Expert: John Zalewski - 9/21/2011

Question
I saw on of your answers to the question how to change from g/ml to kg/l and you answered that you write down 1kg = 1000g so we first divide it by 1000 and then we write down 1000ml = 1l so we multiply it by 1000 my question is that why by the g to kg we divide it and then by ml to l we multiply it why can't we also by the ml to l write down 1l = 1000 ml so we divide it again by 1000? Thanks a million!

Answer
Hello, Chaim.

When you do dimensional analysis, you have to make sure that the units you wish to have cancelled are on opposite sides of the fraction. So, when you convert, say, 10 g/ml to kg/l, you need to write it as such:


10g/ml x 1000 ml/1L x 1 kg/1000 g

When you do so, the 'milliliters' and 'grams' cancel, so we are left with kg/L (10kg/L after doing the math).

If you wrote instead 1L/1000ml, then the milliliters would not cancel. That is what needs to be kept in mind.

I hope this helps. If you have additional questions, please ask.

Regards,
John