Units & Measures

Spec reference: Ratio, proportion and rates of change
Key idea: Convert between metric and imperial units and use compound measures.

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Metric units

Length

$1\text{ km}=1000\text{ m}$, $1\text{ m}=100\text{ cm}$, $1\text{ cm}=10\text{ mm}$

Mass

$1\text{ tonne}=1000\text{ kg}$, $1\text{ kg}=1000\text{ g}$

Capacity

$1\text{ litre}=1000\text{ ml}$, $1{\text{ m}}^3=1000\text{ litres}$

Area and Volume

$1{\text{ m}}^2=10000{\text{ cm}}^2$, $1{\text{ m}}^3=1000000{\text{ cm}}^3$

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Imperial units (approximate conversions)

Metric	Imperial
$1\text{ kg}\approx 2.2\text{ pounds}$
$1\text{ mile}\approx 1.6\text{ km}$
$1\text{ litre}\approx 1.75\text{ pints}$
$1\text{ gallon}\approx 4.5\text{ litres}$
$1\text{ inch}\approx 2.5\text{ cm}$
$1\text{ foot}\approx 30\text{ cm}$

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Compound measures

Density

$$\text{Density}=\frac{\text{Mass}}{\text{Volume}}({\text{g/cm}}^3{\text{ or kg/m}}^3)$$

Pressure

$$\text{Pressure}=\frac{\text{Force}}{\text{Area}}({\text{N/m}}^2\text{ or Pascals})$$

Example

A metal block has mass 240g and volume 30 cm³. Find its density.

$$\text{Density}=\frac{240}{30}=\boxed{{\displaystyle 8{\text{ g/cm}}^3}}$$

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Best buys with units

Always convert to the same unit before comparing.

Example

Juice A: 500 ml for £1.20. Juice B: 2 litres for £4.20. Which is better value?

Juice A: $\pounds 1.20÷500=0.24\text{p/ml}$

Juice B: $\pounds 4.20÷2000=0.21\text{p/ml}$

Juice B is better value.

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Exam tips

Watch out for

• When converting area units, square the conversion factor: $1{\text{m}}^2=10000{\text{cm}}^2$ (not $100$)
• When converting volume units, cube it: $1{\text{m}}^3=\mathrm{1,000,000}{\text{cm}}^3$
• Always write units in your answer

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Test Yourself

Question 1 of 5

Convert 3.5 km to metres