With international collaboration so important to industry and the economy, it is vital to be able to convert between metric and imperial units.

In the UK, we tend to measure large distances in miles, and smaller distances in metres. Before we can understand how to convert between these units, we must first understand the differences between centimetres, metres and kilometres.

A metre is a standard metric unit of length that can be modified by using a metric prefix such as milli, centi or kilo. These prefixes can be applied to any metric unit and you should recognise them from everyday life.

The prefix kilo means 1,000 or 10^{3} in standard form. So a kilometre is 1,000 m, a kilogram is 1,000 g and a kilowatt is 1,000 W.

The prefix centi means 0.01, 10^{-2} or a **hundredth**. A centimetre is 0.01 metres and a centilitre is 0.01L.

The prefix milli means thousandth, 0.001 or 10^{-3}.

What you may notice about the metric prefixes are that they are all **powers of 10**, whereas there are 12 inches in a foot and 5,280 feet in a mile! It’s for this reason that metric was adopted instead of the old imperial system of measures.

Metric | Imperial |
---|---|

centimetres | inches |

metres | feet |

kilometres | miles |

- Question
Convert 43 cm to metres.

1 m = 100 cm.

43 ÷ 100 = 0.43.

So 43 cm = 0.43 m.

- Question
Convert 3.4 m to millimetres.

1 m = 1,000 mm.

3.4 × 1,000 = 3,400.

So 3.4 m = 3,400 mm.

There are two ways to convert between miles and kilometres – exact and approximate conversion:

**1 mile = 1.6093.44 km** or **1 km = 0.6213712 miles.**

To approximate this value, we could say that \(\text {1 mile =}~\frac {8} {5}~\text {km}\). Because this approximation is very close to the true value, it is often used.

To convert from miles to kilometres, you first multiply by 8 then divide by 5.

\[\text{miles}~\rightarrow~\times\text{8}~\rightarrow~\div\text{5}~\rightarrow~\text{kilometres}\]

To convert from kilometres to miles, do the opposite – multiply by 5 then divide by 8.

\[\text{kilometres}~\rightarrow~\div\text{5}~\rightarrow~\times\text{8}~\rightarrow~\text{metres}\]

You do not need to remember the exact conversion, but you will be expected to know the approximation.

- Question
Convert 24 km to miles using both the approximate and exact conversions. You should not use a calculator to do the approximation.

24 × 0.6213712 = 14.91.

24 km is 14.91 miles (to two decimal places).

24 × 5 = 120.

120 ÷ 8 = 15.

24 km is approximately 15 miles.

- Question
Approximately how many km are in 35 miles?

35 ÷ 5 = 7.

7 × 8 = 56.

35 miles is approximately 56 kilometres.