# What Value of Purity Do We Substitute in the Formula C=10PD/M

In the the formula

$$C = 10P\frac{D}{M}$$

$$C$$ is the concentration of a substance in a solution, $$P$$ is the percent concentration (purity) of the substance, $$D$$ is the relative density of the solution and $$M$$ is the molar mass of the substance.

Say $$P = 60\%$$, do we substitute $$60$$ or $$60/100$$ in the formula? The proofs I've read suggest $$60$$.

It all depends on the units other variables are expressed in. By dimensional analysis it's obvious that you don't expect percent to appear in the final result, so $$P$$ is expressed as a fraction. Using percentage number can be justified if $$100\%$$ is conveniently cancelled out.
The $$10$$-multiplier suggests that this might be case here, e.g. if $$D$$ is expressed in $$\pu{g cm-3}$$, $$M$$ — in $$\pu{g mol-1}$$, then in order to obtain $$C$$ in $$\pu{mol dm-3}$$ (or $$\pu{mol L-1}$$, which is the same), you must plug in the value for $$P$$ in percents:
$$[C] = \frac{\pu{g cm-3}}{\pu{g mol-1}} = 10^3\cdot\pu{g dm-3} = 10\cdot [P~\text{in}~\%]\cdot\pu{g dm-3}$$