1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

General equation for fractional error

  1. Oct 1, 2008 #1
    1. The problem statement, all variables and given/known data
    Using the error propagation rule for functions of a single variable, derive a general expression for the fractional error, Δq/q, where q(x)=x^n and n is an integer. Explain your answer in terms of n, x, and Δx.


    2. Relevant equations
    The uncertainty of a function of one variable will be Δq=abs(dq/dx)Δx


    3. The attempt at a solution
    Okay, so I figured I could divide both sides of the equation above by dq, which will give a fractional uncertainty. This seems okay, but having dx in the denominator doesn't seem like a good idea. Any ideas on where to begin? Thanks.
     
  2. jcsd
  3. Oct 1, 2008 #2

    LowlyPion

    User Avatar
    Homework Helper

    Isn't what they are asking is for you to apply the propagation rule for multiplication? Addition and subtraction are the sum of the absolute errors and multiplication and division are the sum of the relative (fractional) uncertainties. So xn results in how many multiplications?
     
  4. Oct 1, 2008 #3
    Right, the propagation rule for multiplication says Δq/q=sqrt[(Δx/x)2+...(Δz/z)2]
    But if it's only for one variable, it reduces to Δq/q=sqrt[(Δx/x)2] ---> Δq/q=Δx/x right?

    xn results in n multiplications... of what, though, beside x?

    Thanks.
     
  5. Oct 1, 2008 #4

    LowlyPion

    User Avatar
    Homework Helper

    X is the only independent variable it says.
     
  6. Oct 1, 2008 #5
    Well yeah. So the original question asked for a general equation for fractional uncertainty where q(x)=x^n. But that's not the answer obviously. If you just take the reduced form of the propagation of uncertainty, you get Δq/q=Δx/x. So...
    q(x)=(Δx/x)1. That doesn't seem right. Maybe I need to set xn equal to Δx/x, then the result of that is my q(x)?
     
  7. Oct 1, 2008 #6

    LowlyPion

    User Avatar
    Homework Helper

    Just wondering why you are avoiding saying Δq/q = n*(Δx/x)
     
  8. Oct 1, 2008 #7
    I'm afraid I don't see why that's true...
    What is n representing in this case?
     
  9. Oct 1, 2008 #8

    LowlyPion

    User Avatar
    Homework Helper

    Isn't your function q = xn ?

    Δq/q = Δx/x + Δx/x + Δx/x ... Δx/x

    n times?

    Δq/q = n*(Δx/x)
     
  10. Oct 1, 2008 #9

    Oooh okay. I guess I was getting caught up with incorporating the exponential n in the final equation.
    Δx/x + Δx/x + Δx/x ... Δx/x is all the uncertainties added together, each which is dependent only on x. I think I got it, thanks for the help.
     
    Last edited: Oct 1, 2008
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: General equation for fractional error
  1. Derive Error Equation (Replies: 1)

Loading...