GCSE Maths · Ratio & proportion

Unit conversions GCSE Questions and Worked Answers

A unit conversion describes the same measurement in different-sized units. Use the relationship between the units, multiplying when you need more smaller units and dividing when you need fewer larger units. Square or cube length factors for area or volume.

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Start with the meaning

What you need to know about unit conversions

A metre ruler can also be labelled as 100 centimetres. These are two descriptions of the same length. A centimetre is smaller, so more of them are needed to measure the ruler. Converting units changes the number and unit together; it does not change the object being measured.

See the idea first

A square metre is a whole grid, not one edge

Length measures one direction: 1 m = 100 cm. A square metre has two edges of 100 cm, so it contains 100 × 100 = 10,000 square centimetres. A cubic metre contains 100 × 100 × 100 cubic centimetres. Area and volume factors come from counting squares and cubes, not from copying the length factor.

The factor depends on the dimension
Same measurement	Reason	Factor
1 m = 100 cm	100 centimetres along one edge	100
1 m² = 10,000 cm²	100 rows of 100 centimetre squares	100²
1 m³ = 1,000,000 cm³	100 layers of 100 × 100 cubes	100³

From problem to method

Typical problems you need to be able to solve

These are the main kinds of question in this topic. Each card first states the problem, then explains how to solve it.

Convert a length, mass or capacity

What the problem asks: Convert 2.4 kg to grams.

How to solve it: 1 kg = 1000 g. Each kilogram contributes 1000 grams, so 2.4 × 1000 = 2400 g.

Convert area or volume

What the problem asks: Convert 3 m² to cm².

How to solve it: 1 m² = 100² = 10,000 cm². Multiply by 3 to get 30,000 cm².

Convert time

What the problem asks: Write 1 hour 45 minutes as decimal hours.

How to solve it: 45 minutes is 45/60 = 0.75 hours. The total is 1.75 hours, not 1.45.

Convert a rate

What the problem asks: Convert 72 km/h to m/s.

How to solve it: 72 km is 72,000 m and one hour is 3600 s. The rate is 72,000/3600 = 20 m/s. Both the distance and time units change.

A reliable routine

Convert a measurement without changing its value

Use this whenever equivalent units describe the same quantity. A conversion factor comes from an equality such as 1 kg = 1000 g, so using it changes the label while preserving the measurement.

Write a correct one-unit relationship.
Decide whether the answer counts smaller or larger units.
Square or cube a length factor only for area or volume; handle time with its own 60/24 relationships.
Calculate and check that the numerical size changes in the expected direction.

Check: Useful exact metric facts: 1 km = 1000 m; 1 m = 100 cm = 1000 mm; 1 kg = 1000 g; 1 litre = 1000 ml; 1 ml = 1 cm³. An hour has 60 minutes, not 100.

Fully worked

Unit conversions GCSE worked examples

Each solution explains the clue, why the method fits and how to check the result.

Example 1

Length to smaller units

2 marks

Question

Convert 3.6 km to metres.

1\text{ km}=1000\text{ m}

3.6\times1000=3600\text{ m}

Smaller units require a larger count.

Example 2

Mass to larger units

2 marks

Question

Convert 2750 g to kilograms.

Each kilogram groups 1000 grams.

2750\div1000=2.75\text{ kg}

Example 3

Area

3 marks

Question

Convert 0.8 m² to cm².

1\text{ m}^2=100^2=10000\text{ cm}^2

0.8\times10000=8000\text{ cm}^2

The factor 100 converts an edge, not the area.

Example 4

Volume and capacity

3 marks

Question

Convert 2500 cm³ to litres.

1 cm³ = 1 ml, so 2500 cm³ = 2500 ml.

2500\div1000=2.5\text{ litres}

Example 5

Decimal time

3 marks

Question

Convert 2.35 hours to hours and minutes.

Keep the 2 whole hours. Convert only the fractional hour:

0.35\times60=21\text{ minutes}

The result is 2 hours 21 minutes, not 2 hours 35 minutes.

Example 6

A compound unit

3 marks

Question

Convert 54 km/h to m/s.

54\text{ km}=54000\text{ m}

1\text{ hour}=3600\text{ s}

54000\div3600=15\text{ m/s}

We convert the distance travelled during the same one-hour interval.

10 original questions · total 18 marks

Unit conversions GCSE exam-style questions

Try each question before opening its fully worked answer. The difficulty rises through the set.

Before you startAllow about 23 minutes · Show your working. Give exact answers unless a question asks you to round, and include units where needed. · answers start collapsed

Centimetres

1 mark

Convert 4.2 m to cm.

Show worked answer

4.2\times100=420\text{ cm}

Metres

1 mark

Convert 85 mm to m.

Show worked answer

85\div1000=0.085\text{ m}

Grams

1 mark

Convert 0.075 kg to g.

Show worked answer

0.075\times1000=75\text{ g}

Litres

1 mark

Convert 650 ml to litres.

Show worked answer

650\div1000=0.65\text{ litres}

Square millimetres

2 marks

Convert 7 cm² to mm².

Show worked answer

1 cm = 10 mm, so 1 cm² = 100 mm².

7\times100=700\text{ mm}^2

Square metres

2 marks

Convert 45,000 cm² to m².

Show worked answer

45000\div10000=4.5\text{ m}^2

Cubic centimetres

2 marks

Convert 0.003 m³ to cm³.

Show worked answer

1\text{ m}^3=100^3=1000000\text{ cm}^3

0.003\times1000000=3000\text{ cm}^3

Decimal hours

2 marks

Convert 3 hours 24 minutes to hours.

Show worked answer

24/60=0.4

Total = 3.4 hours.

Metres per second

3 marks

Convert 90 km/h to m/s.

Show worked answer

90000/3600=25\text{ m/s}

Convert both kilometres and hours.

Given conversion

3 marks

Using 1 mile ≈ 1.6 km, estimate 12 miles in kilometres and 40 km in miles.

Show worked answer

12\times1.6=19.2\text{ km}

40\div1.6=25\text{ miles}

Both are estimates because the supplied conversion is approximate.

Examiner-style feedback

Common unit conversions mistakes

Same factor for length and area

A metre-to-centimetre factor is 100 for lengths but 10,000 for areas.

Decimal minutes

0.25 hour is 15 minutes, not 25.

Changing only half a rate

For km/h to m/s, convert kilometres to metres and hours to seconds.

30-second recap

Choose, carry out, check

Translate the wording before you reach for a rule.

Same quantity, different unit size.
Start from a known equality.
Dimensions determine powers of the factor.
Check direction and time units.

Quick answers

Unit conversions FAQ

How do I know whether to multiply or divide?

Smaller units need a larger count; larger units need a smaller count. Confirm with the written unit relationship.

Is 1 litre equal to 1 cubic metre?

No. 1 litre is 1000 cm³, while 1 m³ is 1,000,000 cm³ = 1000 litres.

Build connected skills

What to revise next

Related guide

Scale drawings

Match map and real-world units.

Revise scale drawings

Related guide

Speed, distance and time

Apply rate conversions.

Revise speed, distance and time

Content standards

Curriculum and rights review

R1/G14 standard and compound unit conversions across tiers. Any non-metric conversion required by a question is supplied. Questions, suggested marks, solutions and diagrams are original practice material, not official past-paper questions.

Official specification references

AQA GCSE Maths subject content