Units of Measure
Units of Measure
Choosing appropriate units and converting between them accurately are fundamental quantitative skills. At GCSE, units span length, area, volume, mass, time and money, with conversions required both within the metric system and between metric and imperial.
Metric Conversions — Key Facts
| Quantity | Key conversions |
|---|---|
| Length | \( 1\text{ km}=1000\text{ m} \), \( 1\text{ m}=100\text{ cm} \), \( 1\text{ cm}=10\text{ mm} \) |
| Mass | \( 1\text{ tonne}=1000\text{ kg} \), \( 1\text{ kg}=1000\text{ g} \) |
| Volume / Capacity | \( 1\text{ litre}=1000\text{ ml} \), \( 1\text{ m}^3=1{,}000{,}000\text{ cm}^3 \), \( 1\text{ cm}^3=1\text{ ml} \) |
| Area | \( 1\text{ m}^2=10{,}000\text{ cm}^2 \), \( 1\text{ km}^2=1{,}000{,}000\text{ m}^2 \), \( 1\text{ hectare}=10{,}000\text{ m}^2 \) |
| Time | \( 1\text{ hour}=60\text{ min}=3600\text{ s} \) |
Imperial–Metric Approximations
| Imperial | Metric (approx.) |
|---|---|
| 1 inch | 2.54 cm |
| 1 foot | 30 cm |
| 1 mile | 1.6 km (8 km ≈ 5 miles) |
| 1 pound (lb) | 454 g (≈ 0.45 kg) |
| 1 gallon | 4.5 litres |
| 1 pint | 568 ml |
Area and Volume Unit Conversions
Linear conversion factor \( k \) → area factor \( k^2 \) → volume factor \( k^3 \).
Example: \( 1\text{ m}=100\text{ cm} \), so \( 1\text{ m}^2=100^2=10{,}000\text{ cm}^2 \) and \( 1\text{ m}^3=100^3=1{,}000{,}000\text{ cm}^3 \).
Key Takeaways
- Metric prefixes: kilo- (×1000), centi- (÷100), milli- (÷1000).
- Area units: square the linear conversion factor. Volume units: cube it.
- Imperial conversions are approximate — always say "approximately" when using them.
- 1 cm³ = 1 ml; 1 litre = 1000 cm³ — the volume–capacity link is exact.