Converting units

Foundation and Higher

The idea

Metric units go up in steps of $10$ , $100$ or $1000$ : $1\text{ m} = 100\text{ cm}$ and $1\text{ kg} = 1000\text{ g}$ . Area and volume scale by the square and the cube.

Converting to a smaller unit makes the number bigger, so multiply.
For area, square the length factor: $1\text{ m}^2 = 100^2 = 10\,000\text{ cm}^2$ .
For volume, cube it: $1\text{ m}^3 = 1\,000\,000\text{ cm}^3$ , and $1\text{ litre} = 1000\text{ cm}^3$ .

Watch out $1\text{ m}^2$ is not $100\text{ cm}^2$ : area needs the factor squared.

See it worked

Worked exampleNon-calculator1 mark

A walking route is 3.6 km long. What is its length in metres?

1 km = 1000 m.
Multiply by 1000: 3.6 $\times$ 1000 = 3600 m.

Answer 3600 m

Your turn

Question 1Non-calculator4 marks

Answer each part without a calculator.

(a) Change $3.5$ km to metres.

(b) Change $2450$ g to kilograms.

Question 2Non-calculator5 marks

A rectangular floor measures 4.5 m by 3.2 m. Square tiles have side length 20 cm. Ignore gaps and cutting waste.

(a) Work out the minimum number of tiles needed by area.

(b) Tiles come in packs of 16. Work out how many full packs to buy.

Question 3Non-calculator6 marks

A fish tank is a cuboid measuring $1.2$ m by $80$ cm by $50$ cm. It is filled from a hose that delivers $4$ litres of water per minute. $1$ litre $= 1000\ \text{cm}^3$ .

(a) The tank starts empty. Work out how long it takes to fill the tank. Give your answer in hours.

(b) After the tank is full, a pump removes water at $1.5$ litres per minute. Work out how long it takes to remove $\frac{1}{4}$ of the water. Give your answer in hours and minutes.

In past papers

499 official questions in 200 papers since 2017. The latest:

All GCSE Maths past papers

GCSE Maths Pro

£119 once

At least 12 months of access

By paying you agree to our Terms and get access straight away, which ends your 14-day cancellation right.

Start free

No VAT is charged.