Unit Conversions

In an exam question, you may be asked to give your answer in a different unit than you normally use. To do this, you need to know how to convert units .

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SI Units

SI units are the standard units we use to measure quantities. The main SI units are shown in the table below.

Quantity	Unit	Symbol
time	second	\text
length	metre	\text
mass	kilogram	\text
electric current	amp	\text
temperature	kelvin	\text
amount of a substance	mole	\text
luminous intensity	candela	\text

All other units can be made by combining SI units . You can work out which SI units make up another unit using the equation for that quantity.

Example: Express 1 \text < N>(newton) in SI units.

[2 marks]

The newton is the unit of force and the equation we use to calculate force is \bold

The unit of mass is the kilogram \text

The unit of acceleration is metres per square second \text<(m/s>^2\text

Because mass and acceleration are multiplied together in the equation, you multiply these units together.

\bold \textbf < N>\bold \textbf < kgm/s>\bold

Unit Prefixes

Prefixes are used to avoid writing large numbers or standard form. You should be aware of the following prefixes and their meanings:

Prefix	Symbol	Standard Form	Number
giga	G	\times 10^9	\times 1\, 000 \, 000 \, 000
mega	M	\times 10^6	\times 1 \, 000 \, 000
kilo	k	\times 10^3	\times 1 \, 000
milli	m	\times 10^	\times 0.001
micro	\mu	\times 10^	\times 0.000\, 001
nano	n	\times 10^	\times 0.000 \, 000\, 001

1 \text< GW>= 10^9 \text < W>= 1 \, 000 \, 000 \, 000 \text
5 \, \mu \text = 5 \times 10^ \text < m>= 0.000 \, 005 \text < m>.
2.5 \text < kg>= 2.5\times 10^3 \text < g>= 2500 \text
500 \text < nm>= 500 \times 10^ \text < m>= 5 \times 10^ \text < m>= 0.000 \, 000 \, 7 \text

You should also know the meaning of the following words:

Name	Number	Standard Form	Number of Zeros
Thousand	1 \, 000	1 \times 10^3	3
Million	1 \, 000 \, 000	1 \times 10^6	6
Billion	1\, 000 \, 000 \, 000	1 \times 10^9	9

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Common Conversions

There are some common conversions you should also know.

Miles \bold Kilometres

There are 1.61 \text < km>in every mile. This means we can use the following equations to convert between kilometres and miles:

Degrees Celsius \bold Kelvin

Absolute zero, 0\text < K>is equal to -273 \degree \text . This means we can use the following equations to convert between degrees Celsius and kelvin.

\text=\degree \text + 273 \, \, \, \, \, \, \degree \text=\text - 273

\text= the temperature in kelvin \text
\degree \text= the temperature in degrees Celsius (\degree \text)

Tonne \bold Kilogram

1 tonne is equal to 1000 kilograms. You therefore use the following equations to convert between tonnes and kilograms: