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Calculation of uncertainty

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  1. Dec 12, 2015 #1
    1. The problem statement, all variables and given/known data

    a=12.26 +/- 0.08
    b=0.25 +/- 0.05
    e=1.2 +/- 0.2

    Evaluate the uncertainty of following calculations

    Part 1. z= 5(ab/e)

    Part 2. p= 3e - b

    3. The attempt at a solution
    I attempted part 1 like this
    Δz/z = 5 (Δa/a + Δb/b + Δe/e)
    ...
    Calculated Δz to be 20 but the answer is
    Δz/z = (Δa/a + Δb/b + Δe/e)
    ...
    Δz = +/- 5 (to 1 sf)

    Then I saw part 2's answer like this:
    Δp = 3Δe + Δb
    ...
    Δp= +/- 0.7 (to 1 sf)

    Now I'm confused. Why is it that in part 1 the constant 5 in not taken into account when calculating uncertainty, but in part 2 the constant 3 is included? Am I doing it wrong?
     
  2. jcsd
  3. Dec 12, 2015 #2

    Samy_A

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    Science Advisor
    Homework Helper

    In part 2 you are computing an absolute uncertainty, so the absolute uncertainty on 3e is 3 times the absolute uncertainty on e.
    In part 1 you are computing a relative uncertainty, so a constant doesn't matter.

    Imagine (for part 1) that 5 is a measured value d, with d=5 +/- 0.
    Then for the relative uncertainty of z we get:
    Δz/z =(Δd/d + Δa/a + Δb/b + Δe/e)=(0+Δa/a + Δb/b + Δe/e) =(Δa/a + Δb/b + Δe/e)
    A value with 0 uncertainty has no impact on the relative uncertainty, that's why you ignore multiplication by a constant when computing a relative uncertainty.

    (Reference)
     
    Last edited: Dec 12, 2015
  4. Dec 12, 2015 #3
    Thank you for the really helpful explanation!
     
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