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UNIVERSITY OF GLOUCESTERSHIRE
USE OF
CALCULATOR
For Numeracy Workshopand
SLE 103 'Confidence Counts' module
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Week 3
USE OF CALCULATOR
Aims
At the end of this session you should have:
revised the use of basic calculator functions: +, -, x, , ( )
considered the use of new functions:a) Powers
b) Rootsc) Fractionsd) Reciprocale) Factorialf) Exponential
learned to put the calculator into statistics mode.
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THE CALCULATOR
You will almost certainly be familiar with the use of a calculator forthe basic arithmetic functions. We will be looking at calculatorfunctions in more depth.
Different makes and models of calculators have different keys forsome functions.
As you work through the exercises in this chapter highlight thekeys which you use on your calculator.
Now try the following:
EXERCISE A
Can you find :
1) (-) or +/-
2) xy
3) xy or x1/y
4) ab/c
5) MODE
6) ( or [(..
7) x!
8)x
1or x-1
9) EXP
10) M+
3
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CALCULATIONS
Before each calculation make an estimate of roughly what you
expect the answer might be. The full answers are given at the end
of the chapter.
Eg
Use your calculator to evaluate:
12.3 x 4.027.36
Rough check: (12 x 4) 7 = 48 7 7
Calculator answer 6.7182065
Try the following exercise, giving a rough estimate of the answerbefore doing the calculation. You will find answers on page 14.
EXERCISE B
Evaluate:
1) 0.05 x 3.264.9
2) 5.78 + 3.936 6.482
3) 2.63 3.72 + 7.41
4) 3.2(5.1 + 2.78)
5) (0.007 - 1.56)3.5
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Use of brackets
Eg
Calculate 20_6 + 4
20_ = 20 = 26 + 4 10
But this may not be the answer given by your calculator.
So, is your calculator faulty?
Not really. It is just answering a slightly different question.
It has calculated 20 6 , and then added 4.
To make your calculator perform the correct calculation, use brackets
as shown:
20_(6 + 4)
AC 20 [(.. 6 + 4 ..)] = 2
In the following exercise use brackets where necessary.
EXERCISE CFind the value of:
1) 35____7.2 3.6
2) 4.01 + 2.359.7
3) 3.81 + 12.30.4 6.5
Answers can be found on page 14.
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The FACTORIAL key x!
Use your calculator to evaluate 6!
Press 6 and then the x! key.
6! = 720
Why? Because 6! is short-hand for 6 x 5 x 4 x 3 x 2 x 1 = 720
In the same way 9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362880
Factorials are used in the mathematics of choosing and arranging, in
probability and in permutations and combinations.
EXERCISE D
Calculate:
1) 5!
2) 7!
3) 8!
4) 6!3!
5) 10!4!
Answers can be found on page 14.
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The RECIPROCAL key
On some calculators this is x
1and on others x-1
This is a very useful facility to use when dealing with formulae,
including those used in present value and discountcalculations.
Eg Calculate 1_25
Enter 25 and then use the reciprocal key:
1 = 0.0425
Now try this exercise:
EXERCISE E
1) 1__1000
2) 1__0.05
3) 1______
(14.2 2.7)
4) 1_152
Answers can be found on page 14.
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The FRACTIONS key ab/c
This is definitely one of the most useful and time-saving keys on yourcalculator.
To input a fraction such as
4
3enter 3 ab/c 4
The calculator will display it as 3 4
To input a mixed number such as 13
2, enter 1 ab/c 2 ab/c 3
The calculator will display it as 1 2 3
Then add, subtract, multiply and divide as you would with whole
numbers.
Eg3
2+
5
4
2 ab/c 3 + 4 ab/c 5 = 1 7 15 = 115
7
Now try the following exercise:
EXERCISE F
1)4
1+
7
3
2)8
3-
12
5
8
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3)2
1(
4
3+
5
2)
4) (42
1+ 2
3
1) x
4
1
5) 231 x 1
71 +
81
Answers can be found on page 14.
The associated d/c key is also very useful for converting mixed
numbers into improper (or top-heavy) fractions and back again.
Eg 23
1=
3
7
2 ab/c 1 ab/c 3 d/c gives 7 3 in the calculator
display.
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POWERS
If a number is to be squared, you can use the x2 key.
For higher powers you should use the xy or ^ key.
Eg Evaluate 4.562 (Rough check: 5 x 5 = 25)
4.56 x2 = 20.7936
Eg Find 2.355
2.35 xy 5 = 71.670315
Eg Find (-2)7
( (-) 2 ) xy 7 = -128
Powers can be positive or negative and need not be whole numbers.
Now try the following exercise
EXERCISE G
1) 74
2) 0.135
3) (-4)8
4) 3-2
5) 24 x 52.8
6) 1.53.2 + 0.91.3
Answers can be found on page 15.
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ROOTS
For square roots a key is provided and some calculators
also have a 3 key for cube roots.
For higher roots look for either
y
x orx
or x . This
y/1
is usually close to the powers key.
Eg
Find 5 32
5y
x 32 = 2
On older calculators the order of operating the keys may be different
i.e. 32 y x 5 = 2
Powers and roots can also be combined:
Eg
Calculate ( 3 570. )4
3y
x 0.57 = xy 4 = 0.4726066
Now try the following exercise
EXERCISE H
1) (2.3)1/4 or 4 32. 2) 0360.
3) (1.54)1/5 or 5 541. 4) (12.7)2/3
5) ( 1420. )5 6) (3.56)1.5
Answers can be found on page 15.
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The EXPONENTIAL key EXP
This is used for dealing with very large or very small numberspresented in standard form.
Eg
Find 2.3 x 105
Enter 2.3 EXP 5 = 230000
Eg
Calculate 3.142 x 10-2 + 5.32 x 103
3.142 EXP ( -) 2 + 5.32 EXP 3 = 5320.03142
Eg
Calculate 5.089 x 104
4.78 x 10-3
5.089 EXP 4 4.78 EXP ( -) 3 = 10646443.51
EXERCISE J
1) 4.3 x 102 - 2.1 x 103
2) -7.82 x 10-1 + 3.2 x 102
3) 4.56 x 10-3 x 8.3 x 104
4) 1.78 x 1023.5 x 104
5) 3.7 x 105 + 1.02 x 1027.8 x 103
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Using other MODES
Scientific calculators function in several modes to enable you to
calculate:
statistical information such as the mean and standard
deviation from a given set of numerical data.
the Pearson Correlation Coefficient and regression line
equation coefficients for given data.
arithmetic in other number bases such as binary.
Use your MODE key.
It will offer you between 2 and 10 possible different modes
(depending on make and model). One will be STATISTICS,
indicated by SD or STAT appearing in the calculator display.Check that you can find STATISTICS mode and return to ordinary
computational mode afterwards.
Using the memory keys: M M+ M- STO RCL
It is difficult to give general guides to the use of the memory keys
because of the lack of standardisation of calculator keyboards and
functions. If you would like to find out how to use your calculators
memory keys (and do not have the instruction booklet) ask the tutor
for help.
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ANSWERS
Exercise B 1. 0.033265306
2. 3.234
3. 1.06
4. 25.216
5. 5.4355
Exercise C 1. 9.722222222
2. 0.655670103
3. 2.640983607
Exercise D 1. 120
2. 5040
3. 40320
4. 1205. 151200
Exercise E 1. 0.001 or 1-03
2. 20
3. 0.086956521
4. 0.004444444 or 4.444444444-03
Exercise F
1.28
192. -
24
13.
40
234. 1
24
175. 2
24
19
14
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Exercise G
1. 2401
2. 0.0000371293 or 3.71293-05
3. 65536
4. 0.111111111
5. 1449.559327
6. 4.532089773
Exercise H
1. 1.231493032
2. 0.189736659
3. 1.0901948954. 5.443386192
5. 7.598377408-03 or 0.0075983774
6. 6.716994566
Exercise J
1. 1670
2. 319.218
3. 378.48
4. 5.085714286-03 or 0.0050857143
5. 47.44897436