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Percentage Uncertainty

  1. Feb 7, 2014 #1
    Two lengths, a and b, are measured to be 51+/-1cm and 49+/-1cm respectively. In which of the following is the percentage uncertainty the largest?

    A a+b
    B a-b
    C a x b
    D a/b

    The answer should be b but I can't figure out why. I know that for / and x you add the percentage errors so if the error is approx 2% then each of C and D have errors of 4% of their answers ie

    C 51 x 49 = 2499 and 4% is ~100
    D 51/49 = 1 and 4 % is 0.04

    I think that for + and - you add absolute uncertainties ie 0,02 + 0.02 = 0.04 ie

    A 51 + 49 = 100 and 100 x 0.04 = 4
    B 51 - 49 = 2 and 2 x 0.04 = 0.08

    But that makes C the largest error.

    What am I missing here? It's supposed to be multiple choice, non calculator so I'm probably overthinking it?
     
  2. jcsd
  3. Feb 7, 2014 #2

    BvU

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    Don't see how absolute uncertainties of 1 each can add up to 0.04 ...
     
  4. Feb 7, 2014 #3

    haruspex

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    100 is the absolute error. You are only interested in percentage errors, so stop the calculation at 4%.
    I'm guessing calculator20 is considering +/-1 as a range of 2.
     
  5. Feb 7, 2014 #4

    BvU

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    @calc: 0.02 is the relative error! You want the absolute error here !

    for error read uncertainty - saves confusion
     
    Last edited: Feb 7, 2014
  6. Feb 7, 2014 #5

    HallsofIvy

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    Then a+ b= 100 +/- 2 cm (NOT 4) so the percentage error is 2/100= 2%

    a- b= 2+/- 2 cm so the percentage error is 2/2= 100%

    The percentage errors for a and b separately are 1/51= 0.0196 or about 2% and 1/49= 0.02041 or about 2% so the percentage errors of a x b and a/b are 2+ 2= 4%

     
  7. Feb 7, 2014 #6

    BvU

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    @Ivy: I thought we wanted calc to learn something, not have the answers dumped in his lap !
     
  8. Feb 7, 2014 #7

    BvU

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    All in good spirit, of course...
     
    Last edited: Feb 7, 2014
  9. Feb 8, 2014 #8
    Thank you everyone. I'd gone with fractions rather than whole values. I can see where things went wrong now. Many thanks!
     
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