There is no unit for specific gravity.

Specific gravity is defined as the ratio of an object's density to that of a reference material. Furthermore, the specific gravity of an object can tell us whether it will sink or float in reference material. Furthermore, the reference material is water, which has a density of one gramme per cubic centimetre or one gramme per millimetre.

True, the specific gravity has no unit because the numerator and denominator units are the same, so they cancel each other out.