##”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)##
