Unitless

Ratios, proportions, and angles

It has been argued that quantities defined as ratios Q = A/B having equal dimensions in numerator and denominator are actually only unitless quantities and still have physical dimension defined as dim Q = dim A × dim B. For example, moisture content may be defined as a ratio of volumes (volumetric moisture, m⋅m, dimension L⋅L) or as a ratio of masses (gravimetric moisture, units kg⋅kg, dimension M⋅M); both would be unitless quantities, but of different dimension. Alternatively, the dimension may be denoted raising the dividend's dimension to zeroth power, as in (L) or M.