Question

Specific gravity (relative density) of a substance is defined as the ratio of its density to the density of water. What is the SI unit of specific gravity?

Hint:

Specific gravity is a ratio of two densities, so its units cancel out.

Answer 1

Specific gravity has no unit, it is a dimensionless quantity, because it is defined as a ratio.

Step 1: Definition.
Specific gravity of a substance is defined as \(\text{Specific gravity} = \dfrac{\text{density of the substance}}{\text{density of water}}\).

Step 2: Why it has no unit.
Since both the numerator and the denominator are densities, measured in the same unit such as kg per cubic metre, their units cancel out completely when one is divided by the other.

Step 3: Result.
What remains after the units cancel is just a pure number, for example, the specific gravity of mercury is about 13.6, meaning mercury is 13.6 times as dense as water, with no unit attached to that number.

Step 4: Answer.
So specific gravity has no SI unit, it is a dimensionless ratio.