Units and conversions

A surprising number of OCR J560 marks are lost on unit conversion errors — converting metres to centimetres incorrectly, or muddling minutes with hours. This topic underpins every applied question across all six papers.

Length

Unit	Symbol	Conversion
Millimetre	mm	10 mm = 1 cm
Centimetre	cm	100 cm = 1 m
Metre	m	1000 m = 1 km
Kilometre	km	—

Mass

Unit	Symbol	Conversion
Milligram	mg	1000 mg = 1 g
Gram	g	1000 g = 1 kg
Kilogram	kg	1000 kg = 1 tonne
Tonne	t	—

Volume / capacity

Unit	Conversion
1 cm³	= 1 ml
1000 ml	= 1 litre
1000 litres	= 1 m³

So 1 m³ = 1,000,000 cm³.

Time

• 60 seconds = 1 minute.
• 60 minutes = 1 hour.
• 24 hours = 1 day.
• 7 days = 1 week.
• ~52 weeks = 1 year.

Convert minutes to hours by dividing by 60. 45 minutes = 0.75 hours, NOT 0.45.

Money

• 100 pence = £1.
• Always give monetary answers to 2 decimal places: £4.50, not £4.5.

Speed–distance–time

s = d / t. Units must agree: km/h needs km and hours; m/s needs metres and seconds.

To convert m/s to km/h: × 3.6. To convert km/h to m/s: ÷ 3.6 (or × 1000 ÷ 3600).

Compound units (Higher)

• Density = mass / volume (kg/m³ or g/cm³).
• Pressure = force / area (N/m² = pascals).
• Speed = distance / time (m/s, km/h).

When converting compound units (e.g. g/cm³ to kg/m³): convert each part separately. 1 g/cm³ = 0.001 kg / 0.000001 m³ = 1000 kg/m³.

OCR mark scheme conventions

• B1 for correct unit on the final answer.
• M1 for the conversion (e.g. ÷ 100 for cm → m).
• A1 for the converted value.
• Final answers without units lose the B1 even if the number is right.