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Significant figures

  1. Sep 16, 2013 #1

    Zondrina

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    Homework Helper

    1. The problem statement, all variables and given/known data

    A 200. kg sample of MgO is given (Notice 3 sig figs). How many kg of magnesium ions would there be?

    2. Relevant equations

    %Mg = 62%
    %O = 38%

    3. The attempt at a solution

    Just a quick question I had about significant figures.

    The sample of MgO given is 200.kg (3 sig figs). The percent composition of magnesium is 62% (2 sig figs). Therefore 62% of the 200.kg will be magnesium.

    (62%/100%)(200.kg) = (0.62)(200.kg) = 124kg, but because the answer must have 2 sig figs, the final answer would be 120kg ( This is my suspicion ).

    Notice if the kg of oxygen is calculated :

    (38%/100%)(200.kg) = (0.38)(200.kg) = 76kg. This answer already has 2 sig figs, so nothing needs to be changed.

    Now when added together : 120kg + 76kg = 196kg < 200.kg.

    Is this result a fault of the rules or a fault of my own?
     
  2. jcsd
  3. Sep 16, 2013 #2

    Borek

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    Staff: Mentor

    Rounding often messes the result in some way. And as significant digits are far from being perfect (generally speaking they are a poor man's way of dealing with uncertainties) there is nothing strange in the fact calculations done using them yield strange results.
     
  4. Sep 16, 2013 #3

    Zondrina

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    Homework Helper

    Yes, rounding leaves a sour taste every time. Thank you for the confirmation though, I just wanted to make sure.
     
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