Unit Conversions Revision Notes for Edexcel GCSE Maths

Unit conversions

Unit conversions are a fundamental skill in mathematics and science. This guide will help you understand how to convert between different units of measurement confidently and accurately.

Understanding metric and imperial units

There are two main systems of measurement you'll encounter: metric and imperial. Each system has its own units for measuring length, area, volume, weight, and speed.

Metric units

The metric system is based on powers of 10, making it straightforward to convert between units. Here are the main metric units you need to know:

Length: millimetres (mm), centimetres (cm), metres (m), kilometres (km)
Area: square millimetres (mm²), square centimetres (cm²), square metres (m²), square kilometres (km²)
Volume: cubic millimetres (mm³), cubic centimetres (cm³), cubic metres (m³), millilitres (ml), litres
Weight: grammes (g), kilogrammes (kg), tonnes
Speed: kilometres per hour (km/h), metres per second (m/s)

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The metric system's base-10 structure makes conversions much simpler than imperial conversions. Each unit is typically 10, 100, or 1000 times larger than the next smaller unit.

Imperial units

The imperial system uses different relationships between units, which you need to memorise. Here are the key imperial units:

Length: inches, feet, yards, miles
Area: square inches, square feet, square miles
Volume: cubic inches, cubic feet, gallons, pints
Weight: ounces, pounds, stones, tonnes
Speed: miles per hour (mph)

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Unlike the metric system, imperial units have irregular relationships (like 12 inches = 1 foot, 3 feet = 1 yard, 8 pints = 1 gallon, 14 pound = 1 stone, 16 ounces = 1 pound). These relationships must be memorised as they don't follow a consistent pattern.

Key conversion facts to memorise

To work effectively with unit conversions, you need to memorise these essential facts:

Metric conversions

$1 \text{ cm} = 10 \text{ mm}$
$1 \text{ m} = 100 \text{ cm}$
$1 \text{ km} = 1000 \text{ m}$
$1 \text{ kg} = 1000 \text{ g}$
$1 \text{ tonne} = 1000 \text{ kg}$
$1 \text{ litre} = 1000 \text{ ml}$
$1 \text{ cm}^3 = 1 \text{ ml}$

Approximate metric-imperial conversions

These are the conversions you'll be given in exams when needed:

$1 \text{ kg} \approx 2.2 \text{ pounds (lb)}$
$1 \text{ foot} \approx 30 \text{ cm}$
$1 \text{ litre} \approx 1\frac{3}{4} \text{ pints}$
$1 \text{ gallon} \approx 4.5 \text{ litres}$
$1 \text{ mile} \approx 1.6 \text{ km}$ (or $5 \text{ miles} \approx 8 \text{ km}$ )

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These metric-imperial conversions are approximate values. In exams, you'll be provided with the conversion factors you need, so focus on understanding the method rather than memorising exact values.

Converting between metric and imperial units

When converting between different measurement systems, you need to multiply or divide by the conversion factor. The key is to set up your calculation correctly and always check that your answer makes sense.

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Worked Example: Converting Pounds to Kilograms

Convert 10 pounds to kilogrammes.

Step 1: Identify the conversion factor $1 \text{ kg} \approx 2.2 \text{ lb}$

Step 2: Decide whether to multiply or divide Since we're going from a smaller unit (lb) to a larger unit (kg), we divide.

Step 3: Perform the calculation $10 \div 2.2 = 4.5 \text{ kg}$

Step 4: Check your answer Since kilogrammes are heavier than pounds, we expect fewer kilogrammes than pounds. Our answer of 4.5 kg < 10 lb makes sense.

The conversion method follows these steps:

Identify the conversion factor you need
Decide whether to multiply or divide
Perform the calculation
Check your answer is reasonable

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Always verify your answer makes sense in context. If you're converting to a larger unit, you should get a smaller number. If you're converting to a smaller unit, you should get a larger number.

Converting speed units

Speed conversions require a two-step process because speed involves both distance and time. You need to convert the distance unit and the time unit separately.

To convert speeds, remember that:

$1 \text{ hour} = 60 \text{ minutes}$
$1 \text{ minute} = 60 \text{ seconds}$
Therefore, $1 \text{ hour} = 3600 \text{ seconds}$

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Worked Example: Converting km/h to m/s

Convert 56 km/h to m/s.

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

Step 2: Convert the time unit (h to s) $56,000 \div 3600 = 15.6 \text{ m/s}$

Check: Since m/s gives smaller numbers than km/h for the same speed, our answer makes sense.

Converting area and volume measurements

Area and volume conversions can be tricky because they involve squared and cubed relationships. Understanding these relationships is crucial for avoiding common mistakes.

Area conversions

When converting area measurements, remember that you're dealing with two dimensions:

$1 \text{ m}^2 = 100 \text{ cm} \times 100 \text{ cm} = 10,000 \text{ cm}^2$
$1 \text{ cm}^2 = 10 \text{ mm} \times 10 \text{ mm} = 100 \text{ mm}^2$

To convert from m² to cm², multiply by 10,000. To convert from cm² to m², divide by 10,000.

Volume conversions

Volume conversions involve three dimensions:

$1 \text{ m}^3 = 100 \text{ cm} \times 100 \text{ cm} \times 100 \text{ cm} = 1,000,000 \text{ cm}^3$
$1 \text{ cm}^3 = 10 \text{ mm} \times 10 \text{ mm} \times 10 \text{ mm} = 1000 \text{ mm}^3$

To convert from m³ to cm³, multiply by 1,000,000. To convert from cm³ to m³, divide by 1,000,000.

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Common mistake: Don't just multiply by 100 when converting m² to cm². You need to multiply by 10,000 because area involves two dimensions (100 × 100). Similarly, for volume conversions, multiply by 1,000,000 because volume involves three dimensions (100 × 100 × 100).

Using conversion graphs

Conversion graphs are powerful tools for solving complex problems involving multiple conversions. They're particularly useful when you need to convert between different currencies or when dealing with rates.

To use a conversion graph effectively:

Draw a line from a value on one axis
Continue until you reach the conversion line
Change direction and go straight to the other axis
Read the converted value from this axis

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This method is especially helpful when you need to perform multiple conversions in sequence, such as converting currency and then changing units of measurement. The graph eliminates the need for complex calculations.

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Key Points to Remember:

Always memorise the key metric conversion facts ( $1 \text{ m} = 100 \text{ cm}$ , $1 \text{ kg} = 1000 \text{ g}$ , etc.)
For metric-imperial conversions, you'll be given the conversion factors in exams
Speed conversions require two steps: convert distance, then convert time
Area conversions involve squaring the conversion factor
Volume conversions involve cubing the conversion factor
Always check that your final answer makes sense in the context of the problem

Unit Conversions (Edexcel GCSE Maths): Revision Notes