Measurement and Units
What you must understand
Measurement questions test conversion within and between metric units, reading scales accurately, and choosing sensible units. Know the metric prefixes (kilo, centi, milli) and their powers of ten, plus common time, length, mass, and capacity relationships. You should also handle perimeter, area, and volume formulas, and convert between compound units such as speed (km/h to m/s) or density.
Traps to watch for
- Squared and cubed conversions: 1 m² = 10,000 cm², not 100 cm², because the scale factor is squared. Likewise 1 m³ = 1,000,000 cm³.
- Direction of conversion: multiplying when you should divide, e.g. converting small units to large.
- Time in base 60: 1.5 hours is 1 hour 30 minutes, not 1 hour 50 minutes.
- Compound units: to convert km/h to m/s, multiply by 1000 and divide by 3600 (divide by 3.6).
- Scale drawings: a scale of 1:50 means every length is 50 times smaller on the drawing, but areas scale by 50².
Worked example
A rectangular tank is 2 m long, 50 cm wide, and 40 cm deep. Find its capacity in litres. Convert to consistent units: 2 m = 200 cm. Volume = 200 × 50 × 40 = 400,000 cm³. Since 1000 cm³ = 1 litre, capacity = 400 litres.
Rule of thumb: convert everything to one unit before calculating, and for area or volume remember the conversion factor is squared or cubed.