Module 12 of 30Lesson 1 of 4· M-F1 Units and Conversions
Mensuration strand · Unit M-F1 · Builds towards C5.1
Units & Conversions
🟢 Foundation levelmm to km without tears
1 Learn it
Length ladder: 10 mm = 1 cm · 100 cm = 1 m · 1000 m = 1 km. Mass: 1000 g = 1 kg. Capacity: 1000 ml = 1 litre.
🔑 AREA units square the conversion: 1 m = 100 cm, so 1 m² = 100 × 100 = 10 000 cm². VOLUME units cube it: 1 m³ = 100³ = 1 000 000 cm³. And the bridge to capacity: 1 cm³ = 1 ml, so 1 m³ = 1 000 litres.
Direction check: converting to a SMALLER unit → MORE of them (multiply). To a bigger unit → divide. 3.5 m = 350 cm; 4 500 g = 4.5 kg.
2 Watch it work
EXAMPLE 1
Convert 3.5 m to cm, and 4 500 g to kg.
3.5 × 100 = 350 cm; 4 500 ÷ 1000 = 4.5 kg
EXAMPLE 2
Convert 2.4 m² to cm².
2.4 × 10 000 = 24 000 cm² — the squared factor.
EXAMPLE 3
A tank holds 0.75 m³. How many litres?
0.75 × 1000 = 750 litres
EXAMPLE 4
Convert 45 000 cm² to m².
45 000 ÷ 10 000 = 4.5 m²
3 Your turn — try first, then reveal
🚫 No calculator[1 mark]
Q1. Convert 7.2 km to metres.
👀 Show answer
✍️ How your working should look in the exam
7.2 × 1000 = 7 200 m ✓ B1
Why this works
Smaller unit, more of them.
🚫 No calculator[1 mark]
Q2. Convert 850 ml to litres.
👀 Show answer
✍️ How your working should look in the exam
850 ÷ 1000 = 0.85 litres ✓ B1
Why this works
Bigger unit, fewer of them.
🚫 No calculator[2 marks]
Q3. Convert 3 m² to cm².
👀 Show answer
✍️ How your working should look in the exam
3 × 100² = 3 × 10 000 ✓ M1 = 30 000 cm² ✓ A1
Why this works
Area doubles the exponent: ×100 becomes ×10 000. Writing ×100 only is THE classic error.
🚫 No calculator[2 marks]
Q4. A water tank holds 2.5 m³. How many litres is that?
👀 Show answer
✍️ How your working should look in the exam
2.5 × 1000 = 2 500 litres ✓ M1 A1
Why this works
1 m³ = 1000 litres — the capacity bridge.
🚫 No calculator[1 mark]
Q5. How many ml is 1 cm³?
👀 Show answer
✍️ How your working should look in the exam
1 ml ✓ B1
Why this works
The tiny bridge everything else builds on.
🚫 No calculator[2 marks]
Q6. Convert 5 600 000 cm³ to m³.
👀 Show answer
✍️ How your working should look in the exam
÷ 100³ = ÷ 1 000 000 ✓ M1 = 5.6 m³ ✓ A1
Why this works
Volume cubes the factor: 100³.
4 Common mistakes — don’t lose easy marks
Area converted with the length factor: m² → cm² is ×10 000, never ×100.
Direction flipped: smaller units mean MORE units.
m³ ↔ litres bridge forgotten: ×1000.
Mixed units in one formula: convert EVERYTHING to matching units before calculating.
5 Where this leads
Every area and volume answer ahead depends on clean units — and the cm³↔ml bridge turns geometry into litres of water, fuel and paint on real Paper 3 questions.
✅ Take the Check Yourself quiz below, then continue to M-F2 Perimeter and Area Basics.