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Unit Conversions

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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}^2

Therefore,

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

 

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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
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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
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Unit Conversions Example Questions

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