• Support PF! Buy your school textbooks, materials and every day products Here!

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

  • #1
117
2
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.
Thanks in advance.

Homework Equations



##E = E_c + \delta E##


The Attempt at a Solution

 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,833
955

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.
Thanks in advance.

Homework Equations



##E = E_c + \delta E##


The Attempt at a Solution

 
  • #3
117
2
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...
 
  • #4
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,617
1,252
One part in a thousand means ##|\delta E/E_c|## needs to be less than 1/1000.
 
  • Like
Likes 1 person

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

  • Last Post
Replies
6
Views
3K
Replies
6
Views
1K
  • Last Post
Replies
3
Views
2K
Replies
16
Views
2K
Replies
1
Views
3K
Replies
3
Views
4K
Replies
3
Views
2K
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
4
Views
5K
Top