Standard units and conversions

WJEC Foundation and Intermediate examinations test conversion fluency. Higher uses these inside multi-step problems.

Length

• 1 km = 1000 m
• 1 m = 100 cm = 1000 mm
• 1 cm = 10 mm

Mass

• 1 tonne = 1000 kg
• 1 kg = 1000 g
• 1 g = 1000 mg

Capacity / volume

• 1 litre = 1000 ml
• 1 litre = 1000 cm³ (so 1 ml = 1 cm³)
• 1 m³ = 1000 litres

Time

• 1 minute = 60 seconds
• 1 hour = 60 minutes = 3600 seconds
• 1 day = 24 hours
• 1 year ≈ 365 days (366 in leap year)

Money

• £1 = 100p
• WJEC may convert across currencies on Calculator paper given an exchange rate (£1 = €1.18 or similar). Multiply to go from £ to €; divide to go from € to £.

Conversion strategy

1. Decide direction (smaller → larger or vice versa).
2. Larger → smaller: multiply.
3. Smaller → larger: divide.
4. Compound conversions chain — m to mm: × 100 then × 10 = × 1000.

Time arithmetic — the trap

Time is base-60, NOT base-100. 1 hour 45 minutes is NOT 1.45 hours; it is 1.75 hours (45/60 = 0.75).

Equally, 2 h 30 m + 1 h 50 m: add hours (3 h) and minutes (80 m = 1 h 20 m) → 4 h 20 m.

Compound area/volume conversions

• 1 m² = 100 × 100 = 10 000 cm².
• 1 m³ = 100 × 100 × 100 = 1 000 000 cm³.

Many candidates write 1 m² = 100 cm² — losing marks immediately.

WJEC exam tip

Money problems on Calculator paper often hide a unit-conversion test. £1.20 + 75p = ? Convert 75p to £0.75 first, then add. Mixing units in one calculation is a guaranteed mark loss.