# Dimensional analysis questio

Nellen2222

## 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 don't 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 don't 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 don't 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.

Gold Member
3200 kg m-3 = 3200 kg m-3 X 1000 g kg-1/ 100000 cm3 m-3

Nellen2222
? what

Gold Member
Convert kg into g. (multiplying 1000 g per kg)

Convert cubic metre into cubic centimetre (dividing 1000000 cc per cubic metre)

Dimensions are matched, so we get the right answer.

Nellen2222
The dimensions can match but the coefficiant(value in front) can be in either spot.. so technically can still have the wrong answer..

Gold Member
Man, they are correct. If you are adamant to make mistake, even God can't help it then. Using dimensions in coefficients helps us to determine if we are going on the right path.

Ask yourself - How many grams in a kilogram? How many cc in a litre -> how many litres in a cubic metre?

Nellen2222
yeah- its all about 'ask yourself' - I just don't get why I am dividing by a million if a m^3 is bigger than a metre^3..

Gold Member
? What are you saying!? Isn't metre is shorted as m?