S.I. units: (m), centi

The idea

The metre (symbol m) is the S.I. base unit of length. The prefix centi (symbol c) means one hundredth, so it multiplies a unit by 10⁻². Combining them gives the centimetre (cm), where 1 cm = 10⁻² m = 0.01 m, and conversely 1 m = 100 cm. To convert a length from centimetres to metres, divide by 100, or equivalently multiply by 10⁻²; to convert metres to centimetres, multiply by 100. For example, 250 cm = 250 × 10⁻² m = 2.5 m. In calculations you should normally convert all lengths to metres before substituting into equations, because derived units such as the newton and joule are defined in terms of the metre. A multiple-choice question may ask you to identify the correct prefix value, the correct symbol, or the result of a conversion.

What earns the marks

• States that the metre (m) is the S.I. base unit of length.
• States that centi (c) denotes a factor of 10⁻², i.e. one hundredth.
• Applies the conversion 1 cm = 10⁻² m = 0.01 m and 1 m = 100 cm.
• Converts correctly in either direction, for example 250 cm = 2.5 m.
• Recognises that quantities should be expressed in metres before substitution into equations.

Common mistakes and how to put them right

• Treating centi as 10⁻³ rather than 10⁻².

  Put it right: The correct factor is one hundredth, so 1 cm = 0.01 m.

• Multiplying by 100 when converting centimetres to metres instead of dividing.

  Put it right: The correct operation is to divide by 100.

• Confusing the symbol c for centi with other uses of c, such as the speed of light.

  Put it right: In a unit prefix context c always means 10⁻².

Exam tips

• Write the prefix as a power of ten before doing any arithmetic, so 1 cm becomes 1 × 10⁻² m.
• Check the direction of the conversion by asking whether the numerical value should get larger or smaller.
• Keep the unit symbol with the number throughout your working to avoid losing track of the prefix.