# The density of balsa wood is about #170# #kg##/##m^3#. How do you convert it to #g##/##cm^3#?

##### 1 Answer

#### Explanation:

You need to use two **conversion factors**, one to take you from *kilograms* to *grams* and one to take you from *cubic meters* to *cubic centimeters*.

So, grab a *metric prefix* table and break down the two conversion factors

Start by focusing on the mass. As you can see, **multiply** whatever value you have by

Let's convert *kilograms per cubic meter* to *grams per cubic meter*

#170 color(red)(cancel(color(black)("kg")))/"m"^3 * (10^3"g")/(1color(red)(cancel(color(black)("kg")))) = 170 * 10^3"g/m"^3#

Now focus on the volume. First, you know that

#"1 m"^3 = "1 m" xx "1 m" xx "1 m"#

By the same logic,

#"1 cm"^3 = "1 cm" xx "1 cm" xx "1 cm"#

As you an see in the table,

#"1 cm" = 1/10^2 "m" = 10^(-2)"m"#

Therefore,

#"1 cm"^3 = 10^(-2)"m" xx 10^(-2)"m" xx 10^(-2)"m" = 10^(-6)"m"^3#

Finally, you can convert the density from *grams per cubic meter* to *grams per cubic centimeter*

#170 * 10^3"g"/color(red)(cancel(color(black)("m"^3))) * (10^(-6)color(red)(cancel(color(black)("m"^3))))/("1 cm"^3) = color(green)("0.17 g/cm"^3)#