S.I. units: (n), micro (μ), milli

The idea

The prefixes micro, symbol μ, and milli, symbol m, represent 10⁻⁶ and 10⁻³ respectively. A micrometre (1 μm) is 1 × 10⁻⁶ m and a millimetre (1 mm) is 1 × 10⁻³ m. To convert to metres, multiply by the prefix factor: 25 μm = 25 × 10⁻⁶ m = 2.5 × 10⁻⁵ m, and 25 mm = 25 × 10⁻³ m = 2.5 × 10⁻² m. To convert from metres, multiply by 10⁶ for micrometres or 10³ for millimetres. The symbol m for milli must not be confused with the unit symbol m for metre; context and spacing show which is meant.

What earns the marks

• State that micro (μ) represents 10⁻⁶ and milli (m) represents 10⁻³.
• Convert a value given with the micro or milli prefix into the base unit by multiplying by 10⁻⁶ or 10⁻³ respectively.
• Convert a base-unit value into micro or milli units by multiplying by 10⁶ or 10³ respectively.
• Distinguish the prefix symbol m for milli from the unit symbol m for metre.

Common mistakes and how to put them right

• Confusing micro with milli.

  Put it right: Micro is 10⁻⁶ while milli is 10⁻³, so a micrometre is one thousandth of a millimetre.

• Multiplying by 10⁶ when converting from micrometres to metres.

  Put it right: Multiply by 10⁻⁶ to go from μm to m, and multiply by 10⁶ to go from m to μm.

• Reading the prefix m in mm as the unit metre.

  Put it right: In mm the first m is the prefix milli and the second m is the unit metre, so 1 mm = 1 × 10⁻³ m.

Exam tips

• Replace the prefix with its power of ten before doing any other arithmetic.
• Check the direction of the conversion by deciding whether the numerical value should increase or decrease.
• Write the prefix and unit symbols together without a space, for example μm or mm.