Convert between mm, cm, m and km, between g and kg, and between ml and litres, so every calculation uses one unit. It is a Foundation topic, aimed at grade 1. Free questions with answers are on this page. Worked examples show each line before you try the questions.
Metric units of length go in tens: 10 mm =1 cm, 100 cm =1 m, 1000 m =1 km. Mass and capacity go in thousands: 1000 g =1 kg, 1000 ml =1 litre. Moving to a smaller unit means multiplying (more of the little units); moving to a larger unit means dividing.
45 mm =4.5 cm (divide by 10). 0.75 kg =750 g (multiply by 1000). 3200 ml =3.2 litres. If your converted mass of a bag of sugar comes out as 0.75 g, the decimal point has jumped the wrong way.
Area and volume conversions are not the same as length — a later topic. Here, stay with one-dimensional units: length, mass, capacity.
Objectives
Convert length units.
Convert mass and capacity units.
Pick the sensible unit for a measurement.
Key points
Know the conversion facts between the metric units of length, mass and capacity.
Decide whether to multiply or divide when changing units.
Convert all measurements to the same unit before adding, subtracting or comparing.
Solve simple problems such as 'how many 300 ml cups from a 2 litre bottle?'
Worked examples
Example 1
A ribbon is 2.4 m long. How many centimetres is that?
2 marks
1 m = 100 cm.
2.4 × 100 = 240.
The ribbon is 240 cm.
Answer: 240
Common slips
Slip: 1 m = 10 cm. A metre is 100 centimetres, not 10.
Slip: 2.4 × 10 = 24. Metres to centimetres needs two zeros (× 100), not one.
Slip: The ribbon is 2 400 cm. 2 400 cm would be 24 m.
Example 2
A jug holds 1.25 litres. How many millilitres is that?
2 marks
1 litre = 1 000 ml.
1.25 × 1 000 = 1 250.
The jug holds 1 250 ml.
Answer: 1250
Common slips
Slip: 1 litre = 100 ml. Capacity uses thousands, like grams in a kilogram.
Slip: 1.25 × 100 = 125. Three zeros, because 1 000 has three zeros.
Slip: The jug holds 12.5 ml. 12.5 comes from × 10. Litres to millilitres is × 1 000.
Example 3
A path is 2 km and 350 m. How many metres is the whole path?
3 marks
2 km = 2 000 m.
2 000 + 350 = 2 350.
The path is 2 350 m.
Answer: 2350
Common slips
Slip: 2 km = 200 m. A kilometre is 1 000 metres.
Slip: 2 000 + 350 = 2 000350. Add the amounts. Do not glue the digits on the end.
Slip: The path is 2.35 m. 2.35 m would be a short step, not a 2 km path.
Questions and answers
GCSE Maths metric conversions questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
How many millimetres are in 7 cm?
Show answer
Answer: 70
7 × 10 = 70.
There are 70 mm.
M1 — 7 × 10 = 70.
A1 — Answer 70
Question 2 Easy2 marks
How many grams are in 3 kg?
Show answer
Answer: 3000
3 × 1 000 = 3 000.
There are 3 000 g.
M1 — 3 × 1 000 = 3 000.
A1 — Answer 3000
Question 3 Medium2 marks
A book has mass 650 g. How many kilograms is that?
Show answer
Answer: 0.65
650 ÷ 1 000 = 0.65.
The mass is 0.65 kg.
M1 — 650 ÷ 1 000 = 0.65.
A1 — Answer 0.65
Question 4 Medium2 marks
How many millilitres are in 0.4 litres?
Show answer
Answer: 400
0.4 × 1 000 = 400.
There are 400 ml.
M1 — 0.4 × 1 000 = 400.
A1 — Answer 400
Question 5 Hard2 marks
A parcel is 1 kg 250 g. How many grams is that?
Show answer
Answer: 1250
1 kg = 1 000 g.
1 000 + 250 = 1 250 g.
M1 — 1 kg = 1 000 g.
A1 — Answer 1250
Question 6 Hard2 marks
A race is 3.5 km. How many metres is that?
Show answer
Answer: 3500
3.5 × 1 000 = 3 500.
The race is 3 500 m.
M1 — 3.5 × 1 000 = 3 500.
A1 — Answer 3500
Question 7 Exam-style3 marks
A roll of fabric is 4 m long. A student cuts off 80 cm. How many centimetres are left?
Show answer
Answer: 320
4 m = 400 cm.
400 − 80 = 320.
M1 — Converts 4 m to centimetres
M1 — Subtracts 80 cm
A1 — Answer 320
Common mistakes
Most lost marks on this topic are one slip.
Using 100 for every conversion.
mm↔cm is × 10. cm↔m is × 100. m↔km, g↔kg and ml↔litre are × 1 000.
Multiplying when changing to a larger unit.
A larger unit needs division, so the count gets smaller.
Gluing a leftover onto the digits, so 2 km 350 m becomes 2 000350 m.
Convert, then add the two amounts in the same unit.
Spot the slip
Which is longer, 3 m or 300 cm?
They are equal
3 m
300 cm
Show the slip
They are equal 1 m = 100 cm, so 3 m = 300 cm.
Exam tips
This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Write the conversion fact you are using as the first line of working (1 kg = 1000 g); it is quick and can earn a method mark.
Convert everything to the smaller unit if you want to avoid decimals (e.g. work in ml, then change back at the end).
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.