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
 
Volume
  
Mass
  $1$ stone $= 14$ pounds
 $1$ pound $= 16$ ounces
 $1$ ton $= 160$ pounds
 
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 $\underline{3 \ feet \ \ 6 \ inches}$.