GCSEMathsAQARevision Notes3. Ratio, Proportion & Rates of ChangeStandard & Compound UnitsUnit Conversions

Unit Conversions (AQA GCSE Maths)

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Converting Units

How do I convert between units for lengths?

  • For metric units, conversion can be done by simply multiplying or dividing by powers of 10
  • You need to know the basic conversions
    • 1 cm = 10 mm
    • 1 m = 100 cm
    • 1 km = 1000 m
  • To decide whether to multiply or divide you need to ask yourselves does the number of units increase or decrease
    • e.g. The number of mm is 10 times bigger than the number of cm so mm = cm × 10
  • You can do the conversion in stages
    • First convert kilometres into metres then metres into centimetres
  • If you are given an imperial conversion (such as miles to kilometres) then you can use ratios to help with the conversions
    • There are 5 miles in 8 kilometres so to find how many miles are in 13 kilometres you would solve 5 space colon space 8 equals x space colon space 13

How do I convert units for mass?

  • For metric units, conversion can be done by simply multiplying or dividing by powers of 10
  • You need to know the basic conversions
    • 1 g = 1000 mg
    • 1 kg = 1000 g
    • 1 tonne = 1000 kg
  • If you are given an imperial conversion (such as pounds to kilograms) then you can use ratios to help with the conversions
    • e.g. There are 2.2 pounds in 1 kilogram so to find how many kilograms are in 10 pounds you would solve 2.2 ∶ 1 equals 10 ∶ x

How do I convert units for volume/capacity?

  • For metric units, conversion can be done by simply multiplying or dividing by powers of 10
  • You need to know the basic conversions
    • 1 l = 1000 ml
    • 1 cl = 10 ml
    • 1 ml = 1 cm3
  • If you are given an imperial conversion (such as pints to litres) then you can use ratios to help with the conversions
    • e.g. There are 1.75 pints in 1 litre so to find how many litres are in 5 pints you would solve 1.75 ∶ 1 equals 5 ∶ x

Worked example

Convert

a)

54 cm to mm,

1 cm = 10 mm

54 cm = (54 × 10) mm = 540 mm

540 mm

b)

12 300 cm to km,

First convert from cm to m.
100 cm = 1 m

12 300 cm = (12 300 ÷ 100) m = 123 m

Now convert from m to km.
1000 m = 1 km

123 m = (123 ÷ 1000) km = 0.123 km

0.123 km

c)

485 g to kg.

1000 g = 1 kg

450 g = (450 ÷ 1000) kg

0.45 kg

Squared & Cubic Units

How do I convert between squared units?

  • Converting squared units (usually used for areas) is slightly trickier
  • You need to remember to square the conversion rates
    • This is because area is 2D
    • The fact the units have a "squared" on them will help you remember
  • You need to be able to use the basic conversions
    • 1 cm2 = 102 mm2 = 100 mm2
    • 1 m2 = 1002 cm2 = 10 000 cm2
    • 1 km2 = 10002 m2 = 1 000 000 m2
  • There are also less common conversions
    • 1 hectare (ha) = 10 000 m2
  • If you are given an imperial conversion (such as miles to kilometres) for lengths:
    • Write the conversion as a ratio
      • e.g.  Miles to kilometres is 5 : 8
    • Square the numbers to get the ratio for the conversion of the units for area
      • e.g.  Miles2 to kilometres2 is 25 : 64

How do I convert between cubed units?

  • You need to cube the normal conversion rates
    • This is because volume is 3D
    • The fact the units have a “cubed” on them will help you remember
  • You need to be able to use the basic conversions
    • 1 cm3 = 103 mm3 = 1000 mm3
    • 1 m3 = 1003 cm3 = 1 000 000 cm3
    • 1 km3 = 10003 m3 = 1 000 000 000 m3
  • If you are given an imperial conversion (such as miles to kilometres) for lengths:
    • Write the conversion as a ratio
      • e.g.  Miles to kilometres is 5 : 8
    • Cube the numbers to get the ratio for the conversion of the units for volume
      • e.g.  Miles3 to kilometres3 is 125 : 512

Worked example

Convert

a)

8254 mm2 to cm2,

10 mm = 1 cm

100 mm2 = 1 cm2

8254 mm2 = (8254 ÷ 100) cm2 = 82.54 cm2

82.54 cm2  

b)

2.54 m3 to cm3.

1 m = 100 cm
1 m3 = 1 000 000 cm3

2.54 m3 = (2.54 × 1 000 000) cm3 = 2 540 000 cm3

2 540 000 cm3

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    Dan

    Author: Dan

    Expertise: Maths

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.