S.I. units: (kg), length

The idea

This row continues the list of S.I. base quantities: mass has the base unit kilogram (kg), and length is the next base quantity, with the base unit metre (m). Length measures the separation between two points and underpins derived quantities such as area (m²) and volume (m³). In calculations, convert centimetres or millimetres to metres before substituting: 25 cm = 0.25 m and 250 mm = 0.250 m. Prefixes scale the metre, for example 1 km = 10³ m and 1 nm = 10⁻⁹ m, but the base unit itself remains the metre.

What earns the marks

• Identifies length as an S.I. base quantity with base unit the metre (m).
• Links the kilogram (kg) to mass and the metre (m) to length as base units.
• Converts lengths from cm or mm to m by dividing by 100 or 1000 respectively.
• Recognises derived units such as m² for area and m³ for volume built from the metre.

Common mistakes and how to put them right

• Treating the centimetre as the base unit.

  Put it right: The base unit of length is the metre (m).

• Substituting centimetres directly into an equation.

  Put it right: Divide by 100 to obtain metres first.

• Writing area or volume units without the correct exponent.

  Put it right: Use m² for area and m³ for volume.

Exam tips

• Convert every length to metres before substituting into an equation.
• Check that area and volume answers carry m² and m³ respectively.
• Use prefix powers of ten, such as 10⁻⁹ for nano and 10³ for kilo, to move between scaled units and metres.