S.I. units: (d), kilo

The idea

The metre (symbol m) is the S.I. base unit of length. The prefix kilo (symbol k) means one thousand, so it multiplies a unit by 10³. Combining them gives the kilometre (km), where 1 km = 10³ m = 1000 m, and conversely 1 m = 10⁻³ km. To convert a length from kilometres to metres, multiply by 1000, or equivalently multiply by 10³; to convert metres to kilometres, divide by 1000. For example, 2.4 km = 2.4 × 10³ m = 2400 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 kilo (k) denotes a factor of 10³, i.e. one thousand.
• Applies the conversion 1 km = 10³ m = 1000 m and 1 m = 10⁻³ km.
• Converts correctly in either direction, for example 2.4 km = 2400 m.
• Recognises that quantities should be expressed in metres before substitution into equations.

Common mistakes and how to put them right

• Treating kilo as 10² or 10⁶ rather than 10³.

  Put it right: The correct factor is one thousand, so 1 km = 1000 m.

• Dividing by 1000 when converting kilometres to metres instead of multiplying.

  Put it right: The correct operation is to multiply by 1000.

• Confusing the symbol k for kilo with other uses of k, such as a spring constant or Boltzmann constant.

  Put it right: In a unit prefix context k always means 10³.

Exam tips

• Write the prefix as a power of ten before doing any arithmetic, so 1 km becomes 1 × 10³ 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.