7  density

There are several flavors of densities, but usually we mean mass density:

How much mass is there in a given volume?

For instance, the density of iron is 7.87 g/cm^3

What is the density of iron in kg/m^3?

\begin{align} &7.87\, &&\mathrm{g}&&\mathrm{cm}^{-3} \\ &7.87\, &&\left(10^{-3}10^3\,\mathrm{g}\right) &&(10^{-2}\,\mathrm{m})^{-3}\\ &7.87\, &&\left(10^{-3}\,\mathrm{kg}\right) &&(10^{-2})^{-3}\, (\mathrm{m})^{-3}\\ &7.87\, &&10^{-3}\, \mathrm{kg} &&10^{6}\, \mathrm{m}^{-3}\\ &7.87\cdot10^{-3}10^{6} &&\mathrm{kg} &&\mathrm{m}^{-3}\\ &7.87\cdot10^{3} &&\mathrm{kg} &&\mathrm{m}^{-3}\\ \end{align}

There are 7870 kg of iron in a cubic meter.

Make sure you are comfortable with what’s going on in each of the equations above.