Question

Are dimensionless quantities always unitless​

Answer 1

Important thing is that all unitless quantity is dimensionless quantity. .A dimensionless physical quantity may have an unit

Answer 2

Important thing is that all unitless quantity is dimensionless quantity. ... A dimensionless physical quantity may have an unit (e.g. Mechanical equivalent of heat) but a unitless physical quantity is always dimensionless (e.g. Coefficient of friction , refractive index