From IVoM:

quantity of dimension one
dimensionless quantity
quantity for which all the exponents of the factors corresponding to the base quantities in its quantity dimension are zero

NOTES

1 — The term “dimensionless quantity” is commonly used 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 (see ISO 31-0:1992, subclause 2.2.6).

2 — The measurement units and values of quantities of dimension one are numbers, but such
quantities convey more information than a number.

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

4 — Quantities of dimension one can also be numbers of entities.
EXAMPLES
number of turns in a coil, number of molecules in a given sample, degeneracy (number of energy levels) in quantum mechanics

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