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Basic numeracy - exact meaning of accurate to one part in a thousand

  1. Aug 31, 2013 #1
    Basic numeracy - exact meaning of "accurate to one part in a thousand"

    1. The problem statement, all variables and given/known data

    I have a standard Coulomb model for the ground-state energy of a hydrogen atom. I have used peturbation theory to calculate a (fictitious) first order correction to the model, which contains a constant a.
    I now have to find the largest value of a which will be consistent with the fact that the Coulomb model is accurate to one part in a thousand.
    It's a basic numeracy problem, despite being a complicated topic. Does accurate to one part in a thousand mean that the correction shouldn't contribute more than +/- 0.001 J to the energy calculated using the Coulomb model, or does it mean it shouldn't add more than +/- 0.00049999 J?
    A bit basic, I know, but I don't want to fail at this final hurdle.
    Thanks in advance.

    2. Relevant equations

    ##E = E_c + \delta E##


    3. The attempt at a solution
     
  2. jcsd
  3. Aug 31, 2013 #2

    HallsofIvy

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    Why "-.00049999"? Why exactly 4 "9"s? "Accurate to one part in a thousand" means within [itex]\pm 0.0005[/tex].

     
  4. Aug 31, 2013 #3
    Well, perhaps that was a bit sloppy. My point was that shouldn't it be ##\delta E < 0.0005## (instead of ##\delta E \leq 0.0005##) because if the correction was actually 0.0005 then it could be rounded up to 0.001, thereby altering the one part in a thousand?
    I don't know if I've explained my dilemma properly there...
     
  5. Aug 31, 2013 #4

    vela

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    One part in a thousand means ##|\delta E/E_c|## needs to be less than 1/1000.
     
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