On the algebra of quantities and their units

Abstract

The International System of Units is presented in the SI brochure, where not only are the base units of the System defined, but many of the System's derived units are also proposed. The latter are of quantities that the brochure names but does not define; they are well-known quantities or are derived in definitions to be found elsewhere. However, many of the brochure's derived units have been subject to algebraic manipulation that makes them unrecognizable as units of the defined quantity. They do not conform to the VIM's definition of ‘unit’ and are in no sense units of the quantities with which they are associated. This paper questions their usefulness and suggests that derived units be defined only by the definitions of their quantities and of the base units of the system. They cannot be simplified algebraically and remain units of those quantities.