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Coherent and non-coherent SI units

The base units and the derived units formed as the product of powers of the base units with a numerical factor of one form a coherent system of units. Every physical quantity has exactly one coherent SI unit. For example, 1 m/s = 1 m / (1 s) is the coherent derived unit for velocity. With the exception of the kilogram (for which the prefix kilo- is required for a coherent unit), when prefixes are used with the coherent SI units, the resulting units are no longer coherent, because the prefix introduces a numerical factor other than one. For example, the metre, kilometre, centimetre, nanometre, etc. are all SI units of length, though only the metre is a coherent SI unit. The complete set of SI units consists of both the coherent set and the multiples and sub-multiples of coherent units formed by using the SI prefixes.

The kilogram is the only coherent SI unit whose name and symbol include a prefix. For historical reasons, the names and symbols for multiples and sub-multiples of the unit of mass are formed as if the gram were the base unit. Prefix names and symbols are attached to the unit name gram and the unit symbol g respectively. For example, 10 kg is written milligram and mg, not microkilogram and μkg.

Several different quantities may share the same coherent SI unit. For example, the joule per kelvin (symbol J/K) is the coherent SI unit for two distinct quantities: heat capacity and entropy; another example is the ampere, which is the coherent SI unit for both electric current and magnetomotive force. This illustrates why it is important not to use the unit alone to specify the quantity. As the SI Brochure states, "this applies not only to technical texts, but also, for example, to measuring instruments (i.e. the instrument read-out needs to indicate both the unit and the quantity measured)".

Furthermore, the same coherent SI unit may be a base unit in one context, but a coherent derived unit in another. For example, the ampere is a base unit when it is a unit of electric current, but a coherent derived unit when it is a unit of magnetomotive force.