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Multiplying mass as kg and grams= 2 different results?

  1. Aug 6, 2015 #1
    Hi, I'm just wondering. If you mulitiply 1kg with 0.5kg you get 0.5kg

    But if you do the multiplication in grams you get
    1000g *500g = 500.000g = 500kg. a dompletely different result.

    Why is that? How do you avoid this problem?
     
  2. jcsd
  3. Aug 6, 2015 #2

    e.bar.goum

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    Science Advisor
    Education Advisor

    No, when you multiply 1kg with 0.5 kg you get 0.5 kg2 - square kilograms. You must also multiply the units!

    1000g *500g = 500 000 g2

    Now, to convert square kilograms to square grams,

    1kg * 1kg = 1000 g * 1000 g = 1 000 000 g2

    So, now we take 500 000/ 1 000 000 g2 = 0.5 kg2. Precisely the same result.
     
  4. Aug 6, 2015 #3

    ShayanJ

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    Gold Member

    ## 1 \ kg \ \times \ 0.5 \ kg=0.5 \ (kg)^2=0.5 \ \times \ 10^6 \ g^2 ##
    ## 1000 \ g \ \times \ 500 \ g=0.5 \ \times \ 10^6 \ g^2 ##
     
  5. Aug 6, 2015 #4

    Mark44

    Staff: Mentor

    Without any context, I can't think of any reason you would want to multiply two quantities in kilogram units.

    As already posted, the units of the product would be kg2, which by itself isn't very meaningful.
     
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