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Absolute Uncertainty of a Negative Power

  1. Sep 10, 2014 #1
    1. Determine the relative and absolute uncertainties of R-2 if R is measured to be 4.5 ± 0.005 m

    2. The attempt at a solution
    So according to what I know so far, multiplication and division of uncertainties requires the addition of relative uncertainties...

    First I tried to get the relative uncertainty of R-2. I assumed that a power of negative 2, that would be division twice (which I got to be 0.005/4.5 + 0.005/4.5 or just 2*(0.005/4.5)).

    According to the CAPA answers, the resulting answer I got was the correct relative uncertainty of R-2.
    The relative uncertainty I got had a value of 2.3 x10-3 or just 2x10-3

    But then when I tried to solve for the absolute uncertainty
    I multiplied this to the value of 4.5
    = 1x10-4 m-2
    However the the question posted on the CAPA problems tells me that my answer is incorrect. I'm not sure what I did wrong; the system didn't allow more than 1 digit so I rounded it down from 1.2
    Last edited: Sep 10, 2014
  2. jcsd
  3. Sep 10, 2014 #2


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    I don't know who CAPA is, but I'm on your side: relative error of .0011 in R, .0022 (not .0023 !?) in R2, so .0022 in R-2 as well.

    R-2 = .00494 and .0022 times that is .00011 (not .00012, though...).

    That the system doesn't allow more than one digit is strange: it is a good habit to provide two digits if the first digit is a 1.
  4. Sep 10, 2014 #3
    Okay. I see my mistake... I inputted 4.4 instead of 4.5 to get 0.0012; but since it was still 2x10-3 the system gave me a correct answer for that part
    I guess the program simply had the wrong answer since the only digit it wanted was the first one
    Thanks for the help
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