Question

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

Answer 1

If you meant `"g/mL"`, then it requires little effort. `"1 cm"^3` is known to be equivalent to `"1 mL"`, so you're done.

If you meant `"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:

`"g"/"cm"^3` `stackrel("reciprocate"" ")(->)` `"cm"^3/"g"`

`"cm"^3/cancel"g" xx cancel"g" = "cm"^3 = "mL"`

So, you would take a mass `m` in `"g"` and divide it by a density `rho` in `"g/cm"^3` or `"g/mL"`, giving you the volume `V` in `"mL"`:

`rho = m/V`

`=> color(blue)(V = m/rho)`