How do I convert kg/m3 to g/cm3 and understand the logic behind it?

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Discussion Overview

The discussion centers around the conversion of density units from kilograms per cubic meter (kg/m³) to grams per cubic centimeter (g/cm³), specifically addressing the logic and reasoning behind the conversion process. Participants explore the dimensional analysis involved in this conversion and seek clarification on the underlying principles.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant presents a specific conversion example (3200 kg/m³ to 3.2 g/cm³) and expresses confusion about the steps involved in the conversion process.
  • Another participant suggests a method for conversion by multiplying by the conversion factor for grams per kilogram and dividing by the conversion factor for cubic meters to cubic centimeters.
  • Concerns are raised about the logic of dividing by a million when converting from m³ to cm³, with one participant questioning why a smaller volume results in a smaller density value.
  • Some participants emphasize the importance of understanding the relationship between the units and the need for dimensional consistency in the conversion process.
  • There is a suggestion that the coefficients in the conversion must also be correctly placed to ensure the accuracy of the answer.
  • One participant expresses frustration over the misunderstanding and reiterates the need to ask fundamental questions about unit relationships.

Areas of Agreement / Disagreement

Participants express differing levels of understanding regarding the conversion process, with some agreeing on the method while others remain confused about the logic behind dividing by a million. The discussion does not reach a consensus on the reasoning behind the conversion steps.

Contextual Notes

Participants highlight the need for clarity on the relationship between different units of measurement, particularly in the context of density, but do not resolve the underlying confusion regarding the conversion logic.

Nellen2222
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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 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.

Please help me understand where my logic goes wrong.
 
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3200 kg m-3 = 3200 kg m-3 X 1000 g kg-1/ 100000 cm3 m-3
 
? what
 
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.
 
The dimensions can match but the coefficiant(value in front) can be in either spot.. so technically can still have the wrong answer..
 
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?
 
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..
 
? What are you saying!? Isn't metre is shorted as m?
 

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