One unit of density is #"g"/"cm"^3#. How do you say that unit in words?

1 Answer
Aug 23, 2016

Grams per cubic centimeter.


One important thing to remember about units that use fractions is that the fraction itself is pronounced as per.

In this case, you are given a unit of density, #"g"/"cm"^3#. As you know, density is defined as the mass of exactly one unit of volume of a substance.

This tells you that the unit that goes on top of the fraction, i.e. in the numerator, will be a unit of mass and the unit that goes on the bottom of the fraction, i.e. in the denominator, will be a unit of volume.

Here you have grams, #"g"#, as the unit of mass and cubic centimeters, #"cm"^3#, as the unit of volume. You can thus say that the unit of density given to you is

#"g"/"cm"^3 = "grams"/"cubic centimer"#

Now all you have to do is use the fact that the fraction is pronounced per to get

#"g"/"cm"^3 = "grams"/"cubic centimer" = color(darkgreen)("grams per cubic centimer")#

You'll sometimes see density given as #"g cm"^(-3)#. This is equivalent to #"g"/"cm"^3# because it uses the fact that the negative exponent can be written as

#"cm"^(-3) = 1/"cm"^3#

This is once again read as

#"g cm"^(-3) = "g"/"cm"^3 = "grams"/"cubic centimeter" = color(darkgreen)("grams per cubic centimer")#