Pretty much everywhere I've read, the numerical value of the equilibrium constant gives you information about the relative concentrations of products and reactants in the equilibrium mixture; the larger the value.
However, for reactions with an unequal number of moles on the reactant and product side, the equilibrium constant has units in terms of concentration or pressure, allowing me to make the numerical value arbitrarily large or small by choosing the appropriate units. Does the numerical value give no qualitative information about the position of the equilibrium in this case? Or are there a specific set of units that I'm supposed to use?
I am aware of a thermodynamic equilibrium constant that uses activities and is thus dimensionless, but equilibrium constants are only defined in terms of molar concentrations or partial pressures at my level