# Converting numbers to standard form and vice-versa

## Introduction

When working with really large or small numbers it is common to write the numbers in **standard form** as a power of ten.

A number written in standard form is of the form \(a\) × 10\(^{n}\) where \(a\) must be a number between 1 and 10.

For example, 730 = 7.3 × 100 = 7.3 × 10\(^{2}\) and 0.006 = 6 ÷ 1000 = 6 × 10\(^{-3}\).

*For large numbers the power of 10 will be positive. For small numbers the power of 10 will be negative.*

## Example questions on converting numbers to standard form and vice-versa

### Example 1 - Converting a number into standard form

Write the numbers a) 5 600 000 and b) 0.000465 in standard form.

a) 5 600 000 = 5.6 × 1 000 000 = 5.6 × 10\(^{6}\).

b) 0.000465 = 4.65 ÷ 10 000 = 4.65 × 10\(^{-4}\).

### Example 2 - Converting from standard form into an ordinary number

Write the numbers a) 7.63 × 10\(^{4}\) and b) 9.01 × 10\(^{-3}\) in standard form.

a) 7.63 × 10\(^{4}\) = 7.63 × 10 000 = 76 300.

b) 9.01 × 10\(^{-3}\) = 9.01 ÷ 1 000 = 0.00901.

## Worksheets to practise converting to and from standard form

Try these worksheets to practise your skills.