# What is the density in #"g/cm"^3# of a material that has a mass of #"17200"# mg and volume of #"10.0 cm"^3#?

##### 1 Answer

#### Explanation:

Notice that the problem provides you with *milligrams* as the unit for mass and *cubic centimeters* as the unit for volume, but that the density must be expressed in **grams** per cubic centimeter.

This means that you're going to have to convert the mass of the sample from milligrams to grams by using the conversion factor

#color(purple)(bar(ul(|color(white)(a/a)color(black)("1 g" = 10^3"mg")color(white)(a/a)|)))#

In your case, the mass of the sample will be equivalent to

#17200 color(red)(cancel(color(black)("mg"))) * "1 g"/(10^3color(red)(cancel(color(black)("mg")))) = "17.20 g"#

Now, the density of a substance gives you the mass of exactly **one unit of volume** of said substance. Since the unit for volume is the *cubic centimeter*, one unit of volume will simply mean

In order to find the mass of

#"17.20 g"/"10.0 cm"^3 = "1.72 g/cm"^3#

and there you have ,the density of the material expressed in *grams per cubic centimeter*.