Converting between standard and compound units

WJEC tests unit conversion on every Unit 2 (calculator) paper and frequently on Unit 1 short-answer items. The technique is the same at all three tiers — Foundation, Intermediate and Higher — but the contexts get harder.

Standard length, mass and capacity conversions

Memorise these — they are not given on the WJEC formula sheet:

• 10 mm = 1 cm; 100 cm = 1 m; 1000 m = 1 km
• 1000 mg = 1 g; 1000 g = 1 kg; 1000 kg = 1 tonne
• 1000 ml = 1 litre; 100 cl = 1 litre; 1 ml = 1 cm^3

Time

• 60 seconds = 1 minute; 60 minutes = 1 hour; 24 hours = 1 day
• WJEC always wants times in 24-hour clock or as a clear "h min" — never decimal hours unless asked. 2.5 hours is 2 hours 30 minutes.

Area and volume — beware the squared/cubed factor

This is the single biggest WJEC trap.

• 1 m = 100 cm, but 1 m^2 = 10 000 cm^2 (square the linear factor)
• 1 m^3 = 1 000 000 cm^3 (cube the linear factor)
• 1 hectare = 10 000 m^2 (Welsh farming questions love this one)

Compound units (Intermediate / Higher)

A compound unit combines two base units.

• Speed — m/s, km/h, mph. Convert via speed = distance ÷ time. To go from m/s to km/h, multiply by 3.6.
• Density — g/cm^3, kg/m^3. density = mass ÷ volume.
• Pressure — N/m^2 (pascals), N/cm^2. pressure = force ÷ area.

WJEC exam tip

Always write the conversion factor explicitly before substituting. A clear line such as "1 km = 1000 m so 4.2 km = 4200 m" earns the M1 method mark even if a later arithmetic slip loses A1. The British/metric crossovers (1 inch ≈ 2.54 cm, 5 miles ≈ 8 km) appear regularly on Foundation Unit 2 in real-world contexts.