Conversion factors
In a nutshell
Conversion factors are used to convert between different units of measure. You need to be able to recall common conversions and apply them to find out harder conversions involving areas and volumes.
Common units of measure
These are the most common units that are used in daily life as well as what each unit measures.
Measurement  units of measure (simplified unit) 
Length  millimetres ($mm$), centimetres ($cm$), metres ($m$), kilometres ($km$) 
Area  square millimetres ($mm^2$), square centimetres ($cm^2$), square metres ($m^2$), square kilometres ($km^2$) 
Volume  cubic millimetres ($mm^3$), cubic centimetres ($cm^3$), cubic metres ($m^3$), millilitres ($ml$), litres ($l$) 
Mass  grams ($g$), kilograms ($kg$), tonnes ($tonnes$) 
Speed  kilometres per hour ($km/h$), metres per second ($m/s$) 
Note: These units are called metric units.
Note: Mass is the scientific term for how heavy something is. In everyday language, people say 'weight', which is related, but not exactly the same.
Converting between units
Here's a table of all the different conversion rates:
measurement  conversion rates 
Length   $1cm=10mm$
 $1m=100cm$
 $1km=1000m$

Volume   $1l =1000cm^3=1000ml$
 $1cm^3=1ml$

Mass   $1kg=1000g$
 $1\,tonne=1000kg$

Example 1
i) How many kilograms are in $4500$ grams?
ii) How many millimetres are in $5$ metres?
i)
Use the table to find the conversion ratio from kilograms to grams:
$1kg =1000g$
Divide both sides by $1000$ to find the value of $1g$:
$1g=0.001kg$
Multiply both sides by $4500$ to find the value of $4500g$:
$4500g=4500\times0.001kg$
$\underline{4500g=4.5kg}$
ii)
First, convert from metres to centimetres:
$1m=100cm$
$5m=5\times100cm$
$5m=500cm$
Then, convert from centimetres to millimetres:
$1cm=10mm$
$500cm=500\times10mm$
$\underline{500cm=5000mm}$
Harder conversions: areas and volumes
It is possible to apply length conversions to areas and volumes.
Example 2
Convert $1m^2$ to $cm^2$.
To convert between areas, recall the conversion from metres to centimetres:
$1m=100cm$
To find the conversion from square metres to square centimetres, square both sides of this equation:
$(1m)^2=(100cm)^2$
$1^2m^2=100^2cm^2$
$\underline{1m^2=10000cm^2}$
Note: Notice how $1m^2\neq100cm^2$! That is a very common mistake to make.
Example 3
Convert $2500mm^3$ to $cm^3$.
First write down the conversion from millimetres to centimetres:
$1cm=10mm$
For cubic millimetres, cube both sides:
$(1cm)^3=(10mm)^3$
$1^3cm^3=(10)^3mm^3$
$1cm^3 = 1000mm^3$
This is the conversion rate. Now, proceed as normal.
Divide both sides by $1000$ to find the value of $1mm^3$:
$1mm^3=(1\div1000)cm^3=0.001cm^3$
Multiply both sides by $2500$ to find the value of $2500cm^3$:
$2500mm^3=2500\times0.001cm^3$
$\underline{2500mm^3=2.5cm^3}$
Harder conversions: speed
The common metric units of speed are $km/h$ (kilometres per hour) and $m/s$ (metres per second). You will need to know how to convert between these two.
Example 4
Convert $3km/h$ to $m/s$ to two decimal places.
Recall the conversions from kilometres to metres and hours to seconds:
$1km=1000m$
$1h=60m=60\times60s$
$1h=3600s$
Substitute these directly into the speed to convert:
$3km/h=3\times(1000m)/(3600s)=\frac{3\times1000}{3600}m/s$
$3km/h=\frac{3000}{3600}m/s$
$\underline{3km/h=0.83m/s}$