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

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, ${\text{g"/"cm}}^{3}$. 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, $\text{g}$, as the unit of mass and cubic centimeters, ${\text{cm}}^{3}$, as the unit of volume. You can thus say that the unit of density given to you is

$\text{g"/"cm"^3 = "grams"/"cubic centimer}$

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 ${\text{g cm}}^{- 3}$. This is equivalent to ${\text{g"/"cm}}^{3}$ because it uses the fact that the negative exponent can be written as

${\text{cm"^(-3) = 1/"cm}}^{3}$

This is once again read as

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