Question

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`?

Answer 1

`"1.72 g/cm"^3`

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 `"1 cm"^3`.

In order to find the mass of `"1 cm"^3`, all you need to do is divide the mass of the sample by the total volume it occupies

`"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.