Question

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

Answer 1

`"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, `"1 kg"` is equivalent to `10^3"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 `"1 m"^3` is equivalent to

`"1 m"^3 = "1 m" xx "1 m" xx "1 m"`

By the same logic, `"1 cm"^3` will be equivalent to

`"1 cm"^3 = "1 cm" xx "1 cm" xx "1 cm"`

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

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

Therefore, `"1 cm"^3` will be

`"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)`