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

Dec 16, 2015

${\text{0.17 g/cm}}^{3}$

#### 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, $\text{1 kg}$ is equivalent to ${10}^{3} \text{g}$. This means that in order to convert from kilograms to grams, you need to multiply whatever value you have by ${10}^{3}$.

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 ${\text{1 m}}^{3}$ is equivalent to

$\text{1 m"^3 = "1 m" xx "1 m" xx "1 m}$

By the same logic, ${\text{1 cm}}^{3}$ will be equivalent to

$\text{1 cm"^3 = "1 cm" xx "1 cm" xx "1 cm}$

As you an see in the table, $\text{1 m}$ is equivalent to ${10}^{2} \text{cm}$, i.e. a centimeter is the ${100}^{\text{th}}$ part of a meter. This means that

$\text{1 cm" = 1/10^2 "m" = 10^(-2)"m}$

Therefore, ${\text{1 cm}}^{3}$ will be

${\text{1 cm"^3 = 10^(-2)"m" xx 10^(-2)"m" xx 10^(-2)"m" = 10^(-6)"m}}^{3}$

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)