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QUESTION

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

##"0.17 g/cm"^3##

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 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)##