IGCSE · Practice questions · Units of measure and conversions

Convert with confidence.

Six original Cambridge-style questions on metric units: converting lengths, masses and capacities, square and cubic units, and multi-step problems with mixed units.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

The method

Length factor first, then square or cube it.

Direction: to a smaller unit, multiply; to a bigger unit, divide.
Length: 10 mm = 1 cm, 100 cm = 1 m, 1000 m = 1 km.
Area: square the length factor, e.g. $1\text{ m}^2 = 10\,000\text{ cm}^2$.
Volume: cube it, e.g. $1\text{ m}^3 = 1\,000\,000\text{ cm}^3$.
Capacity: $1\text{ cm}^3 = 1$ ml, $1000\text{ cm}^3 = 1$ l, $1\text{ m}^3 = 1000$ l.
Mixed units: change everything to one unit before calculating.

Recall

[3 marks]

Convert (a) 4.7 km to metres (b) 380 g to kilograms (c) 2.05 litres to millilitres.

(a) $4.7 \times 1000 = 4700$ m ✓
(b) $380 \div 1000 = 0.38$ kg ✓
(c) $2.05 \times 1000 = 2050$ ml ✓

Recall

[2 marks]

Convert (a) $5\text{ m}^2$ to $\text{cm}^2$ (b) $830\text{ mm}^2$ to $\text{cm}^2$.

(a) $5 \times 10\,000 = 50\,000\text{ cm}^2$ ✓
(b) $830 \div 100 = 8.3\text{ cm}^2$ ✓

Calculation

[2 marks]

A container has a volume of $0.024\text{ m}^3$. Write this volume in (a) $\text{cm}^3$ (b) litres.

(a) $0.024 \times 1\,000\,000 = 24\,000\text{ cm}^3$ ✓
(b) $24\,000 \div 1000 = 24$ litres ✓

Calculation

[3 marks]

A rectangular carpet measures 3.5 m by 280 cm. Carpet costs $12.50 per square metre.

Calculate the cost of the carpet.

$280\text{ cm} = 2.8\text{ m}$. ✓
Area $= 3.5 \times 2.8 = 9.8\text{ m}^2$. ✓
Cost $= 9.8 \times 12.50 = \$122.50$. ✓

Analysis

[2 marks]

A solid cube has edges of 2 cm. It is cut into small cubes with edges of 2 mm.

How many small cubes are made?

2 cm = 20 mm, so each edge holds $20 \div 2 = 10$ small cubes. ✓
Number of cubes $= 10 \times 10 \times 10 = 1000$. ✓

Analysis

[4 marks]

A water tank is a cuboid 1.2 m long, 75 cm wide and 50 cm high. It is full of water.

The water is used to fill bottles that each hold 330 ml.

Calculate the greatest number of bottles that can be completely filled.

Same units: 1.2 m = 120 cm. ✓
Volume $= 120 \times 75 \times 50 = 450\,000\text{ cm}^3 = 450\,000$ ml. ✓
$450\,000 \div 330 = 1363.6...$ ✓
Only whole bottles count, so round DOWN: 1363 bottles. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.