S.I. units: (k), mega (M), giga (G), tera (T)

The idea

The metre (symbol m) is the S.I. base unit of length. The prefixes kilo (k), mega (M), giga (G) and tera (T) mean 10³, 10⁶, 10⁹ and 10¹² respectively. Combining them with the metre gives the kilometre (km), megametre (Mm), gigametre (Gm) and terametre (Tm), where 1 km = 10³ m, 1 Mm = 10⁶ m, 1 Gm = 10⁹ m and 1 Tm = 10¹² m. To convert from a prefixed unit to metres, multiply by the corresponding power of ten; to convert from metres to a prefixed unit, divide. For example, 3.5 Mm = 3.5 × 10⁶ m = 3.5 × 10⁶ m. Note that the symbols are case-sensitive: k is lower case, while M, G and T are upper case. In calculations, convert all lengths to metres before substituting into equations.

What earns the marks

• States that the metre (m) is the S.I. base unit of length.
• States that kilo (k), mega (M), giga (G) and tera (T) denote 10³, 10⁶, 10⁹ and 10¹² respectively.
• Applies the conversions 1 km = 10³ m, 1 Mm = 10⁶ m, 1 Gm = 10⁹ m and 1 Tm = 10¹² m.
• Converts correctly in either direction, for example 3.5 Mm = 3.5 × 10⁶ m.
• Recognises that prefix symbols are case-sensitive, with k lower case and M, G and T upper case.

Common mistakes and how to put them right

• Treating mega as 10⁹ or giga as 10⁶.

  Put it right: The correct values are mega = 10⁶ and giga = 10⁹.

• Writing the symbol for kilo as an upper-case K.

  Put it right: The correct symbol is lower-case k, while M, G and T are upper case.

• Dividing by the power of ten when converting from a prefixed unit to metres instead of multiplying.

  Put it right: The correct operation is to multiply.

Exam tips

• Write each prefix as a power of ten before doing any arithmetic, so 1 Mm becomes 1 × 10⁶ 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.