Units of Measure
Length, mass, capacity, area and volume — and moving between units
The metric system works in powers of 10, so converting is just multiplying or dividing by 10, 100 or 1000. These are the facts to know by heart:
| Quantity | Units | Key facts |
|---|---|---|
| Length | mm, cm, m, km | 10 mm = 1 cm, 100 cm = 1 m, 1000 m = 1 km |
| Mass | g, kg, t (tonne) | 1000 g = 1 kg, 1000 kg = 1 t |
| Capacity | ml, l (litre) | 1000 ml = 1 l |
| Area | mm², cm², m², km² | 1 cm² = 100 mm², 1 m² = 10 000 cm² |
| Volume | mm³, cm³, m³ | 1 cm³ = 1 ml, 1000 cm³ = 1 l, 1 m³ = 1000 l |
Which way? Going to a smaller unit gives a bigger number, so multiply (3 m = 300 cm). Going to a larger unit gives a smaller number, so divide (300 cm = 3 m).
Before you add or compare quantities, put them all in the same unit.
Sensible units: choose a unit that gives a sensible-sized number — the distance from Gaborone to Maun in km, the length of a pencil in cm, the mass of a bag of sugar in kg, a teaspoon of medicine in ml.
Convert: (a) 3.5 km to m (b) 250 cm to m (c) 45 mm to cm (d) 0.8 m to cm
(a) Smaller unit → multiply: 3.5 × 1000 = 3500 m. (b) Larger unit → divide: 250 ÷ 100 = 2.5 m.
(c) 45 ÷ 10 = 4.5 cm. (d) 0.8 × 100 = 80 cm.
Convert: (a) 2.4 kg to g (b) 750 g to kg (c) 1.5 litres to ml (d) 3 tonnes to kg
(a) 2.4 × 1000 = 2400 g. (b) 750 ÷ 1000 = 0.75 kg.
(c) 1.5 × 1000 = 1500 ml. (d) 3 × 1000 = 3000 kg.
(a) Change 3.2 m² to cm². (b) Change 4500 cm² to m².
Use 1 m² = 10 000 cm².
(a) 3.2 × 10 000 = 32 000 cm². (b) 4500 ÷ 10 000 = 0.45 m².
Sense check: a square metre is a lot of square centimetres, so the cm² number must be much bigger.
A water container is a cuboid 50 cm long, 40 cm wide and 30 cm high. How many litres does it hold when full?
Volume = 50 × 40 × 30 = 60 000 cm³.
1000 cm³ = 1 litre, so 60 000 ÷ 1000 = 60 litres.
Choose a sensible unit for: (a) the length of a classroom; (b) the mass of an egg; (c) the distance from Gaborone to Francistown; (d) the water in a bath.
(a) m (b) g (c) km (d) litres. Each gives a number that is easy to picture — nobody measures a road trip in centimetres!
Q1. Convert: (a) 4.2 km to metres (b) 365 cm to metres (c) 8 mm to centimetres
👀 Show answer
(b) 365 ÷ 100 = 3.65 m ✓ B1
(c) 8 ÷ 10 = 0.8 cm ✓ B1
Q2. Convert: (a) 3.25 kg to grams (b) 600 ml to litres (c) 2.5 tonnes to kilograms
👀 Show answer
(b) 600 ÷ 1000 = 0.6 l ✓ B1
(c) 2.5 × 1000 = 2500 kg ✓ B1
Q3. A combi travels 12.6 km and then a further 850 m. Find the total distance in kilometres.
👀 Show answer
12.6 + 0.85 = 13.45 km ✓ A1
Q4. (a) A can of juice holds 330 ml. Find the total amount in 6 cans, in litres.
(b) How many 250 ml glasses can be filled from a 1.5 litre bottle?
👀 Show answer
(b) 1.5 l = 1500 ml, 1500 ÷ 250 = 6 glasses ✓ B1
Q5. (a) Change 2.5 m² to cm². (b) Change 7500 cm² to m².
👀 Show answer
(b) 7500 ÷ 10 000 = 0.75 m² ✓ B1
Q6. Square floor tiles measure 30 cm by 30 cm. How many tiles are needed to cover a floor of area 3.6 m²?
👀 Show answer
3.6 m² = 36 000 cm² ✓ M1
36 000 ÷ 900 = 40 tiles ✓ A1
Q7. A box is a cuboid measuring 20 cm by 15 cm by 10 cm. (a) Find its capacity in litres. (b) How many 500 ml bottles of water are needed to fill it?
👀 Show answer
(b) 3000 ÷ 500 = 6 bottles ✓ B1
Q8. Choose the most sensible metric unit for: (a) the mass of a cow; (b) the length of a pencil; (c) the capacity of a teaspoon.
👀 Show answer
(b) cm ✓ B1
(c) ml ✓ B1
Q9. Write these masses in order, starting with the smallest: 0.6 kg, 650 g, 0.065 kg, 605 g
👀 Show answer
0.065 kg, 0.6 kg, 605 g, 650 g ✓ A1
Q10. A shop in Maun receives 40 bags of mealie meal. Each bag has a mass of 12.5 kg. Find the total mass in tonnes.
👀 Show answer
500 ÷ 1000 = 0.5 t ✓ A1
- Multiplying when you should divide: to a larger unit the number gets smaller. 250 cm is 2.5 m, not 25 000 m.
- Using ×100 for area: 1 m² = 10 000 cm², not 100 cm².
- Thinking 1 litre = 100 ml: it is 1000 ml, which is also 1000 cm³.
- Adding mixed units: 12.6 km + 850 m — change to one unit first.
- Leaving out the unit in the answer: “13.45” alone can lose the mark when the question asks for a unit.
- Paper 1 (no calculator) often has a 1-mark “Change 3.5 km into metres” or “Write 750 g in kilograms”.
- Conversions hide inside bigger questions on Paper 3: a tank in cm³ with the answer wanted in litres, or tiles in cm with a floor in m².
- Command words: change, convert, write … in …, give your answer in …. Always check which unit the answer line asks for.
(then move on to the next unit in the Mensuration strand)