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

1 Answer
Dec 16, 2015

Answer:

#"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

http://www.lsua.info/MetricSystem/MetricPrefix.html

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)#