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Relative uncertainty question

  1. Sep 18, 2009 #1
    1. The problem statement, all variables and given/known data
    A distance R is measured to be 4.000±0.002 m
    What is the relative uncertainty in the square root of R?


    2. Relevant equations
    Relative uncertainty is the ratio of the absolute uncertainty of a measurement to the best estimate. It expresses the relative size of the uncertainty of a measurement (its precision).

    relative uncertainty = absolute uncertainty / best estimate of value x 100%.
    So the abosulute is 0.002, where estimated value of R is 4 m


    3. The attempt at a solution
    all I got is that the square root of R is 2 m, but relative uncertainity of R is 0.002 / 4, however when I square root R, I don't know how I reflect the change in the +-0.002 m.
     
  2. jcsd
  3. Sep 19, 2009 #2
    one more peice of info I believe is correct

    If say, I had to calculate the relative uncertainty of R^2, then I could write R^2 as R x R, and when multiplying or dividing, I realize I have to add the relative uncertainties, Therefore, the relative uncertainty of R^2 is 0.002 + 0.002 = 0.004 (or 0.4%)

    I can not reflect this situation if using R^(1/2), because I do not know what to add...

    any suggestions?

    thanks
     
  4. Sep 19, 2009 #3
    when i said "Therefore, the relative uncertainty of R^2 is 0.002 + 0.002 = 0.004 (or 0.4%)" i meant to say, the relative uncertainty of R^2 is 0.002/4 + 0.002/4 = 0.0005 or 0.05%.
     
  5. Sep 19, 2009 #4
    i am still relatively uncertain about how to do this question

    any suggestions would be great!
     
  6. Sep 20, 2009 #5
    ive looked into this more, and if R was already the squareroot, and I know that squaring it would have to give 0.0005, that would mean R x R = R^2, which addes 2 values to give 0.0005, which would be 0.00025 + 0.00025,

    so would the answer to my very original question be 0.00025?!?! (A distance R is measured to be 4.000±0.002 m
    What is the relative uncertainty in the square root of R?)

    please could someone help
     
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