Definition of Density in Physics
Definition
The mass $m$ per unit volume $V$ is called the density. $$ \rho := {\frac{ m }{ V }} \left[ {\frac{ \mathrm{kg} }{ \mathrm{m}^{3} }} \right] $$
Explanation
Because good explanations of density are readily available elsewhere, this post will briefly introduce how density is convenient when working with formulas.
Put simply, when density $\rho$ appears in an expression, its ‘scale’ can generally be ignored. Leaving aside whether the density is uniform or not, in typical systems an increase in mass is accompanied by an increase in volume, and an increase in volume is accompanied by an increase in mass. However, when their ratio — the density — appears, how large or small the system is becomes implicit in $\rho$.
The density of water at 4°C, that is, when water attains its minimum volume, is $1$; if a material has density $\rho > 1$ it will sink in water, and if it has density $\rho < 1$ it will float.