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

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 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)##