Casio CFX-9970G User manual

Manual Calculations
2-1 Basic Calculations
2-2 Special Functions
2-3 Function Calculations
Chapter 2

36
2-1 Basic Calculations
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kArithmetic Calculations
• Enter arithmetic calculations as they are written, from left to right.
• Use the -key to input the minus sign before a negative value.
• Calculations are performed internally with a 15-digit mantissa. The result is
rounded to a 10-digit mantissa before it is displayed.
• For mixed arithmetic calculations, multiplication and division are given priority
over addition and subtraction.
Example Operation Display
23 + 4.5 – 53 = –25.5 23+4.5-53w–25.5
56 ×(–12) ÷(–2.5) = 268.8 56*-12/-2.5w268.8
(2 + 3) ×102= 500 (2+3)*1E2w*1500
1 + 2 – 3 ×4 ÷5 + 6 = 6.6 1+2-3*4/5+6w6.6
100 – (2 + 3) ×4 = 80 100-(2+3)*4w80
2 + 3 ×(4 + 5) = 29 2+3*(4+5w*229
(7 – 2) ×(8 + 5) = 65 (7-2)(8+5)w*365
6= 0.3 6/(4*5)w*40.3
4×5
*1“(2+3)E2” does not produce the correct result. Be sure to enter this calculation as
shown.
*2Final closed parentheses (immediately before operation of the wkey) may be omitted, no
matter how many are required.
*3A multiplication sign immediately before an open parenthesis may be omitted.
*4This is identical to 6 /4 /5 w.
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kNumber of Decimal Places, Number of Significant Digits,
Exponential Notation Range
• These settings can be made while setting up the display format (Display) with
the set up screen.
• Even after you specify the number of decimal places or the number of signifi-
cant digits, internal calculations are still performed using a 15-digit mantissa,
and displayed values are stored with a 10-digit mantissa. Use Rnd (4) of the
Numeric Calculation Menu (NUM) to round the displayed value off to the
number of decimal place and number of significant digit settings.
P.6
P.43

37
Basic Calculations 2 - 1
• Number of decimal place (Fix) and number of significant digit (Sci) settings
normally remain in effect until you change them or until your change the
exponential display range (Norm) setting. Note also, however, that Sci setting
is automatically initialized to Norm 1 whenever you enter the Financial Mode.
• To change the exponential display range (Norm) setting, press 3(Norm)
while the display format (Display) menu is on the screen. Each time you
perform this operation, the range toggles between the following two settings.
Norm 1 ........... exponential display for values outside the range of 10–2 to 1010
Norm 2 ........... exponential display for values outside the range of 10–9 to 1010
Example 100 ÷6 = 16.66666666...
Condition Operation Display
100/6w16.66666667
4 decimal places !Z ccccccccc
1 (Fix)5(4)Jw 16.6667
5 significant digits !Z ccccccccc
2 (Sci)6(g)1(5)Jw 1.6667E+01
Cancels specification !Z ccccccccc
3 (Norm)Jw 16.66666667
*1Displayed values are rounded off to the place you specify.
Example 200 ÷7 ×14 = 400
Condition Operation Display
200/7*14w400
3 decimal places !Z ccccccccc
1 (Fix)4(3)Jw 400.000
Calculation continues
using display capacity 200/7w28.571
of 10 digits *Ans × _
14w400.000
• If the same calculation is performed using the specified number of digits:
200/7w28.571
The value stored
internally is cut off to K6(g)
the number of 4(NUM)4(Rnd)w28.571
decimal places you *Ans × _
specify. 14w399.994
P.321
*1
*1

38
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kCalculations Using Variables
Example Operation Display
193.2aaAw193.2
193.2 ÷23 = 8.4 aA/23w8.4
193.2 ÷28 = 6.9 aA/28w6.9
2 - 1 Basic Calculations

39
2-2 Special Functions
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kAnswer Function
The unit’sAnswer Function automatically stores the last result you calculated by
pressing w(unless the wkey operation results in an error). The result is stored
in the answer memory.
uu
uu
uTo use the contents of the answer memory in a calculation
Example 123 + 456 = 579
789 – 579 = 210
Abcd+efgw
hij-!Kw
• The largest value that the answer memory can hold in any mode besides the
ALGBR Mode is one with 15 digits for the mantissa and 2 digits for the
exponent.
• Answer memory contents are not cleared when you press the Akey or when
you switch power off.
• Note that answer memory contents are not changed by an operation that
assigns values to value memory (such as: faaAw).
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kPerforming Continuous Calculations
The unit lets you use the result of one calculation as one of the arguments in the
next calculation. To do so, use the result of the previous calculation, which is
currently stored in Answer Memory.
Example 1 ÷3 =
1 ÷3 ×3 =
Ab/dw
(Continuing)*dw
Continuous calculations can also be used with Type A functions (x2,x-1,x!), +, –,
^(xy), x, °’ ”.
P.16

40
2 - 2 Special Functions
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kUsing the Replay Function
The Replay Function automatically stores the last calculation performed into
replay memory. You can recall the contents of the replay memory by pressing d
or e.
If you press e, the calculation appears with the cursor at the beginning. Pressing
dcauses the calculation to appear with the cursor at the end. You can make
changes in the calculation as you wish and then execute it again.
Example To perform the following two calculations
4.12 ×6.4 = 26.368
4.12 ×7.1 = 29.252
Ae.bc*g.ew
dddd
h.b
w
• A calculation remains stored in replay memory until you perform another
calculation or change modes.
• The contents of the replay memory are not cleared when you press the A
key, so you can recall a calculation and execute it even after performing the all
clear operation. Note, however, that replay memory contents are cleared
whenever you change to another mode or menu.
• After you press A, you can press for cto recall previous calculations, in
sequence from the newest to the oldest (Multi-Replay Function). Once you
recall a calculation, you can use eand dto move the cursor around the
calculation and make changes in it to create a new calculation. Note, however,
that multi-replay memory contents are cleared whenever you change to
another menu.
Example
Abcd+efgw
cde-fghw
A
f(One calculation back)
f(Two calculations back)

41
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kMaking Corrections in the Original Calculation
Example 14 ÷0 ×2.3 entered by mistake for 14 ÷10 ×2.3
Abe/a*c.dw
Press dor e.
Make necessary changes.
d![b
Execute it again.
w
kk
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kUsing Multistatements
Multistatements are formed by connecting a number of individual statements for
sequential execution. You can use multistatements in manual calculations and in
programmed calculations. There are two different ways that you can use to
connect statements to form multistatements.
• Colon (:)
Statements that are connected with colons are executed from left to right, without
stopping.
• Display Result Command (^^
^^
^)
When execution reaches the end of a statement followed by a display result
command, execution stops and the result up to that point appears on the display.
You can resume execution by pressing the wkey.
Special Functions 2 - 2
Cursor is positioned automatically at the
location of the cause of the error.

42
Example 6.9 ×123 = 848.7
123 ÷3.2 = 38.4375
AbcdaaA!W6(g)
5(:)g.j*aA!W
5(^)aA/d.cw
w
• Note that the final result of a multistatement is always displayed, regardless of
whether it ends with a display result command.
• You cannot construct a multistatement in which one statement directly uses the
result of the previous statement.
Example 123 ×456: ×5
Invalid
Intermediate result at point
where “
^ ” is used.
2 - 2 Special Functions

43
2-3 Function Calculations
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kFunction Menus
This calculator includes five function menus that give you access to scientific
functions that are not printed on the key panel.
• The contents of the function menu differ according to the mode you entered
from the Main Menu before you pressed the Kkey.The following examples
show function menus that appear in the RUN or PRGM Mode.
uu
uu
uHyperbolic Calculations (HYP) [OPTN]-[HYP]
•{sinh}/{cosh}/{tanh} ... hyperbolic {sine}/{cosine}/{tangent}
•{sinh-1}/{cosh-1}/{tanh-1} ... inverse hyperbolic {sine}/{cosine}/{tangent}
uu
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uProbability/Distribution Calculations (PROB) [OPTN]-[PROB]
•{x!} ... {press after inputting a value to obtain the factorial of the value.}
•{nPr}/{nCr} ... {permutation}/{combination}
•{Ran#}... {pseudo random number generation (0 to 1)}
•{P(}/{Q(}/{R(} ... probability {P(t)}/{Q(t)}/{R(t)}
•{t(} ... {value of normalized variate t(x)}
uu
uu
uNumeric Calculations (NUM) [OPTN]-[NUM]
•{Abs} ... {select this item and input a value to obtain the absolute value of the
value.}
•{Int}/{Frac} ... select the item and input a value to extract the {integer}/
{fraction} part.
•{Rnd} ... {rounds off the value used for internal calculations to 10 significant
digits (to match the value in the Answer Memory), or to the number of
decimal places (Fix) and number of significant digits (Sci) specified by
you.}
•{Intg} ... {select this item and input a value to obtain the largest integer that is
not greater than the value.}
P.272

44
2 - 3 Function Calculations
uu
uu
uAngle Units, Coordinate Conversion, Sexagesimal Operations (ANGL)
[OPTN]-[ANGL]
•{°}/{r}/{g} ... {degrees}/{radians}/{grads} for a specific input value
•{°’ ”} ... {specifies degrees (hours), minutes, seconds when inputting a
sexagesimal value}
←
•{°’ ”} ... {converts decimal value to sexagesimal value}
←
• The {°’ ” } menu option appears only when there is a calculation result shown
on the display.
•{Pol(}/{Rec(} ... {rectangular-to-polar}/{polar-to-rectangular} coordinate
conversion
uu
uu
uEngineering Notation Calculations (ESYM) [OPTN]-[ESYM]
•{m}/{
µ}/{n}/{p}/{f} ... {milli (10-3)}/{micro (10-6)}/{nano (10-9)}/{pico (10-12)}/
{femto (10-15)}
•{k}/{M}/{G}/{T}/{P}/{E} ... {kilo (103)}/{mega (106)}/{giga (109)}/{tera (1012)}/
{peta (1015)}/{exa (1018)}
←
•{ENG}/{ENG} ... shifts the decimal place of the displayed value three digits to
the {left}/{right} and {decreases}/{increases} the exponent by three.
When you are using engineering notation, the engineering symbol is
also changed accordingly.
←
• The {ENG} and {ENG} menu options appear only when there is a calculation
result shown on the display.
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kAngle Units
• Once you specify an angle unit, it remains in effect until you specify a different
one. The specification is retained even if you turn power off.
• Be sure to specify “Comp” for Calculation/binary, octal, decimal, hexadecimal
mode.
Example Operation Display
To convert 4.25 rad to degrees: !Zcccc
1(Deg)J4.25K6(g)
5(ANGL)2(r)w243.5070629
47.3°+ 82.5rad = 4774.20181° 47.3+82.52(r)w4774.20181
P.5

45
Function Calculations 2 - 3
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kTrigonometric and Inverse Trigonometric Functions
• Be sure to set the angle unit before performing trigonometric function and
inverse trigonometric function calculations.
• Be sure to specify “Comp” for Calculation/binary, octal, decimal, hexadecimal
mode.
Example Operation Display
sin 63°= 0.8910065242 !Zcccc
1(Deg)J
s63w0.8910065242
cos ( πrad) = 0.5 !Zcccc
32(Rad)J
c(!7/d)w0.5
tan (– 35gra) =
– 0.6128007881 !Zcccc
3(Gra)J
t-35w–0.6128007881
2 •sin 45°×cos 65°
= 0.5976724775 !Zcccc
1(Deg)J
2*s45*c65w*10.5976724775
cosec 30°= 1 = 2 1/s30w2
sin30°
sin-10.5 = 30°
(xwhen sinx= 0.5) !S0.5*2w30
*1*can be omitted.
*2Input of leading zero is not necessary.
P.5
π
(90°= ––– radians = 100 grads)
2
P.5

46
P.5
2 - 3 Function Calculations
kk
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kLogarithmic and Exponential Functions
• Be sure to specify “Comp” for Calculation/binary, octal, decimal, hexadecimal
mode.
Example Operation Display
log 1.23 (log101.23)
= 8.990511144 ×10–2 l1.23w0.08990511144
In 90 (loge90) = 4.49980967 I90w4.49980967
101.23 = 16.98243652
(To obtain the antilogarithm
of common logarithm 1.23) !01.23w16.98243652
e4.5 = 90.0171313
(To obtain the antilogarithm
of natural logarithm 4.5) !e4.5w90.0171313
(–3)4= (–3) ×(–3) ×(–3)
×(–3) = 81 (-3)M4w81
–34= –(3 ×3 ×3 ×3) = –81 -3M4w– 81
1
7(= 1237)123
= 1.988647795 7!q123w1.988647795
2 + 3 ×3– 4 = 10 2+3*3!q64-4w*110
64
*1^ (xy) and xtake precedence over multiplication and division.
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kHyperbolic and Inverse Hyperbolic Functions
• Be sure to specify “Comp” for Calculation/binary, octal, decimal, hexadecimal
mode.
Example Operation Display
sinh 3.6 = 18.28545536 K6(g)2(HYP)
1(sinh)3.6w18.28545536
cosh 1.5 – sinh 1.5 K6(g)2(HYP)
= 0.2231301601 2(cosh)1.5-1(sinh)1.5w0.2231301601
= e–1.5 I!Kw – 1.5
(Proof of cosh x±sinh x= e±x)
cosh
–1
20 = 0.7953654612 K6(g)2(HYP)
15
5(cosh–1)(20/15)w0.7953654612
Determine the value of x
when tanh4 x= 0.88
x= tanh-10.88
K6(g)2(HYP)
4
= 0.3439419141 6(tanh–1)0.88/4w0.3439419141
P.5

47
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kOther Functions
• Be sure to specify “Comp” for Calculation/binary, octal, decimal, hexadecimal
mode.
Example Operation Display
+=3.65028154 !92+!95w3.6502815425
(–3)2= (–3) ×(–3) = 9 (-3)xw 9
–32= –(3 ×3) = –9 -3xw – 9
(3!X-4!X)
!Xw 12
8! (= 1 ×2 ×3 ×....×8) 8K6(g)3(PROB)
= 40320 1(x!)w40320
3= 42
!#(36*42*49)w 4236 ×42 ×49
Random number generation K6(g)3(PROB)
(pseudo random number 4(Ran#)w(Ex.) 0.4810497011
between 0 and 1)
What is the absolute value of
the common logarithm of 3?
4
|
log 3
|
= 0.1249387366 K6(g)4(NUM)
41(Abs)l(3/4)w0.1249387366
What is the integer part of K6(g)4(NUM)
– 3.5? 2(Int)-3.5w– 3
What is the decimal part of K6(g)4(NUM)
– 3.5? 3(Frac)-3.5w– 0.5
What is the nearest integer K6(g)4(NUM)
not exceeding – 3.5? 5(Intg)-3.5w– 4
P.5
Function Calculations 2 - 3
1
––––––––––– = 12
11
––– – –––
34

48
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kCoordinate Conversion
uu
uu
uRectangular Coordinates uu
uu
uPolar Coordinates
• With polar coordinates, θ can be calculated and displayed within a range of
–180°< θ <180°(radians and grads have same range).
• Be sure to specify “Comp” for Calculation/binary, octal, decimal, hexadecimal
mode.
Example To calculate rand θ° when x= 14 and y= 20.7
Operation Display
!Zcccc1(Deg)J
K6(g)5(ANGL)6(g)
1(Pol()14,20.7)wAns
1–24.989–→24.98979792 (r)
2–55.928–→55.92839019 ( θ )
Example To calculate xand ywhen r= 25 and θ = 56°
Operation Display
!Zcccc1(Deg)J
K6(g)5(ANGL)6(g)
2(Rec()25,56)wAns
1–13.979–→13.97982259 (x)
2–20.725–→20.72593931 (y)
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kPermutation and Combination
uu
uu
uPermutation uu
uu
uCombination
• Be sure to specify “Comp” for Calculation/binary, octal, decimal, hexadecimal
mode.
P.5
2 - 3 Function Calculations
n!n!
nPr= ––––– nCr= –––––––
(n– r)! r! (n– r)!
P.5

49
Example To calculate the possible number of different arrangements
using 4 items selected from among 10 items
Formula Operation Display
10P4= 5040 10K6(g)3(PROB)
2(nPr)4w5040
Example To calculate the possible number of different combinations of
4 items that can be selected from among 10 items
Formula Operation Display
10C4= 210 10K6(g)3(PROB)
3(nCr)4w210
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kFractions
• Fractional values are displayed with the integer first, followed by the numerator
and then the denominator.
• Be sure to specify “Comp” for Calculation/binary, octal, decimal, hexadecimal
mode.
Example Operation Display
2$5+3$1$4w3{13{20
(Conversion to decimal*1)M3.65
1$2578+1$4572w6.066202547E–04*2
(Norm 1 display format)
1$2*..
..
.5w0.25*3
1$(1$3+1$4)w*41{5{7
*1Fractions can be converted to decimal values and vice versa.
*2When the total number of characters, including integer, numerator, denominator and
delimiter marks exceeds 10, the input fraction is automatically displayed in decimal
format.
*3Calculations containing both fractions and decimals are calculated in decimal format.
*4You can include fractions within the numerator or denominator of a fraction by putting the
numerator or denominator in parentheses.
Function Calculations 2 - 3
P.5
2113
–– + 3 ––= 3 –––
5420
= 3.65
11
––––– + –––––
2578 4572
= 6.066202547 ×10–4
1
–– ×0.5 = 0.25
2
15
–––––– = 1––
11 7
–– + ––
34

50
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kEngineering Notation Calculations
Input engineering symbols using the engineering notation menu.
• Be sure to specify “Comp” for Calculation/binary, octal, decimal, hexadecimal
mode.
Example Operation Display
!Zccccc
cccc4(Eng)J
999k (kilo) + 25k (kilo) 999K
= 1.024M (mega) 6(g)6(g)1(ESYM)
6(g)1(k)+251(k)w1.024M
9 ÷10 = 0.9 = 900m (milli) 9/10w900.m
K6(g)6(g)1(ESYM)
6(g)6(g)
←
3(ENG)*10.9
←
3(ENG)*10.0009k
2(ENG)*20.9
2(ENG)*2900.m
*1Converts the displayed value to the next higher engineering unit, by shifting the decimal
point three places to the right.
*2Converts the displayed value to the next lower engineering unit, by shifting the decimal
point three places to the left.
P.44
P.5
2 - 3 Function Calculations

51
kk
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kLogical Operators (AND, OR, NOT) [OPTN]-[LOGIC]
The logical operator menu provides a selection of logical operators.
•{And}/{Or}/{Not} ... {logical multiplication}/{logical addition}/{negation}
• Be sure to specify “Comp” for Calculation/binary, octal, decimal, hexadecimal
mode.
Example What is the logical product of A and B when A = 3 and B = 2?
A AND B = 1
Operation Display
3aaAw
2aaBw
aAK6(g)6(g)
4(LOGIC)1(And)aBw1
Example What is the logical sum of A and B when A = 5 and B = 1?
A OR B = 1
Operation Display
5aaAw
1aaBw
aAK6(g)6(g)
4(LOGIC)2(Or)aBw1
Example Negate A when A = 10.
NOT A = 0
Operation Display
10aaAw
K6(g)6(g)
4(LOGIC)3(Not)aAw0
Function Calculations 2 - 3
P.5

52
2 - 3 Function Calculations
About Logical Operations
• A logical operation always produces either 0 or 1 as its result.
• The following table shows all of possible results that can be produced by AND
and OR operations.
Value or ExpressionA Value or Expression B AAND B A OR B
A G0BG011
A G0 B = 0 0 1
A = 0 B G001
A = 0 B = 0 0 0
• The following table shows the results produced by the NOT operation.
Value or Expression A NOTA
A G00
A = 0 1