# Question 5257f

Sep 14, 2015

Here's how you can solve this problem.

#### Explanation:

To go from grams per cubic centimeter to short tons (US tons) per cubic inch you need to use two conversion factors.

You got the first one approximately right. You know that one gram is equal to approximately 1.1023 * 10^(-6)" short tons, which means that the mass will indeed be

11.3color(red)(cancel(color(black)("g"))) * (1.1023 * 10^(-6)"tons")/(1color(red)(cancel(color(black)("g")))) = 1.25 * 10^(-5)"tons"

Now, you know that one inch is equivalent to 2.54 centimeters, and that one cubic inch can be written as

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

To get the conversion factor between cubic centimeters and cubic inches, simply replace the inches with centimeters in the above equation

${\text{1 in"""^3 = "2.54 cm" xx "2.54 cm" xx "2.54 cm" = "16.387 cm}}^{3}$

This means that the density will be

11.3color(red)(cancel(color(black)("g")))/(color(red)(cancel(color(black)("cm"^3)))) * (1.1023 * 10^(-6)"tons")/(1color(red)(cancel(color(black)("g")))) * (16.387 color(red)(cancel(color(black)("cm"^3))))/("1 in"""^3) = color(green)(2.04 * 10^(-4)"tons"/"in"^3)#