Sheet № 41 · Foundation + Higher · AQA · Edexcel · OCR
Unit Conversions –
Unit conversions might sound straightforward, but they catch out more GCSE students than you would expect — especially when area and volume units are involved. Every exam board (AQA, Edexcel, OCR) tests conversions in some form, from simple metric changes on Foundation papers to tricky cm² to m² conversions on Higher. Getting these right
§Key definitions
Rule of thumb:
converting to a smaller unit → the number gets bigger → multiply. Converting to a larger unit → the number gets smaller → divide.
Step 1:
1 km = 1,000 m.
Step 2:
We are going from a larger unit to a smaller one, so multiply.
Step 3:
3.5 × 1,000 = 3,500 m.
§Formulas to memorise
1 km = 1,000 m
1 m = 100 cm
1 cm = 10 mm
1 tonne = 1,000 kg
1 kg = 1,000 g
1 litre = 1,000 ml
1 ml = 1 cm³
1 litre = 1,000 cm³
1 m² = 10,000 cm² (because 100 × 100 = 10,000)
1 cm² = 100 mm²
1 m³ = 1,000,000 cm³ (because 100 × 100 × 100 = 1,000,000)
1 cm³ = 1,000 mm³
Worked example
See example below.
Convert 3.5 km to metres.
⚠ Common mistakes
- ✗Forgetting to square or cube for area/volume conversions. Students often use the linear factor (×100) when they should use ×10,000 for area or ×1,000,000 for volume.
- ✗Multiplying when you should divide (or vice versa). Think about whether the answer should be a bigger or smaller number.
- ✗Treating imperial conversions as exact. At GCSE, conversions like 1 mile ≈ 1.6 km are approximate. Use the word "approximately" in your answer.
- ✗Mixing up units of capacity and volume. Remember: 1 ml = 1 cm³ and 1 litre = 1,000 cm³. These are interchangeable.
- ✗Not converting all measurements to the same unit before calculating. If a rectangle has sides given in cm and m, convert both to the same unit before finding area.
✦ Exam tips
- →Learn the key metric conversions by heart — they are not given on the formula sheet.
- →For area and volume conversions, draw a quick diagram showing 1 m = 100 cm, then imagine a 1 m × 1 m square = 100 cm × 100 cm = 10,000 cm².
- →Write the conversion factor before you use it. This earns method marks.
- →In compound measure questions (density, speed, pressure), you may need to convert units part-way through — e.g. converting g to kg or cm² to m². Watch for this.
- →Double-check by estimation. If you convert 3 m² and get 300 cm², that is too small — 3 m² should be 30,000 cm².