S.I. units: (c), deci

The idea

The metre (symbol m) is the S.I. base unit of length. The prefix deci (symbol d) means one tenth, so it multiplies a unit by 10⁻¹. Combining them gives the decimetre (dm), where 1 dm = 10⁻¹ m = 0.1 m, and conversely 1 m = 10 dm. To convert a length from decimetres to metres, divide by 10, or equivalently multiply by 10⁻¹; to convert metres to decimetres, multiply by 10. For example, 35 dm = 35 × 10⁻¹ m = 3.5 m. Although the decimetre is uncommon in A Level work, you should still recognise the prefix and its value. In calculations, 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 deci (d) denotes a factor of 10⁻¹, i.e. one tenth.
• Applies the conversion 1 dm = 10⁻¹ m = 0.1 m and 1 m = 10 dm.
• Converts correctly in either direction, for example 35 dm = 3.5 m.
• Recognises that quantities should be expressed in metres before substitution into equations.

Common mistakes and how to put them right

• Treating deci as 10⁻² rather than 10⁻¹.

  Put it right: The correct factor is one tenth, so 1 dm = 0.1 m.

• Multiplying by 10 when converting decimetres to metres instead of dividing.

  Put it right: The correct operation is to divide by 10.

• Confusing the symbol d for deci with other uses of d, such as distance.

  Put it right: In a unit prefix context d always means 10⁻¹.

Exam tips

• Write the prefix as a power of ten before doing any arithmetic, so 1 dm becomes 1 × 10⁻¹ 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.