|Definition:|| quantity for which all the exponents of the factors corresponding to the base quantities in its dimension are zero
NOTE 1 – The term "dimensionless quantity" is commonly used and is kept for historical reasons. It stems from the fact that all exponents are zero in the symbolic representation of the dimension for such quantities. The term "quantity of dimension one" reflects the convention in which the symbolic representation of the dimension for such quantities is the symbol 1, printed in sans-serif type. This dimension is not the number one, but the neutral element for the multiplication of dimensions.
NOTE 2 – The measurement units and values of quantities of dimension one are numbers, but such quantities convey more information than a number.
NOTE 3 – Some quantities of dimension one are defined as the ratios of two quantities of the same kind. Examples: plane angle, solid angle, refractive index, relative permeability, mass fraction, friction factor, Mach number. Unless a special name exists, the name of such a quantity often includes one of the terms factor or ratio, or sometimes number, fraction, or index, or the adjective relative (see section 112-03). The coherent derived unit is one. The dimension of such quantities may be denoted by the dimension of the dividend raised to power zero. Examples:
dim(plane angle) = L0,
dim(refractive index n = c0/c) = (LT–1)0,
dim(mass fraction) = M0,
dim(friction factor μ = Fr /Fn) = dim(force)0 = (MLT–2)0.
NOTE 4 – Quantities of dimension one can also be numbers of entities (IEV 112-01-09).