Question

The density of brass is `8.89" g/cm"^3`. What is the density in kilograms per cubic meter?

Answer 1

`8890" kg/m"^3`

Explanation:

Begin the dimensional analysis by writing the given as a fraction:

`(8.89" g")/"cm"^3`

Multiply by the conversion factor from grams to kilograms:

`(8.89" g")/"cm"^3(1" kg")/(1000" g")`

Multiply by the conversion factor from cubic centimeters to cubic meters:

`(8.89" g")/"cm"^3(1" kg")/(1000" g")(100" cm")^3/(1" m")^3`

Make sure that all of the units cancel, except `" kg/m"^3`:

`(8.89cancel" g")/cancel("cm"^3)(1" kg")/(1000cancel" g")(100cancel" cm")^cancel(3)/(1" m")^3= 8890" kg/m"^3`