Units of measure Revision Notes

Length is measured using units such as millimetres (mm), centimetres (cm), metres (m), and kilometres (km). These units are related by powers of ten: 10 mm = 1 cm, 100 cm = 1 m, and 1000 m = 1 km. To convert between these units, multiply or divide by the appropriate power of ten depending on whether you are converting to a larger or smaller unit.

For example, to convert 250 cm to metres, divide by 100 because 1 m = 100 cm:

Calculation: 250 cm ÷ 100 = 2.5 m. Therefore, 250 cm equals 2.5 m.

• 1 m = 100 cm
• 1 cm = 10 mm
• 1 km = 1000 m
• To convert from smaller to larger units, divide by the conversion factor.
• To convert from larger to smaller units, multiply by the conversion factor.

Area units are derived by squaring length units, resulting in square millimetres (mm²), square centimetres (cm²), square metres (m²), and square kilometres (km²). Because area is two-dimensional, the conversion factors are squared.

For example, to convert 5000 cm² to m², use the fact that 1 m = 100 cm, so 1 m² = (100 cm)² = 10,000 cm².

Calculation: 5000 cm² ÷ 10,000 = 0.5 m². Thus, 5000 cm² equals 0.5 m².

• Area units are squared length units.
• Conversion factors for area are the square of length conversion factors.
• 1 m² = 10,000 cm² (since 100 cm × 100 cm = 10,000 cm²).
• Always square the length conversion factor when converting area units.

Volume units include cubic millimetres (mm³), cubic centimetres (cm³), and cubic metres (m³). Capacity is often measured in millilitres (ml) and litres (l). Since 1 cm³ is exactly equal to 1 ml, volume and capacity units can be converted directly in this case.

For example, to convert 3 m³ to litres, note that 1 m³ = 100 cm × 100 cm × 100 cm = 1,000,000 cm³, and since 1 cm³ = 1 ml, 1 m³ = 1,000,000 ml = 1000 litres.

Calculation: 3 m³ = 3 × 1000 l = 3000 l. Therefore, 3 cubic metres equal 3000 litres.

• Volume units are cubic length units.
• 1 cm³ = 1 ml (capacity).
• 1 m³ = 1000 litres.
• To convert m³ to litres, multiply by 1000.
• Capacity units measure the amount a container can hold, volume units measure space occupied.

Mass is measured in grams (g) and kilograms (kg). The relationship is straightforward: 1 kg = 1000 g. To convert grams to kilograms, divide by 1000; to convert kilograms to grams, multiply by 1000.

For example, to convert 3500 g to kilograms: 3500 g ÷ 1000 = 3.5 kg.

This is useful in real-life contexts such as weighing food or objects.

• 1 kg = 1000 g
• To convert g to kg, divide by 1000.
• To convert kg to g, multiply by 1000.
• Mass measures the amount of matter in an object.

When converting units, always identify whether you are converting length, area, volume, capacity, or mass, as the conversion factors differ.

For length and mass, conversion factors are powers of ten.

For area, square the length conversion factor; for volume, cube the length conversion factor or use the direct relationship to capacity units when applicable (e.g., cm³ to ml). Avoid confusing these powers, as this is a common error in exams and practical problems.

• Check the dimension (length, area, volume, mass) before converting.
• Square or cube the conversion factor for area and volume respectively.
• Remember 1 cm³ = 1 ml for volume-capacity conversions.
• Write units clearly at each step to avoid mistakes.
• Double-check calculations by converting back to the original unit.