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Homework Help: Dimensional analysis questio

  1. Sep 16, 2012 #1
    1. The problem statement, all variables and given/known data

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

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

    2. Relevant equations

    The question was 3200kg/m3 = 3.2g/cm3. I don't understand the steps involved?
    3. 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.
  2. jcsd
  3. Sep 16, 2012 #2


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    3200 kg m-3 = 3200 kg m-3 X 1000 g kg-1/ 100000 cm3 m-3
  4. Sep 16, 2012 #3
    ? what
  5. Sep 16, 2012 #4


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    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.
  6. Sep 16, 2012 #5
    The dimensions can match but the coefficiant(value in front) can be in either spot.. so technically can still have the wrong answer..
  7. Sep 16, 2012 #6


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    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?
  8. Sep 16, 2012 #7
    yeah- its all about 'ask yourself' - I just dont get why im dividing by a million if a m^3 is bigger than a metre^3..
  9. Sep 16, 2012 #8


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