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Converting units: metric and imperial

Converting units: metric and imperial

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Summary

Converting units: metric and imperial

​​In a nutshell

Converting between units involves multiplying or dividing by a conversion factor. Metric units should be learnt off by heart whereas imperial units will always be given to you in the question - however it's always a good idea to get practice with both!



Common metric units of measure and their conversions

There are units to describe all measures: length, volume and mass. Below are the common metric conversions for each. To figure out whether to multiply or divide, work out whether you are going from big to small or from small to big. Divide if you are converting to the 'bigger' unit and multiply if you are converting to the 'smaller' unit.


Type of measurement

Metric conversion

Abbreviation

Length

Maths; Ratio proportion and rates of change; KS4 Year 10; Converting units: metric and imperial
  • mmmm - millimetres 
  • cmcm -  centimetres   
  • mm - metres
  • kmkm - kilometres​

Volume

Maths; Ratio proportion and rates of change; KS4 Year 10; Converting units: metric and imperial
  • mlml - millilitres
  • clcl​ - centilitres
  • ll​ - litres

Mass

Maths; Ratio proportion and rates of change; KS4 Year 10; Converting units: metric and imperial
  • mgmg​ - milligrams
  • gg​ - grams
  • kgkg​ - kilograms
  • tt​ - tonnes


Note: Another common conversion is that one millilitre is equal to one centimetre cubed: 1ml=1cm31ml=1cm^3.


Example 1

What is 1.341.34  litres in millilitres? 


Work out the conversion factor.

1l=1000ml1l=1000ml so the conversion factor is one thousand.


A millilitre is smaller than a litre: the conversion is from a big unit to a smaller one so multiply the value by the conversion factor.

1.34×1000=1340ml1.34\times 1000 = \underline{1340ml}



Imperial units of measure

Imperial units of measure are much less commonly used and you are not expected to know them off by heart. Conversion factors involving imperial units will always be given but some examples are listed in the table below.


Type of measurement

Common imperial conversion

Conversion factor

Length

  • 11 yard =3=3 feet
  • 11 foot =12=12 inches​
  • 33​​
  • 1212​​

Volume

  • 11 gallon =8= 8 pints
  • 88​​

Mass

  • 11 stone =14= 14 pounds
  • 11​ pound =16= 16 ounces​
  • 11 ton =160= 160 pounds​
  • 1414​​
  • 1616​​

Note: Don't get confused between tonnes and tons - they sound the same but are very different!


Example 2

What is 1818  pounds in stone? Give your answer to two decimal places. (There are 1414​ pounds in a stone.)


Work out the conversion factor. 

1414​​


Fourteen pounds are equal to one stone and so a stone is bigger: the conversion is from a smaller unit to a bigger one so divide by the conversion factor.

18÷14=1.28571429=1.29 (2 d.p.)18\div14=1.28571429=\underline{1.29 \ (2 \ d.p.)} 



Imperial and metric units combined

It is common to need to convert between metric and imperial units when given a conversion rate. Simply work out the conversion factor and decide whether to multiply or divide.


Example 3

11 foot 30cm\approx 30cm and 11 foot =12=12 inches. Andrea's hair is currently 105cm105cm long. How long is her hair in feet and inches?


To go from centimetres to feet, divide by the conversion factor, thirty, since one foot is approximately equal to 3030 centimetres.

105÷30=3.5105\div30=3.5


If a foot is twelve inches, then half a foot must be half of twelve.

12÷2=612\div2=6


Therefore, 105cm105cm is approximately 3 feet  6 inches\underline{3 \ feet \ \ 6 \ inches}.

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FAQs - Frequently Asked Questions

Do I need to know imperial units?

How do I know whether to divide or multiply when converting between units?

How do I convert between the metric units of mass?

How do I convert between metric units of volume?

How do I convert between metric units of length?

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