Cambridge International Mathematics

Exponents and surds (Chapter 6) 131

10 000 = 10^4

1000 = 10^3

100 = 10^2

10 = 10^1

1=10^0

1

10 =10

¡ 1

1

100 =10

¡ 2

1

1000 =10

¡ 3

Consider the pattern alongside. Notice that each time we divide by

10 , theexponentorpowerof 10 decreases by one.

We can use this pattern to simplify the writing of very large and very small numbers.

For example, 5 000 000

=5£1 000 000

=5£ 106

and 0 :000 003

=

3

1 000 000

=

3

1

£

1

1 000 000

=3£ 10 ¡^6

STANDARD FORM

Standard form(orscientific notation) involves writing any given number asa number between 1

and 10 , multiplied by aninteger power of 10 ,

i.e., a£ 10 n where 16 a< 10 and n 2 Z:

Example 11 Self Tutor

Write in standard form: a 37 600 b 0 :000 86

a 37 600 = 3: 76 £10 000

=3: 76 £ 104

fshift decimal point 4 places to the left and£10 000g

b 0 :000 86 = 8: 6 ¥ 104

=8: 6 £ 10 ¡^4

fshift decimal point 4 places to the right and¥10 000g

Example 12 Self Tutor

Write as an ordinary number:

a 3 : 2 £ 102 b 5 : 76 £ 10 ¡^5

a 3 : 2 £ 102

=3: 20 £ 100

= 320

b 5 : 76 £ 10 ¡^5

= 000005: 76 ¥ 105

=0:000 057 6

D STANDARD FORM [1.9]

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÷ 10

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÷ 10

÷ 10

÷ 10

÷ 10

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y:\HAESE\IGCSE01\IG01_06\131IGCSE01_06.CDR Friday, 10 October 2008 9:08:28 AM PETER