Casio fx-7400G User manual

Basic Calculations
In the RUN Mode you can perform arithmetic calculations (addi-
tion, subtraction, multiplication, division) as well as calculations in-
volving scientific functions.
1. Addition and Subtraction
2. Multiplication
3. Division
4. Quotient and Remainder Division
5. Mixed Calculations
6. Other Useful Calculation Features
7. Using Variables
8. Fraction Calculations
9. Selecting Value Display Modes
10. Scientific Function Calculations
Chapter 2

14
Basic Calculations Chapter 2
1. Addition and Subtraction
Example 6.72 + 9.08
g.hc+j.aiw
You can input the operation just as it is written. This capability is called “true alge-
braic logic.”
Be sure to press Ato clear the display before starting a new calculation.
2. Multiplication
Example 3.71 ×4.27
Ad.hb*
e.chw
• The range of this calculator is –9.99999999 ×1099 to +9.99999999 ×1099.
3. Division
Example 64 ÷4
Age/ew
Parentheses also come in handy when performing division. For full details on using
parentheses, see “Parentheses Calculation Priority Sequence”.
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15
Basic Calculations Chapter 2
uu
uu
uTo use parentheses in a calculation
2 ×3 + 4
Example 1 –––––––
5
You should input this calculation as: (2 ×3 + 4) ÷5
A(c*d+e)/fw
6
Example 2 –––––
4×5
You can input this calculation as: 6 ÷(4 ×5) or 6 ÷4 ÷5.
Ag/(e*f)w
Ag/e/fw
4. Quotient and Remainder Division
This calculator can produce either the quotient or the quotient and remainder of
division operations involving two integers. Use Kto display the Option Menu for
the function key menu you need to perform quotient and remainder division.
Operation
Use the RUN Mode for quotient and remainder division.
Quotient Division .......<integer>K2(CALC)2(Int÷)<integer>w
Reminder Division .....<integer>K2(CALC)3(Rmdr)<integer>w
uu
uu
uTo perform quotient division
Example To display the quotient produced by 61 ÷7
AgbK2(CALC)
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Basic Calculations Chapter 2
2(Int÷)hw
• Remember that you can use only integers in quotient division operations. You
cannot use expressions such as 2 or sin60 because their results have a decimal
part.
uu
uu
uTo perform remainder division
Example To display the remainder produced by 857 ÷48
ifh3(Rmdr)eiw
Press Qto clear the Option Menu after you finish your remainder and quotient
calculations.
• Remember that you can use only integers in remainder division operations. You
cannot use expressions such as 2 or sin60 because their results have a decimal
part.
• Quotient and remainder division can also be used with lists to divide a multiple
integers by each other in a single operation.
5. Mixed Calculations
(1) Mixed Arithmetic Calculation Priority Sequence
For mixed arithmetic calculations, the calculator automatically performs multiplica-
tion and division before addition and subtraction.
Example 1 3 + 5 ×6
Ad+f*gw
Example 2 7 ×8 – 4 ×5
Ah*i-e*fw
1234
1234
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Basic Calculations Chapter 2
(2) Parentheses Calculation Priority Sequence
Expressions enclosed inside parentheses are always given priority in a calculation.
Example 1 100 – (2 + 3) ×4
Abaa-(c+d)
*ew
Example 2 (7 – 2) ×(8 + 5)
• Amultiplication sign immediately in front of an open parenthesis can be omitted.
A(h-c)(i+f)
w
• Any closing parentheses at the end of a calculation can be omitted, no matter
how many there are.
Parenthesesarealwaysclosedintheoperationexamplespresentedinthismanual.
(3) Negative Values
Use the -key to input negative values.
Example 56 ×(–12) ÷(–2.5)
Afg*-bc/
-c.fw
(4) Exponential Expressions
Use the Ekey to input exponents.
Example (4.5 ×1075) ×(–2.3 ×10–79)
Ae.fEhf*-c.d
E-hjw
The above shows what would appear when the exponential display range is set to
Norm 1. It stands for –1.035 ×10–3, which is –0.001035.
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Basic Calculations Chapter 2
(5) Rounding
Example 74 ÷3
Ahe/dw
The actual result of the above calculation is 24.66666666… (and so on to infinity),
which the calculator rounds off. The calculator’s internal capacity is 15 digits for the
values it uses for calculations, which avoids accuracy problems with consecutive
operations that use the result of the previous operation.
6. Other Useful Calculation Features
(1) Answer Memory (Ans)
Calculation results are automatically stored in the Answer Memory, which means
you can recall the results of the last calculation you performed at any time.
uu
uu
uTo recall Answer Memory contents
Press !and then K(which is the shifted function of the -key).
This operation is represented as !Kthroughout this manual.
Example To perform 3.56 + 8.41 and then divide 65.38 by the result
Ad.fg+i.ebw
gf.di/!Kw
(2) Consecutive Calculations
If the result of the last calculation is the first term of the next calculation, you can use
the result as it is on the display without recallingAnswer Memory contents.
uu
uu
uTo perform a consecutive calculation
Example To perform 0.57 ×0.27, and then add 4.9672 to the results
Aa.fh*a.chw
+e.jghcw

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Basic Calculations Chapter 2
(3) Replay
While the result of a calculation is on the display, you can usedand eto move the
cursor to any position within the expression used to produce the result. This means
you can back up and correct mistakes without having to input the entire calculation.
You can also recall past calculations you have already cleared by pressing A.
Operation
The first press of edisplays the cursor at the beginning of the expression, while
ddisplays the cursor at the end. Once the cursor is displayed, use eto move it
right and dto move it left.
uu
uu
uTo use Replay to change an expression
Example To calculate 4.12 ×6.4 and then change the calculation to 4.12 ×7.1
Ae.bc*g.ew
d
dddh.bw
Multi-Replay
Pressing Aand then for csequentially recalls and displays past calculations.
(4) Error Recovery
Whenever an error message appears on the display, press dor eto re-display
the expression with the cursor located just past the part of the expression that caused
the error. You can then move the cursor and make necessary corrections before
executing the calculation again.
uu
uu
uTo correct an expression that causes an error
Example To recover from the error generated by performing 148 ÷0. ×3.37
instead of 148 ÷0.3 ×3.37
Abei/a.
*d.dhw

20
Basic Calculations Chapter 2
d(You could also press e.)
![d
(See below for details on making
corrections.)
w
(5) Making Corrections
Use the dand ekeys to move the cursor to the position you want to change, and
then perform one of the operations described below. After you edit the calculation,
you can execute it by pressing w, or use eto move to the end of the calculation
and input more.
uu
uu
uTo change a step
Example To change cos60 to sin60
cga
ddd
s
uu
uu
uTo delete a step
Example To change 369 × × 2 to 369 ×2
dgj**c
ddD
uu
uu
uTo insert a step
Example To change 2.362to sin2.362
c.dgx

21
Basic Calculations Chapter 2
ddddd
![
s
• When you press ![a space is indicated by the symbol ‘‘t’’. The next func-
tion or value you input is inserted at the location of ‘‘t’’. To abort the insert opera-
tion without inputting anything, move the cursor, press ![again, or press
d, eor w.
7. Using Variables
A total of 26 variables, named A through Z, are available for assignment of numeric
values. Variable contents are retained even when you turn the calculator off. Note
that when you assign a value to a variable, the calculator assigns its 15-digit internal
value.
uu
uu
uTo assign a value to a variable
Operation
<value or expression>aa<variable name: Ato Z>
Example 1 To assign 1024 to variable A
AbaceaaAw
Example 2 To display the contents of variableA
AaAw
Example 3 To clear the contents of variable A
To clear a variable, simply assign 0 to it.
AaaaAw

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Basic Calculations Chapter 2
uu
uu
uTo assign the same value to more than one variable
Operation
<value or expression>aa<start variable name>a3(~)a<end variable
name>w
Example To assign the result of 2 to variables A, B, C, D, and E
A!9caaAa3(~)
aEw
uu
uu
uTo clear the contents of all variables
In the Main Menu, select the MEM icon and press w.
Select Memory Usage.
w
Press cto scroll the display until “Alpha” is highlighted.
ccccccc
1(DEL)
Press 1(YES) to clear all variables or 4(NO) to abort the clear operation without
clearing anything.
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Basic Calculations Chapter 2
8. Fraction Calculations
(1) Fraction Display and Input
Example 1 Display of
Example 2 Display of 3
Mixed fractions (such as 3 1/4) are input and displayed as:
integer{numerator{denominator.
Improper fractions (15/7) and proper fractions (such as 1/4) are input and displayed
as: numerator{denominator.
Use the $key to input each part of a fraction.
uu
uu
uTo input a fraction
Operation
Proper Fraction or Improper Fraction Input: <numerator value>$<denominator value>
Mixed Fraction Input: <integer value>$<numerator value>$<denominator value>
Example To input 3
Press d$b$e.
Note that the maximum size of a fractional value is 10 digits, counting the integer,
numerator, and denominator digits and separator symbols. Any value longer than
10 digits is automatically converted to its equivalent decimal value.
(2) Performing Fraction Calculations
Example
Ac$f+d$b$ew
uu
uu
uTo convert between fraction and decimal values
Operation
Fraction to Decimal Conversion: M
Decimal to Fraction Conversion: M
21
–– + 3––
54
3
––
4
1
––
4
1
––
4

24
Basic Calculations Chapter 2
Example To convert the result of the previous example to a decimal and
then back to a fraction
M
M
uu
uu
uTo convert between proper and improper fractions
Operation
Mixed Fraction to Improper Fraction Conversion: !/
Improper Fraction to Mixed Fraction Conversion: !/
Example To convert the result of the previous example to an improper
fraction and then back to a proper fraction
!/
!/
• The calculator automatically reduces the results of fraction calculations. You can
use the procedure described under “Changing the Fraction Simplification Mode”
below to specify manual fraction simplification.
uu
uu
uTo perform a mixed decimal and fraction calculation
Example 5.2 ×
Af.c*b$fw
• The result of a calculation that mixes fractions and decimal values is always a
decimal value.
uu
uu
uTo use parentheses in a fraction calculation
Example
Ab$(b$d+b$e)
+c$hw
1
––
5
12
–––––– + ––
117
–– + ––
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Basic Calculations Chapter 2
(3) Changing the Fraction Simplification Mode
The initial default of the calculator is automatic simplification of fractions produced
by fraction calculations. You can use the following operation to change the fraction
simplification mode to manual.
uu
uu
uTo change the fraction simplification mode
Example To change the fraction simplification mode to manual
!Z
(Displays the Set Up Screen.)
cccc2(Man)
Q
When the fraction simplification is set to manual, you have to use the Option Menu to
simplify fractions.You can let the calculator select the divisor to use for simplification
or you can specify a divisor.
uu
uu
uTo simplify using the calculator’s divisor
Operation
Perform calculations after selecting the RUN icon in the Main Menu to enter the RUN
Mode.
To display the simplification menu: K2(CALC)
To select automatic simplification: 1(Simp)w
To specify the divisor for simplification*: 1(Simp) <Divisor>w
* You can specify only a positive integer as the divisor.
61
Example To perform the calculation 1 –– + 1 –– and reduce the result
27 9
Ab$g$ch+b$
b$jw
(The result that appears when using manual simplification is the least common mul-
tiple of the fractions used in the calculation.)
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26
Basic Calculations Chapter 2
K2(CALC)1(Simp)w
• F = 3 indicates that 3 is the divisor.
• The calculator automatically selects the smallest possible divisor for simplifica-
tion.
Repeat the above operation to simplify again.
1(Simp)w
Try once again.
1(Simp)w
This display indicates that further simplification is impossible.
uu
uu
uTo simplify using your own divisor
Example To perform the above calculation and then specify 9 as the divisor
to use for simplification
1(Simp)jw
• If the value you specify is invalid as a divisor for simplification, the calculator
automatically uses the lowest possible divisor.
1234
1234
1234
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Basic Calculations Chapter 2
9. Selecting Value Display Modes
You can make specifications for three value display modes.
Fix Mode
This mode lets you specify the number of decimal places to be displayed.
Sci Mode
This mode lets you specify the number of significant digits to be displayed.
Norm 1/Norm 2 Mode
This mode determines at what point the display changes over to exponential display
format.
Display the Set Up Screen and use the fand ckeys to highlight “Display”.
uu
uu
uTo specify the number of decimal places (Fix)
1. While the set-up screen is on the display, press 1(Fix).
2. Press the function key that corresponds to the number of decimal places you
want to set (0 to 9).
• Press [to display the next menu of numbers.
Example To specify two decimal places
1(Fix)
3(2)
Pressthe functionkey that corresponds to thenumber
of decimal places you want to specify.
• Displayed values are rounded off to the number of decimal places you specify.
• Anumber of decimal place specification remains in effect until you change the
Norm Mode setting.
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1234
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Basic Calculations Chapter 2
uu
uu
uTo specify the number of significant digits (Sci)
1. While the set-up screen is on the display, press 2(Sci).
2. Press the function key that corresponds to the number of significant digits you
want to set (0 to 9).
• Press [to display the next menu of numbers.
Example To specify three significant digits
2(Sci)
4(3)
Pressthe functionkey that corresponds to thenumber
of significant digits you want to specify.
• Displayed values are rounded off to the number of significant digits you specify.
• Specifying 0 makes the number of significant digits 10.
• Anumber of significant digit specification remains in effect until you change the
Norm Mode setting.
uu
uu
uTo specify the exponential display range (Norm 1/Norm 2)
Press 3(Norm) to switch between Norm 1 and Norm 2.
Norm 1: 10–2 (0.01)>|x|, |x| >1010
Norm 2: 10–9 (0.000000001)>|x|, |x| >1010
10. Scientific Function Calculations
Use the RUN Mode to perform calculations that involve trigonometric functions and
other types of scientific functions.
(1) Trigonometric Functions
Before performing a calculations that involves trigonometric functions, you should
first specify the default angle unit as degrees (°), radians (r), or grads (g).
kk
kk
kSetting the Default Angle Unit
The default angle unit for input values can be set using the set up screen. If you set
degrees (°) for example, inputting a value of 90 is automatically assumed to be 90°
The following shows the relationship between degrees, radians, and grads.
90°= π/2 radians = 100 grads
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29
Basic Calculations Chapter 2
uu
uu
uTo set the default angle unit
Example To change the angle unit from radians to degrees
!Z
cc1(Deg)
Q
• Once you change the angle unit setting, it remains in effect until you change it
again using the set up screen. You also should check the set up screen to find out
what the current angle unit setting is.
kk
kk
kConverting Between Angle Units
You can use the following procedure to input a value using an angle unit that is not
the current default angle unit. Then when you press w, the value will be converted
to the default angle unit.
uu
uu
uTo convert between angle units
Example To convert 4.25 radians to degrees while degrees are set as the
default angle unit
Ae.cfK[
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30
Basic Calculations Chapter 2
2(ANGL)2(r)w
kk
kk
kTrigonometric Function Calculations
Always make sure that the default angle unit is set to the required default before
performing trigonometric function calculations.
uu
uu
uTo perform trigonometric function calculations
Example 1 sin (63°52' 41")
Default angle unit: Degrees
!Zcc1(Deg)Q
sgdK[2(ANGL)[1(°' ")fc1(°' ")eb1(°' ")w
Result: 0.897859012
Example 2
Default angle unit: Radians
!Zcc2(Rad)Q
b/c(!7/d)w
Result: 2
Example 3 tan(–35grad)
Default angle unit: Grads
!Zcc3(Gra)Q
t-dfw
Result: –0.6128007881
(2) Logarithmic and Exponential Function Calculations
• Abase 10 logarithm (common logarithm) is normally written as log10 or log.
• A base e( ) logarithm (natural logarithm) is normally
written as logeor ln.
Note that certain publications use “log” to refer to base elogarithms, so you must
take care to watch for what type of notation is being used in the publications you are
working with. This calculator and manual use “log” to mean base 10 and “ln” for base e.
1234
π1
sec (–– rad) = ––––––––––
3π
cos(––rad)
3
P.29
1n
lim 1 + ––– = 2.71828...
n
n→∞

31
Basic Calculations Chapter 2
uu
uu
uTo perform logarithmic/exponential function calculations
Example 1 log1.23
lb.cdw
Result: 0.0899051114
Example 2 ln90
Ijaw
Result: 4.49980967
Example 3 To calculate the anti-logarithm of common logarithm 1.23 (101.23)
!0b.cdw
Result: 16.98243652
Example 4 To calculate the anti-logarithm of natural logarithm 4.5 (e4.5)
!ee.fw
Result: 90.0171313
Example 5 (–3)4= (–3) ×(–3) ×(–3) ×(–3)
(-d)Mew
Result: 81
Example 6 7123
h!qbcdw
Result: 1.988647795
(3) Other Functions
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)
= 40320 8K4(PROB)1(x!)w40320
3= 42
!#(36*42*49)w 4236 ×42 ×49
Random number generation K4(PROB)
(pseudo random number 4(Ran#)w(Ex.) 0.4810497011
between 0 and 1.)
1
––––––––––– = 12
11
––– – –––
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Basic Calculations Chapter 2
Example Operation Display
What is the absolute value of
the common logarithm of 3?
4
|
log 3
|
= 0.1249387366 K[1(NUM)
41(Abs)l(3/4)w0.1249387366
What is the integer part of K[1(NUM)
2(Int)(7800/96)w81
What is the decimal part of K[1(NUM)
3(Frac)(7800/96)w0.25
200 ÷6= 200/6w33.33333333
×3= *3w100
Round the value used 200/6w33.33333333
for internal calculations K[1(NUM)4(Rnd)w33.33333333
to 11 digits* *3w99.99999999
What is the nearest integer K[1(NUM)[1(Intg)
not exceeding – 3.5? -3.5w– 4
* When a Fix (number of decimal places) or Sci (number of significant digits) is in effect, Rnd
rounds the value used for internal calculations in accordance with the current Fix or Sci
specification. In effect, this makes the internal value match the displayed value.
(4) Coordinate 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).
Example To calculate rand θ° when x= 14 and y= 20.7
Operation Display
!Zcc1(Deg)Q
K[2(ANGL)[[
1(Pol()14,20.7)wAns
1–24.989–→24.98979792 (r)
2–55.928–→55.92839019 ( θ )
7800
––––– ?
96
7800
––––– ?
96