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Maths

Powers and roots - Higher

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In this Revision Bite we are going to look at standard index form and zero, negative and fractional powers.

Standard index form

Standard index form is also known as standard form. It is very useful when writing very big or very small numbers.

earth and sun

In standard form, a number is always written as: A × 10 n

A is always between 1 and 10. n tells us how many places to move the decimal point.

Example : Write 15 000 000 in standard index form.

Solution

15 000 000 = 1.5 × 10 000 000

This can be rewritten as:

1.5 × 10 × 10 × 10 × 10 × 10 × 10 × 10

= 1. 5 × 10 7

You can convert from standard form to ordinary numbers, and back again. Have a look at these examples:

3 x 104 = 3 × 10 000 = 30 000 (Since 104 = 10 × 10 × 10 × 10 = 10 000)

2 850 000 = 2.85 × 1 000 000 = 2.85 × 106 Make the first number between 1 and 10.

0.000467 = 4.67 × 0.0001 = 4.67 × 10 -4

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