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Uncertainty in 1/x

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

  1. Newstein

    Newstein New commenter

    If x = (10.0 +- 0.1) cm, 1/x = (0.10 +- ?)
  2. sparkleghirl

    sparkleghirl Star commenter

    As a scientist, I'd look at it like this:

    1/10.1 = 0.099 and 1/9.9 = 0.101
    Both of these are 0.001 away from your value for 1/10 so that's what I'd give for the uncertainty.

    Another way of looking at it in science wouold be to say the original uncertainty as a % is 0.1/10 which is 1%, so we'd expect an uncertainty of 1% on the answer as well, which is what 0.001 out of 0.1 would give.

    This might not be mathematically rigourous, i don't know, but it's what we'd do in a lab. I think.
    rehaank, CheeseMongler, BG54 and 3 others like this.
  3. gainly

    gainly Star commenter

    Sparkleghirl's analysis seems perfect to me.
    Newstein likes this.
  4. BG54

    BG54 Occasional commenter

    Yes - also if we use fractions as exact values, then the mid-point for the range of 1/x would strictly be 1000/9999 or 0.100010001.... rather than 0.1, but that's probably nit-picking. :)
  5. rehaank

    rehaank Occasional commenter

    I just did exactly this on a post it note - inverse propagation of uncertainty i think
  6. Newstein

    Newstein New commenter

    Take a micrometer reading like x = (0.10 +- 0.01) cm. The uncertainty in 1/x then is
    (1/2) (1/0.09 minus 1/0.11 ) = 1.02 cm^-1
    Well, I have to accept this as well.
  7. Newstein

    Newstein New commenter

    It transpires that x and 1/x have the same % uncertainty.

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