Cambridge International Mathematics

132 Exponents and surds (Chapter 6)

Example 13 Self Tutor

Simplify the following, giving your answer in standard form:

a (5£ 104 )£(4£ 105 ) b (8£ 105 )¥(2£ 103 )

a (5£ 104 )£(4£ 105 )

=5£ 4 £ 104 £ 105

=20£ 10 4+5

=2£ 101 £ 109

=2£ 1010

b (8£ 105 )¥(2£ 103 )

=

8 £ 105

2 £ 103

=^82 £ 105 ¡^3

=4£ 102

To help write numbers in standard form:

² If the original number is> 10 , the power of 10 ispositive(+).

² If the original number is< 1 , the power of 10 isnegative(¡).

² If the original number is between 1 and 10 , leave it as it is and multiply it by 100.

EXERCISE 6D.1

1 Write the following as powers of 10 :

a 100 b 1000 c 10 d 100 000

e 0 : 1 f 0 : 01 g 0 : 0001 h 100 000 000

2 Express the following in standard form:

a 387 b 38 700 c 3 : 87 d 0 : 0387

e 0 :003 87 f 20 : 5 g 205 h 0 : 205

i 20 500 j 20 500 000 k 0 :000 205

3 Express the following in standard form:

a The circumference of the Earth is approximately40 075kilometres.

b The distance from the Earth to the Sun is149 500 000 000m.

c Bacteria are single cell organisms, some of which have a diameter of 0 : 0004 mm.

d There are typically 40 million bacteria in a gram of soil.

e The probability that your six numbers will be selected

for Lotto on Saturday night is 0 :000 000 141 62.

f Superfine sheep have wool fibres as low as 0 : 01 mm in

diameter.

4 Write as an ordinary decimal number:

a 3 £ 102 b 2 £ 103 c 3 : 6 £ 104 d 9 : 2 £ 105

e 5 : 6 £ 106 f 3 : 4 £ 101 g 7 : 85 £ 106 h 9 £ 108

5 Write as an ordinary decimal number:

a 3 £ 10 ¡^2 b 2 £ 10 ¡^3 c 4 : 7 £ 10 ¡^4 d 6 : 3 £ 10 ¡^5

e 1 : 7 £ 100 f 9 : 5 £ 10 ¡^4 g 3 : 49 £ 10 ¡^1 h 7 £ 10 ¡^6

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