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

1 Answer
Stefan V.
Aug 23, 2016

Grams per cubic centimeter.

Explanation:

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")#

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