# Dimensionless Quantities

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.

## Dimensionless Quantities

derived physical quantities which are independent of the simultaneous variation of quantities that are chosen to be fundamental. If, for example, one chooses length *L,* mass *M,* and time *T* as the fundamental quantities and their simultaneous variations have no effect on the value of a given quantity, then the dimensionality of such a quantity is equal to *L*^{0}*M*^{0}*T*^{0} = 1, and the quantity is dimensionless in this system of quantities. For example, a plane angle, defined as the ratio of the length of the arc of a circle enclosed between two radii to the length of the radius, is a dimensionless quantity in the *LMT* system, because it is independent of the length of the radius. All relative quantities—that is, relative density (the density of an object in relation to the density of water), relative elongation, relative magnetic and dielectric permeability, and the like—as well as similarity criteria (Reynolds number and Prandtl number), are also considered dimensionless quantities. Dimensionless quantities are expressed in abstract units. Relative quantities are also expressed in percent (%) and in parts per thousand (‰).

K. P. SHIROKOV