Question 46931

Oct 4, 2015

I assume that the correct option was b) $1.2 \cdot {10}^{- 3} {\text{g/cm}}^{3}$

Explanation:

To convert the given density from kilograms per cubic meter to grams per cubic centimeter, use two conversion factors

$\text{1 kg" = 10^3"g" " }$ and $\text{ " "1 m" = 10^2"cm}$

You can find how many cubic centimeters you get per cubic meter by using

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

Replace $\text{1 m}$ with the above conversion factor to get

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

So, the density will be

1.2color(red)(cancel(color(black)("kg")))/(color(red)(cancel(color(black)("m"""^3)))) * (10^3"g")/(1color(red)(cancel(color(black)("kg")))) * (1color(red)(cancel(color(black)("m"""^3))))/(10^6"cm"""^3) = 1.2 * 10^(-3)"g/cm"""^3#