1 PHYSICAL QUANTITIES AND UNITS

The value of a physical quantity Q can be expressed as the product of a numerical value {Q} and a unit [Q] \(Q = {Q}[Q] \quad (1)\) Neither the name of the physical quantity, nor the symbol used to denote it, implies a particular choice of unit. Physical quantities, numerical values, and units may all be manipulated by the ordinary rules of algebra. Thus we may write, for example, for the wavelength of one of the yellow sodium lines $\lambda = 5.896\ \times 10^{−7}\ \rm{m} = 589.6\ \rm{nm} \quad (2)$ where m is the symbol for the unit of length called the metre (see Section 2.2, p. 11), nm is the symbol for the nanometre, and the units metre and nanometre are related by $1\ \rm{nm} = 10^{−9}\ \rm{m}\ \rm{or}\ \rm{nm} = 10^{−9}\ \rm{m} \quad (3)$ The equivalence of the two expressions for   in Equation (2) follows at once when we treat the units by the rules of algebra and recognize the identity of 1 nm and $10^{−9}\ \rm{m}$ in Equation (3). The wavelength may equally well be expressed in the form $\lambda/\rm{m} = 5.896\ \times 10^{−7}\ \rm{or}\ \lambda/\rm{nm} = 589.6 \quad (4)$ It can be useful to work with variables that are defined by dividing the quantity by a particular unit. For instance, in tabulating the numerical values of physical quantities or labeling the axes of graphs, it is particularly convenient to use the quotient of a physical quantity and a unit in such a form that the values to be tabulated are numerical values, as in Equations (4).