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

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

## Homework Statement

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.

## Homework Equations

$E = E_c + \delta E$

## The Attempt at a Solution

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HallsofIvy
Homework Helper

## Homework Statement

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

A bit basic, I know, but I don't want to fail at this final hurdle.

## Homework Equations

$E = E_c + \delta E$

## The Attempt at a Solution

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...

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