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Error calculation

  1. Mar 27, 2012 #1
    1. The problem statement, all variables and given/known data

    a = 0.00083 ± 0.00002m

    what is 1/a with error

    2. Relevant equations

    rules for combining errors

    z = xy or z=x/y σ(z) = [σ(x)]2[σ(y)]2

    3. The attempt at a solution

    I tried doing 1/a ± 1/error

    but the error gets too big... is there a rule for this kind of situation?
  2. jcsd
  3. Mar 27, 2012 #2


    User Avatar

    Staff: Mentor

    The rule for Z = X*Y or Z = X/Y is
    $$\Delta Z = Z\sqrt{\left(\frac{\Delta X}{X}\right)^2 + \left(\frac{\Delta Y}{Y}\right)^2}$$
    A rule for powers of a value:

    If ##Z = X^n## then
    $$\Delta Z = n x^{(n - 1)} \Delta X$$
    In your case n = -1.

    Can you present your calculations showing that your error result is too large? (and too large as compared to what?)
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