The bulk density of a soil is 1.33g/cm cubed. What is its bulk density in kg/m cubed?

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This is a problem of converting units. I prefer to do these with fractions. I first set up the unit I am starting with, and write the unit I want to get to.

`(1.33g)/(1cm^3)` ......   `[kg]/m^3`

Then, I multiply by fractions that cancel out the current units and get me to the units I need. For this example, I will start with the units of grams to kilograms.

`[1.33g]/[1cm^3]*[1kg]/[1000g]` .....    `[kg]/m^3`

I now have grams on the top and bottom, so they cancel, and because there are 1000 grams in a kilogram, I divided by 1000. Next, I convert the units of cm^3 to m^3. Because these are cubed, I will expand the numbers, just to be sure.

`[1.33g]/[1cm*1cm*1cm]*[1kg]/[1000g]*[100cm*100cm*100cm]/[1m*1m*1m]`  ......     `[kg]/[m^3]`

Each of the units will cancel out, leaving behind just the kg and m^3. All that is left is to do the math, giving you `1330[kg]/[m^3]` .

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