Syllabus Edition

First teaching 2021

Last exams 2024

Unit Conversions (CIE IGCSE Maths: Extended)

Revision Note

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Author

Dan

Last updated

13 March 2023

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 $5 : 8 = x : 13$

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 $2.2 ∶ 1 = 10 ∶ x$

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 $1.75 ∶ 1 = 5 ∶ x$

Worked example

Convert

54 cm to mm,

1 cm = 10 mm

54 cm = (54 × 10) mm = 540 mm

540 mm

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

485 g to kg.

1000 g = 1 kg

485 g = (485 ÷ 1000) kg

0.485 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= 10³mm³ = 1000 mm³
1 m³= 100³cm³ = 1 000 000 cm³
1 km³= 1000³m³ = 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

8254 mm²to cm²,

10 mm = 1 cm

100 mm²= 1 cm²

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

82.54 cm²

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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