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## Homework Statement

How do I convert kg/m3 to g/cm3?.

3200kg/m^3 ---> 3.2g/cm^3

## Homework Equations

The question was 3200kg/m3 = 3.2g/cm3. I don't understand the steps involved?

## The Attempt at a Solution

I know how to do dimensional analysis, but I just dont really understand the logic in this. I'll go step by step and please explain this to me it is crucial!

1) 3200kg/m^3 ----> g/cm^3

2) 3200kg/m^3 * 1000kg/1g*1m^3/1*10^-6cm^3 = 3.2kg/cm^3

I just dont understand why I divide g/m^3 by a million to reach g/cm^3. Isnt one cm^3 a smaller value(or area) than a m^3? Shouldn't I be multiplying by a million?

For instance: if I dont have a density and simply convert 100m^3 to 100cm^3 the answer is 100 000 000 cm^3. This makes sense because a metre is larger than a CM thus the value will be bigger .

So, Why is this not the case for when I have a density? Why do I have to divide by a million in order to go from m^3 to cm^3 in that case and ultimately reach a smaller value.

Please help me understand where my logic goes wrong.