INV][P2]).
    3. Press a sequence of n [INV][RUN] to specify division number N (this will be displayed). This step may be skipped.
    4. Designate the interval of integral, [ a , b ]. (Press a  [RUN] b  [RUN].)
      * 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 [Kout][1]) ...... a
    K2-Register (Press [Kout][2]) ...... b
    K3-Register (Press [Kout][3]) ...... N (= 2n)
    K4-Register (Press [Kout][4]) ...... f (a)
    K5-Register (Press [Kout][5]) ...... f (b)
    K6-Register (Press [Kout][6]) ...... Integral ueberabf (x)dx
    M-Register  (Press [MR])................. a

    8.3 Example

    For f(x) = 2x2 + 3x + 4, calculate Integral ueber25 f (x)dx and Integral ueber28 f (x)dx.
     

    Operation Read-Out
    (Select "LRN" mode) [MODE][0]
    LRN                           .
    0.       P1P2

    (Designate program No.) [P1]
    LRN                           .
    0.       P1    .


    [INV][Min]
    LRN                           .
    0.       P1    .

    (Write f(x)) 2 [x][MR][INV][x^2][+][x][MR][+][=]
    (Select "Integral ueberdx" mode) [MODE][1]
    Integral ueberdx                          .
    4.       P1    .

    (Designate program No.) [P1]
    Integral ueberdx                          .
    0.  ENT P1   .

    (Input n) [INV][RUN]
    Integral ueberdx                          .
    4.  ENT P1   .
    N displayed
    (Input a and b) [RUN][RUN]
    Integral ueberdx                          .
    1.215000000      02        .
    Result displayed in about 4 seconds:
    Integral ueber25 f(x)dx
    (Designate program No.) [P1]
    Integral ueberdx                          .
    0.  ENT P1   .

    (Input a and b) [RUN]8[RUN]
    Integral ueberdx                          .
    4.500000000      02        .
    Result displayed in about 6 seconds:
    Integral ueber28 f(x)dx





    [Kout][1]
     Integral ueberdx                         .
    2.                .
    a

    [Kout][2]
     Integral ueberdx                         .
    8.                .
    b

    [Kout][3]
     Integral ueberdx                         .
    8.                .
    N

    [Kout][4]
     Integral ueberdx                         .
    18.                .
    f(a)

    [Kout][5]
     Integral ueberdx                         .
    156.                .
    f(b)

    [Kout][6]
     Integral ueberdx                         .
    450.                .
    Integral ueberab f(x)dx

    8.4 Remarks for execution of integrals

    9 Specifications

    Basic features

    Scientific functions
    Input range
    Output accuracy
    sinx/cosx/tanx |x| < 1440° (8 Pi 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 ungleich0 "
    Wurzel von x 0 <= x < 1 x 10100 "
    x2 |x| < 1 x 1050 "
    1/x |x| < 1 x 10100(x ungleich0) "
    x! 0 <= x <= 69 (x: natural number) "
    POL ->REC |r| < 1 x 10100
    |ß| < 1440° (8 PiBogenmaß, 1600 Neugrad)
    "
    REC ->POL |x| < 1 x 10100
    |y| < 1 x 10100
    "
    ° ' " up to second
    "
    Pi 10 digits "

    Programmable features:

    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.