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Uncertainty in 1/x

Discussion in 'Mathematics' started by Newstein, Jan 17, 2019.

  1. Newstein

    Newstein New commenter

    If x = (10.0 +- 0.1) cm, 1/x = (0.10 +- ?)
    I placed this qn in Science also.
  2. Newstein

    Newstein New commenter

    If y = 1/x,
    dy/dx = - 1/x^2
    mod delta y = (1/x^2) delta x
    And for x = 10.0, delta y = (1/100) times 0.1 = 0.001
    Sounds incorrect. Can uncertainty in 1/x be less than that of x?
  3. gnulinux

    gnulinux Occasional commenter

    Yes. You have more or less demonstrated that for x=10. What about for other values of x???
  4. briancant

    briancant Occasional commenter

    Well I've had a couple of beers but you work out the percentage uncertainty of 1 and 10 and add them. Given their is no uncertainty in 1 and the percentage uncertainty in 10 is 1% the uncertainty in 0.1 is 1% of 0.1. So = 0.1 +- 0.001.

    And if that make sense tomorrow I'll be amazed!!
  5. NoSuchThingAsNormal

    NoSuchThingAsNormal New commenter

    The error is the same in the reciprocal as it is in x, surely?

    x = 1 +/- 5%
    1/x ~ 1 +/- 5%
  6. briancant

    briancant Occasional commenter

    How does an absolute uncertainty of +-0.1 from a measurement of 10.0 equate to 5%? Surely this is 1%?

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