# Question #5257f

##### 1 Answer

#### Answer:

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 *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

#"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

#"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)#