# How would you convert g/(cm^3) to mL?

Jul 13, 2016

If you meant $\text{g/mL}$, then it requires little effort. ${\text{1 cm}}^{3}$ is known to be equivalent to $\text{1 mL}$, so you're done.

If you meant $\text{mL}$, it's not the same units back, so it's not a proper conversion; you're inputting a density and getting back a volume. Regardless, you would do this:

${\text{g"/"cm}}^{3}$ $\stackrel{\text{reciprocate"" }}{\to}$ $\text{cm"^3/"g}$

$\text{cm"^3/cancel"g" xx cancel"g" = "cm"^3 = "mL}$

So, you would take a mass $m$ in $\text{g}$ and divide it by a density $\rho$ in ${\text{g/cm}}^{3}$ or $\text{g/mL}$, giving you the volume $V$ in $\text{mL}$:

$\rho = \frac{m}{V}$

$\implies \textcolor{b l u e}{V = \frac{m}{\rho}}$