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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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4

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!


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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


7

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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


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


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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


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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

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