EST. 2024 · LONDON·MMXXVI SPECIFICATION
AQA·Edexcel·OCR|Foundation + Higher
Ratio, Proportion & Rates of Change

Sheet № 178 · Foundation + Higher · AQA · Edexcel · OCR

178

Metric and Imperial Conversions –

Unit conversions appear across many GCSE topics, from area and volume calculations to speed and best-buy problems. You need to know the standard metric conversions by heart and the most common imperial approximations.

§Key definitions

Question:

Convert 3.5 km to metres.

Answer:

0.85 litres

Q1 (Foundation):

Convert 4500 g to kilograms.

Q2 (Foundation):

Convert 2.8 m to centimetres.

Q3 (Higher):

A car travels at 60 mph. Use 1 mile ≈ 1.6 km to find the speed in km/h. Then convert to m/s to 1 decimal place.

§Formulas to memorise

Length: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm

Mass: 1 kg = 1000 g, 1 tonne = 1000 kg

Capacity: 1 litre = 1000 ml, 1 cl = 10 ml

Imperial approximations: 1 inch ≈ 2.5 cm, 1 foot ≈ 30 cm, 1 mile ≈ 1.6 km, 1 kg ≈ 2.2 lbs, 1 gallon ≈ 4.5 litres, 1 pint ≈ 568 ml

Worked example

Convert 3.5 km to metres.

Working: 1 km = 1000 m 3.5 km = 3.5 × 1000 = 3500 m

Common mistakes

  • Multiplying when you should divide (or vice versa). Converting from a smaller unit to a larger unit means dividing (e.g., mm to cm, divide by 10). Converting from a larger unit to a smaller unit means multiplying.
  • Confusing metric and imperial. Do not mix up the two systems in the same calculation. Always convert to the same system before comparing.
  • Forgetting area and volume conversions. 1 m² = 10 000 cm² (not 100), and 1 m³ = 1 000 000 cm³ (not 1000). For area, square the conversion factor; for volume, cube it.
  • Using inaccurate approximations. Use the approximation given in the question, not a remembered value that might differ.

Exam tips

  • Metric conversions should be memorised — they are rarely given in the question.
  • Imperial approximations are usually provided in the question — look for them before starting.
  • For area conversions, square the linear factor (e.g., 1 m = 100 cm, so 1 m² = 10 000 cm²).
  • For volume conversions, cube the linear factor (e.g., 1 m = 100 cm, so 1 m³ = 1 000 000 cm³).
  • A useful check: converting to a smaller unit should give a bigger number; converting to a larger unit should give a smaller number.
MMXXVI specification · AQA · Edexcel · OCRgcsemathsai.co.uk/formulas/metric-and-imperial-conversions