In the equation
K appears to have dimensions of concentration. However, since , the equilibrium constant, , cannot have a physical dimension. This apparent paradox can be resolved in various ways. 
# Assume that the quotient of activity coefficients has a numerical value of 1, so that  has the same numerical value as the thermodynamic equilibrium constant .
# Express each concentration value as the ratio c/c, where c is the concentration in a [hypothetical] standard state, with a numerical value of 1, by definition. 
# Express the concentrations on the mole fraction scale. Since mole fraction has no dimension, the quotient of concentrations will, by definition, be a pure number.
The procedures, (1) and (2), give identical numerical values for an equilibrium constant. Furthermore, since a concentration  is simply proportional to mole fraction  and density :
and since the molar mass  is a constant in dilute solutions, an equilibrium constant value determined using (3) will be simply proportional to the values obtained with (1) and (2).
It is common practice in biochemistry to quote a value with a dimension as, for example, "K = 30 mM" in order to indicate the scale, millimolar (mM) or micromolar (μM) of the concentration values used for its calculation.