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Propagation of error if one of the values is 0

  1. Nov 2, 2009 #1
    I'm doing a lab write-up and I've run into a snag. I'm trying to do propagation of error in a product, but one of my quantities that I'm multiplying is 0. The propagation of error formula for z = xy is

    [tex]
    \left ( \frac{\Delta z}{z} \right )^2 = \left( \frac{\Delta x}{x} \right )^2 + \left (\frac{\Delta y}{y} \right )^2
    [/tex]

    But if either x or y = 0, what happens?
     
  2. jcsd
  3. Nov 2, 2009 #2
    Is it 0 by definition or is that just a measurement with low accuracy?
     
  4. Nov 2, 2009 #3
    it's the velocity of a cart that was measured by a motion sensor, so it's a measurement. the value is 0.00 +/- 0.005.
     
  5. Nov 2, 2009 #4

    Delphi51

    User Avatar
    Homework Helper

    If you look into the partial derivative definition used to find that error propagation formula, you will see that x = 0 makes the infinite term disappear. See
    http://www.rit.edu/cos/uphysics/uncertainties/Uncertaintiespart2.html#muldiv [Broken]
     
    Last edited by a moderator: May 4, 2017
  6. Nov 2, 2009 #5
    thank you. i haven't learned partial derivatives yet, so i'll have to take your word for it.
     
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