Unit Conversions Revision Notes for AQA GCSE Maths

Unit conversions

Understanding how to convert between different units is a fundamental skill in mathematics and science. This topic covers converting within metric and imperial systems, as well as between them. Let's explore the key concepts and methods you need to know.

Understanding metric and imperial units

The metric system and imperial system use different units to measure the same quantities. It's essential to memorise metric conversions and be able to work with both systems effectively.

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Critical for Success: You must memorise all metric conversion factors - they are fundamental to success in mathematics and science.

Metric system conversions

The metric system is based on powers of 10, making conversions straightforward:

Length measurements:

1 centimetre equals 10 millimetres
1 metre equals 100 centimetres
1 kilometre equals 1000 metres

Mass measurements:

1 kilogramme equals 1000 grammes
1 tonne equals 1000 kilogrammes

Volume measurements:

1 litre equals 1000 millilitres
1 cubic centimetre equals 1 millilitre

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The relationship between cubic centimetres and millilitres is particularly useful in practical calculations involving liquid volumes.

Imperial system conversions

The imperial system uses different conversion factors that must be memorised:

Length measurements:

1 yard equals 3 feet
1 foot equals 12 inches

Volume measurements:

1 gallon equals 8 pints

Mass measurements:

1 stone equals 14 pounds
1 pound equals 16 ounces

Converting between metric and imperial

Some common conversions between the two systems include:

1 kilogramme is approximately 2.2 pounds
1 foot is approximately 30 centimetres
1 gallon is approximately 4.5 litres
1 mile is approximately 1.6 kilometres

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Notice that metric-imperial conversions are approximations. In examinations, these conversion factors are typically provided, but you should be familiar with the common ones.

Converting between units

To change from one unit to another, you need to multiply or divide by the appropriate conversion factor. The key is determining whether to multiply or divide based on whether you're converting to a larger or smaller unit.

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Essential Rule: When converting to a smaller unit, multiply by the conversion factor. When converting to a larger unit, divide by the conversion factor.

Converting speeds

Speed conversions require special attention because speed involves two measurements: distance and time. You must convert each component separately before combining them.

For example, to convert kilometres per hour to metres per second:

First convert the distance unit (kilometres to metres)
Then convert the time unit (hours to seconds)
Calculate the final result

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Worked Example: Converting Speed

A rabbit's top speed of 56 km/h converts to metres per second as follows:

Step 1: Convert kilometres to metres $56 \text{ km/h} = (56 \times 1000) \text{ m/h} = 56,000 \text{ m/h}$

Step 2: Convert hours to seconds $56,000 \text{ m/h} = \frac{56,000}{60 \times 60} \text{ m/s} = \frac{56,000}{3600} \text{ m/s} = 15.6 \text{ m/s}$

Therefore, 56 km/h = 15.6 m/s

Converting area and volume measurements

Area and volume conversions are particularly important to understand correctly, as they involve squared and cubed relationships respectively.

Area conversions

When converting area measurements, remember that you're working with two dimensions. This means the conversion factor must be applied twice (squared).

Key area conversions:

1 square metre equals 10,000 square centimetres (not 100!)
1 square centimetre equals 100 square millimetres

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Worked Example: Area Conversion

To convert 9 square metres to square centimetres:

Since 1 m = 100 cm, then: $1 \text{ m}^2 = (100 \text{ cm})^2 = 10,000 \text{ cm}^2$

Therefore: $9 \text{ m}^2 = 9 \times 10,000 \text{ cm}^2 = 90,000 \text{ cm}^2$

Volume conversions

Volume conversions involve three dimensions, so the conversion factor must be applied three times (cubed).

Key volume conversions:

1 cubic metre equals 1,000,000 cubic centimetres
1 cubic centimetre equals 1000 cubic millimetres

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Worked Example: Volume Conversion

To convert 60,000 cubic millimetres to cubic centimetres:

Since 1 cm = 10 mm, then: $1 \text{ cm}^3 = (10 \text{ mm})^3 = 1,000 \text{ mm}^3$

Therefore: $60,000 \text{ mm}^3 = \frac{60,000}{1,000} \text{ cm}^3 = 60 \text{ cm}^3$

Common mistakes to avoid

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Critical Warning: A critical point to remember is that 1 m² does NOT equal 100 cm². This is a frequent error in examinations. Always consider whether you're working with length, area, or volume when applying conversion factors.

For area measurements, multiply by 100 twice when converting from metres to centimetres
For volume measurements, multiply by 100 three times when converting from metres to centimetres

Practice and application

Unit conversions appear frequently in real-world contexts and examination questions. You might need to convert units when calculating costs, distances, or rates. Always ensure you're working with consistent units throughout your calculations.

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When tackling conversion problems, take your time to identify what units you're starting with and what units you need to end up with. Then work through the conversion step by step, checking your answer makes sense.

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Key Points to Remember:

Memorise all metric conversion factors - they're fundamental to success
For imperial and metric-imperial conversions, you should be able to use the conversion factors provided
When converting speeds, always convert distance and time separately
Area conversions involve squaring the conversion factor (multiply by 100 twice for m² to cm²)
Volume conversions involve cubing the conversion factor (multiply by 100 three times for m³ to cm³)
Always check your final answer makes sense in the context of the problem

Unit Conversions (AQA GCSE Maths): Revision Notes