Show WorkingWorked example 1: converting metric units
Change 1.2 km into m.
- 1 km = 1,000 m.
- Going to a smaller unit gives a bigger number, so multiply by 1,000: 1.2 × 1,000 = 1,200.
Answer 1,200 m
Geometry and measuresFoundation and Higher
Converting units GCSE questions with answers
8 converting units questions to try, each with the answer and the full working one tap away. Every question here was made and worked out by the Show Working maths engine, not typed in by hand.
Unit conversion questions change between metric units of length, mass and capacity, such as metres to millimetres. You also convert area and volume units, like m² to cm² and m³ to cm³.
01 / Quiz yourselfTry it, then tap to check
Converting units questions to try
Work each one out on paper first. Then open the answer and compare your working with ours, step by step.
01 / Converting metric unitsBoth tiers
Change 0.45 m into mm.
Show the answer and working
- 1 m = 1,000 mm.
- Going to a smaller unit gives a bigger number, so multiply by 1,000: 0.45 × 1,000 = 450.
Answer 450 mm
02 / Converting metric unitsBoth tiers
Change 6.4 km into m.
Show the answer and working
- 1 km = 1,000 m.
- Going to a smaller unit gives a bigger number, so multiply by 1,000: 6.4 × 1,000 = 6,400.
Answer 6,400 m
03 / Converting metric unitsBoth tiers
Change 15 mm into cm.
Show the answer and working
- 1 cm = 10 mm.
- Going to a bigger unit gives a smaller number, so divide by 10: 15 ÷ 10 = 1.5.
Answer 1.5 cm
04 / Converting metric unitsBoth tiers
Change 4 km into m.
Show the answer and working
- 1 km = 1,000 m.
- Going to a smaller unit gives a bigger number, so multiply by 1,000: 4 × 1,000 = 4,000.
Answer 4,000 m
05 / Converting area and volume unitsBoth tiers
Change 0.06 m³ into cm³.
Show the answer and working
- 1 m = 100 cm, so 1 m³ = 100 × 100 × 100 = 1,000,000 cm³.
- 0.06 × 1,000,000 = 60,000 cm³.
Answer 60,000 cm³
06 / Converting area and volume unitsBoth tiers
Change 45,000 cm² into m².
Show the answer and working
- 1 m = 100 cm, so 1 m² = 100 × 100 = 10,000 cm².
- 45,000 ÷ 10,000 = 4.5 m².
Answer 4.5 m²
07 / Converting area and volume unitsBoth tiers
Change 1.75 m² into cm².
Show the answer and working
- 1 m = 100 cm, so 1 m² = 100 × 100 = 10,000 cm².
- 1.75 × 10,000 = 17,500 cm².
Answer 17,500 cm²
08 / Converting area and volume unitsBoth tiers
Change 0.3 cm² into mm².
Show the answer and working
- 1 cm = 10 mm, so 1 cm² = 10 × 10 = 100 mm².
- 0.3 × 100 = 30 mm².
Answer 30 mm²
02 / What's covered2 kinds of question
Converting units at GCSE and where marks go
- Converting metric unitsBoth tiers
- Converting area and volume unitsBoth tiers
Worked example 2: converting area and volume units
Change 50,000 mm² into cm².
- 1 cm = 10 mm, so 1 cm² = 10 × 10 = 100 mm².
- 50,000 ÷ 100 = 500 cm².
Answer 500 cm²
A common mistake
Using the length conversion for area or volume. 1 m = 100 cm, so 1 m² = 100 × 100 = 10,000 cm² and 1 m³ = 100 × 100 × 100 = 1,000,000 cm³.
03 / Practise itiPhone and iPad
More converting units questions in Show Working
In the app, Converting units makes fresh questions every time, so they never run out. Tap Show me one to see a new worked example straight away, or practise ten and open the working whenever you are stuck. Forgotten a method? Type it into Look up and the answer is there.
Coming soon to the App Store