Unit Conversions Worksheets, Questions and Revision

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.

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	$text{s}$
length	metre	$text{m}$
mass	kilogram	$text{kg}$
electric current	amp	$text{A}$
temperature	kelvin	$text{K}$
amount of a substance	mole	$text{mol}$
luminous intensity	candela	$text{cd}$

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 $bold{F=ma}$

The unit of mass is the kilogram $text{(kg)}$

The unit of acceleration is metres per square second $text{(m/s}^2text{)}$

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

$text{ N}=textcolor{00d865}{text{kg}} times textcolor{10a6f3}{text{m/s}^2}=text{kgm/s}^2$

Therefore,

$bold{1} textbf{ N} bold{=1} textbf{ kgm/s} bold{^2}$

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	$times 10^{-3}$	$times 0.001$
micro	$mu$	$times 10^{-6}$	$times 0.000, 001$
nano	n	$times 10^{-9}$	$times 0.000 , 000, 001$

For example:

$1 text{ GW}= 10^9 text{ W} = 1 , 000 , 000 , 000 text{ W}$
$5 , mu text{m} = 5 times 10^{-6} text{ m} = 0.000 , 005 text{ m}$ .
$2.5 text{ kg} = 2.5times 10^3 text{ g} = 2500 text{ g}$
$500 text{ nm} = 500 times 10^{-9} text{ m} = 5 times 10^{-7} text{ m} = 0.000 , 000 , 7 text{ m}$

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	$1, 000 , 000 , 000$	$1 times 10^9$	$9$

Common Conversions

There are some common conversions you should also know.

Miles $bold{rightarrow}$ Kilometres

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

$text{km}= text{miles}times 1.61 , , , , , , text{ miles}=dfrac{text{km}}{1.61}$

$text{km}=$ the number of kilometres
$text{miles}=$ the number of miles

Degrees Celsius $bold{rightarrow}$ Kelvin

Absolute zero, $0text{ K}$ is equal to $-273 degree text{C}$ . This means we can use the following equations to convert between degrees Celsius and kelvin.

$text{K}=degree text{C} + 273 , , , , , , degree text{C}=text{K} – 273$

$text{K}=$ the temperature in kelvin $text{(K)}$
$degree text{C}=$ the temperature in degrees Celsius $(degree text{C})$

Tonne $bold{rightarrow}$ Kilogram

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

$text{kg}=text{tonnes} times 1000 , , , , , , text{tonnes}=dfrac{text{kg}}{1000}$

$text{kg}=$ the number of kilograms
$text{tonnes}=$ the number of tonnes

Unit Conversions Example Questions

Question 1: Express a charge of $1 text{ C}$ of charge in SI units.

Use the following question to help you:

$text{charge}=text{current} times text{time}$

[2 marks]

Current units – Amps $text{(A)}$

Time units – Seconds $text{(s)}$

Charge units – $text{A}times text{s} = As$

So $bold{1} textbf{ C} = bold{1} textbf{ As}$

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Question 2: How many bytes are there in $2$ megabytes?

[1 mark]

$text{Mega} = 1 , 000 , 000 = 10^6$

So in $2$ megabytes there are:
$bold{2 , 000 , 000}$ or $bold{2 times 10^6}$ or $bold{2} textbf{ million}$ bytes

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Question 3: Convert room temperature $(21 degree text{C})$ to kelvin.

[2 marks]

$begin{aligned} text{kelvin} &= degree text{C} + 273 &= 21 + 273 &= bold{294} textbf{ K} end{aligned}$

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Unit Conversions