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Unit Conversions
Unit Conversions 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}^2\text{)}
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}^2Therefore,
\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} = 2.5\times 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, 0\text{ 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}
Question 2: How many bytes are there in 2 megabytes?
[1 mark]
So in 2 megabytes there are:
\bold{2 \, 000 \, 000} or \bold{2 \times 10^6} or \bold{2} \textbf{ million} bytes
Question 3: Convert room temperature (21 \degree \text{C}) to kelvin.
[2 marks]
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