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Determine the uncertainties

  1. Aug 21, 2014 #1
    1. The problem statement, all variables and given/known data
    what is the uncertainty of [tex] \frac{a+b}{c+d} [/tex] if a=b=c=d and [tex] σ_a = σ_b =σ_c=_d [/tex]


    2. Relevant equations

    [tex] σ_{a+b}=√(σ_a^2+σ_b^2) [/tex]

    [tex] σ_{\frac{a}{b}}=√((\frac{σ_a}{a})^2+(\frac{σ_b}{b}^2)) [/tex]

    3. The attempt at a solution
    since a=b=c=d

    [tex]
    σ_{a+b}=√2 σ_a [/tex]

    [tex] σ_{\frac{a}{b}}=√2 \frac{σ_a}{a} [/tex]

    so [tex] σ_{\frac{a+b}{c+d}} = \frac{√2 √2 σ _a}{2a} = \frac{σ_a}{a} [/tex]

    is this correct?!

    Thanks
     
    Last edited: Aug 21, 2014
  2. jcsd
  3. Aug 21, 2014 #2

    gneill

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    Staff: Mentor

    The result looks good to me!
     
  4. Aug 21, 2014 #3
    Great thanks :) any idea why it is the same as the uncertainty in a single measurement... Just doesn't seem right to me! Xxx
     
  5. Aug 21, 2014 #4

    BvU

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    Science Advisor
    Homework Helper
    Gold Member

    It is NOT the same as the uncertainty in a single measurement! That would be ##\sigma_a##. Since you are evaluating a ratio, only relative errors matter. The factors ##\sqrt 2## and 2 just happen to cancel.

    You can repeat the exercise with ##{a+b+c}\over e+f+g## and see what happens...
     
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