Converting units: metric and imperial

In a nutshell

Converting between units involves multiplying or dividing by a conversion factor. Metric units should be learnt off by heart whereas imperial units will always be given to you in the question - however it's always a good idea to get practice with both!

Common metric units of measure and their conversions

There are units to describe all measures: length, volume and mass. Below are the common metric conversions for each. To figure out whether to multiply or divide, work out whether you are going from big to small or from small to big. Divide if you are converting to the 'bigger' unit and multiply if you are converting to the 'smaller' unit.

Type of measurement	Metric conversion	Abbreviation
Length		$mm$ - millimetres $cm$ - centimetres $m$ - metres $km$ - kilometres
Volume		$ml$ - millilitres $cl$ - centilitres $l$ - litres
Mass		$mg$ - milligrams $g$ - grams $kg$ - kilograms $t$ - tonnes

Note: Another common conversion is that one millilitre is equal to one centimetre cubed: $1ml=1cm^3$ .

Example 1

What is $1.34$ litres in millilitres?

Work out the conversion factor.

$1l=1000ml$ so the conversion factor is one thousand.

A millilitre is smaller than a litre: the conversion is from a big unit to a smaller one so multiply the value by the conversion factor.

$1.34\times 1000 = \underline{1340ml}$

Imperial units of measure

Imperial units of measure are much less commonly used and you are not expected to know them off by heart. Conversion factors involving imperial units will always be given but some examples are listed in the table below.

Type of measurement	Common imperial conversion	Conversion factor
Length	$1$ yard $=3$ feet $1$ foot $=12$ inches	$3$ $12$
Volume	$1$ gallon $= 8$ pints	$8$
Mass	$1$ stone $= 14$ pounds $1$ pound $= 16$ ounces $1$ ton $= 160$ pounds	$14$ $16$

Note: Don't get confused between tonnes and tons - they sound the same but are very different!

Example 2

What is $18$ pounds in stone? Give your answer to two decimal places. (There are $14$  pounds in a stone.)

Work out the conversion factor.

$14$

Fourteen pounds are equal to one stone and so a stone is bigger: the conversion is from a smaller unit to a bigger one so divide by the conversion factor.

$18\div14=1.28571429=\underline{1.29 \ (2 \ d.p.)}$

Imperial and metric units combined

It is common to need to convert between metric and imperial units when given a conversion rate. Simply work out the conversion factor and decide whether to multiply or divide.

Example 3

$1$ foot $\approx 30cm$ and $1$ foot $=12$ inches. Andrea's hair is currently $105cm$ long. How long is her hair in feet and inches?

To go from centimetres to feet, divide by the conversion factor, thirty, since one foot is approximately equal to $30$ centimetres.

$105\div30=3.5$

If a foot is twelve inches, then half a foot must be half of twelve.

$12\div2=6$

Therefore, $105cm$ is approximately $\underline{3 \ feet \ \ 6 \ inches}$ .