Convert 3 m into cm.
1 m = 100 cm.
3 × 100 = 300 cm.
Units and Conversions
Unit conversion involves changing measurements between different units such as length, mass and time. Accuracy is essential and links closely to area, volume and speed calculations.
Overview
Unit conversion means changing a measurement from one unit to another without changing the actual size or amount.
Same quantity, different unit
For example, \(2.5 \text{ m}\) and \(250 \text{ cm}\) describe exactly the same length.
The number changes, but the actual length stays the same.
What you should understand after this topic
- Convert between common metric units
- Know when to multiply and when to divide
- Understand why area and volume conversions are different
- Handle units correctly in exam questions
- Avoid mixing units in formulas
Key Definitions
Unit
A standard measurement such as cm, m, kg or litres.
Convert
Change a measurement from one unit to another.
Metric System
A system of units based mainly on powers of 10.
Length
A measurement of distance, such as mm, cm, m or km.
Mass
A measurement such as g or kg.
Capacity
How much liquid a container can hold, such as mL or litres.
Area Units
Square units such as \( \text{cm}^2 \) or \( \text{m}^2 \).
Volume Units
Cubic units such as \( \text{cm}^3 \) or \( \text{m}^3 \).
Key Rules
Length
10 mm = 1 cm, 100 cm = 1 m, 1000 m = 1 km.
Mass
1000 g = 1 kg.
Capacity
1000 mL = 1 litre.
Metric method
Smaller unit: multiply. Bigger unit: divide.
Important:
Area and volume conversions do not work the same way as length conversions. Square units and cubic units must be converted using powers.
Common Metric Facts
Length facts
- \(1 \text{ cm} = 10 \text{ mm}\)
- \(1 \text{ m} = 100 \text{ cm}\)
- \(1 \text{ km} = 1000 \text{ m}\)
Mass and capacity facts
- \(1 \text{ kg} = 1000 \text{ g}\)
- \(1 \text{ litre} = 1000 \text{ mL}\)
- \(1 \text{ cm}^3 = 1 \text{ mL}\)
Important:
Area and volume conversions do not work the same way as length conversions. Square units and cubic units must be converted using powers.
How to Solve
Step 1: Identify the type of unit
Different measurements use different rules.
Length
mm, cm, m, km
Mass
g, kg
Capacity
mL, litres
Area & Volume
cm², m², cm³, m³
Step 2: Multiply or divide
Bigger → smaller → multiply
Smaller → bigger → divide
Memory tip: Smaller units = bigger numbers
Step 3: Key conversions
\(1\text{ m} = 100\text{ cm}\)
\(1\text{ km} = 1000\text{ m}\)
\(1\text{ kg} = 1000\text{ g}\)
\(1\text{ L} = 1000\text{ mL}\)
Step 4: Area conversions
Square the conversion.
\(1\text{ m}^2 = 100^2 = 10000\text{ cm}^2\)
Key idea: Area → square the number
Step 5: Volume conversions
Cube the conversion.
\(1\text{ m}^3 = 100^3 = 1000000\text{ cm}^3\)
Key idea: Volume → cube the number
Step 6: Real exam use
Perimeter
Same units before adding
Area
Convert lengths first
Volume
Convert before formula
Speed
Match time and distance
Step 7: Exam method
See speed distance time.
- Identify unit type.
- Decide multiply or divide.
- Apply conversion.
- Square or cube if needed.
- Write correct units.
Example Questions
Edexcel
Exam-style questions focusing on basic metric unit conversions.
Edexcel
Convert 7 m to cm.
Give your answer in centimetres.
Edexcel
Convert 4500 g to kg.
Give your answer in kilograms.
AQA
Exam-style questions focusing on capacity, area conversions and mixed units.
AQA
Convert 2.8 litres to mL.
Give your answer in millilitres.
AQA
Convert 5 m² to cm².
Give your answer in square centimetres.
AQA
A rectangle is 2 m by 60 cm.
Find its area in cm².
OCR
Exam-style questions focusing on volume conversions and conversion reasoning.
OCR
Convert 0.03 m³ to cm³.
Give your answer in cubic centimetres.
OCR
A student converts 3 m² to cm² by multiplying by 100.
Explain the mistake.
OCR
A cube has side length 1 m.
Explain why 1 m³ equals 1,000,000 cm³.
Exam Checklist
Step 1
Check what type of unit is being converted.
Step 2
Decide whether the new unit is bigger or smaller.
Step 3
Use squared or cubed scale factors for area and volume.
Step 4
Make sure all units match before using a formula.
Most common exam mistakes
Wrong direction
Multiplying instead of dividing, or dividing instead of multiplying.
Area mistake
Using \( \times 100 \) instead of \( \times 10000 \).
Volume mistake
Using \( \times 100 \) instead of \( \times 1000000 \).
Mixed units
Leaving dimensions in different units before calculating area or volume.
Common Mistakes
These are common mistakes students make when converting units in GCSE Maths.
Using the wrong conversion factor
Incorrect
A student multiplies or divides by the wrong number.
Correct
Learn key conversions (e.g. 1 km = 1000 m, 1 kg = 1000 g) and apply the correct factor carefully.
Multiplying instead of dividing (or vice versa)
Incorrect
A student applies the operation in the wrong direction.
Correct
When converting to a smaller unit, multiply. When converting to a larger unit, divide.
Forgetting squared or cubed conversions
Incorrect
A student converts area or volume using the linear factor.
Correct
For area, square the conversion factor (e.g. \(1\text{ m}^2 = 10{,}000\text{ cm}^2\)). For volume, cube it (e.g. \(1\text{ m}^3 = 1{,}000{,}000\text{ cm}^3\)).
Mixing units within a calculation
Incorrect
A student uses different units in the same formula.
Correct
Convert all values into the same unit before performing any calculations.
Missing or incorrect units in the answer
Incorrect
A student gives a number without units or uses the wrong unit.
Correct
Always include the correct unit in your final answer, matching what the question requires.
Try It Yourself
Practise converting between metric and imperial units.
Foundation
Foundation Practice
Convert between common metric units and simple real-life contexts.
Convert 250 cm into metres.
Divide by 100.
250 ÷ 100 = 2.5 m.
Convert 4 kg into grams.
1 kg = 1000 g.
4 × 1000 = 4000 g.
Convert 750 g into kilograms.
Divide by 1000.
750 ÷ 1000 = 0.75 kg.
Convert 2.5 litres into millilitres.
1 litre = 1000 ml.
2.5 × 1000 = 2500 ml.
Convert 600 ml into litres.
Divide by 1000.
600 ÷ 1000 = 0.6 litres.
Convert 5 km into metres.
1 km = 1000 m.
5 × 1000 = 5000 m.
Convert 1200 m into kilometres.
Divide by 1000.
1200 ÷ 1000 = 1.2 km.
Which is the largest unit?
Think scale.
A kilometre is the largest unit.
Convert 45 mm into cm.
10 mm = 1 cm.
45 ÷ 10 = 4.5 cm.
Higher
Higher Practice
Convert compound units and work with metric–imperial conversions.
Convert 72 km/h into m/s.
Divide by 3.6.
72 ÷ 3.6 = 20 m/s.
Convert 15 m/s into km/h.
Multiply by 3.6.
15 × 3.6 = 54 km/h.
1 mile ≈ 1.6 km. Convert 8 miles into km.
Multiply by 1.6.
8 × 1.6 = 12.8 km.
Convert 5000 cm² into m².
100 cm = 1 m, so square conversion is ÷10000.
5000 ÷ 10000 = 0.5 m².
Convert 2 m³ into cm³.
1 m = 100 cm, so cube conversion is ×1,000,000.
2 × 1,000,000 = 2,000,000 cm³.
A car travels 150 km in 2 hours. Find its speed in km/h.
Speed = distance ÷ time.
150 ÷ 2 = 75 km/h.
Convert 3 tonnes into kilograms.
1 tonne = 1000 kg.
3 × 1000 = 3000 kg.
Convert 2500 ml into litres.
Divide by 1000.
2500 ÷ 1000 = 2.5 litres.
Which conversion is correct?
Square conversion.
1 m² = 100 × 100 = 10,000 cm².
A runner completes 400 m in 50 seconds. Find their speed in m/s.
Speed = distance ÷ time.
400 ÷ 50 = 8 m/s.
Games
Practise this topic with interactive games.
Games coming soon.
Frequently Asked Questions
Why are unit conversions important?
They ensure answers are consistent.
What happens with area conversions?
You square the conversion factor.
What happens with volume conversions?
You cube the conversion factor.