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Quick question about uncertainty calculation

  1. Sep 29, 2008 #1
    1. The problem statement, all variables and given/known data
    lets say we have A * B
    A=12.8 + 0.2
    B=3.75 + 0.08
    how would we calculate the new uncertainty value
    ive seen soo many ways of doing this im a bit confused
    thanks in advance

    2. Relevant equations
    any equation used to calculate uncertainty


    3. The attempt at a solution
    the 2 main ways ive seen is one involving partial dervatives and the other is taking the square root of the answer times the (uncertainties/value)2
    im a little confused about which one to use
     
  2. jcsd
  3. Sep 29, 2008 #2

    rock.freak667

    User Avatar
    Homework Helper

    If C=AB, then

    [tex]\frac{\delta C}{C}=\frac{\delta A}{A}+ \frac{\delta B}{B}[/tex]


    this is obtained using differential calculus.
     
  4. Sep 29, 2008 #3
    (A+ε1)*(B+ε2)
    AB+Aε2+Bε11ε2

    so if we disregard the final term the incertainty would be Aε2+Bε1

    partial derivative of AB with respect to A is B
    partial derivative of AB with respect to B is A

    does that help?
     
  5. Sep 29, 2008 #4
    whats that called? I want to look that up. it looks interesting.
     
  6. Sep 30, 2008 #5
    nevermind I found it.looks like the derivative rule is the most general.

    if the uncertainties are independent you can take the square root of the sum of the squares of the partial derivatives times the uncertainties. that would be probable error not maximum error though.

    http://web.mit.edu/fluids-modules/www/exper_techniques/2.Propagation_of_Uncertaint.pdf
     
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