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

Homework help: Uncertainty with negative power

  • #1
5
0
Question:
A distance R is measured to be 3.400 ± 0.007m. What is the absolute uncertainty in R^−2?

Attempted solution:
Relative uncertainty: 2* (0.007/3.4) = 4.11E-3;
R^-2 = 3.4^-2 = 0.0865 m^-2;
Absolute uncertainty = R^-2 * relative = 0.0865 * 4.11E-3 = 3E-4 m^-2;

Any help would be greatly appreciated!!

EDIT: instead of 3E-4, the correct rounding should be 4E-4.
 
Last edited:

Answers and Replies

  • #2
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,252
970
Question:
A distance R is measured to be 3.400 ± 0.007m. What is the absolute uncertainty in R^−2?

Attempted solution:
Relative uncertainty: 2* (0.007/3.4) = 4.11E-3;
R^-2 = 3.4^-2 = 0.0865 m^-2;
Absolute uncertainty = R^-2 * relative = 0.0865 * 4.11E-3 = 3E-4 m^-2;

Any help would be greatly appreciated!!
Hello @Jerry Z . Welcome to PF !

What's your question?
 
  • #3
5
0
Hello @Jerry Z . Welcome to PF !

What's your question?
i cannot get the right answer for the question stated
 
  • #4
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,252
970
i cannot get the right answer for the question stated
Perhaps there is a problem with significant figures and/or rounding off at intermediate steps.
 
  • #5
5
0
Perhaps there is a problem with significant figures and/or rounding off in intermediate steps.
So I'm solving it correctly?
 
  • #6
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,252
970
So I'm solving it correctly?
What you did looks reasonable.

The details of getting uncertainties and applying rules for significant figures vary somewhat from book to book, instructor to instructor, discipline to discipline .

I suggest keeping two extra digits (over what's required for sig. figs.) .

OR

Do the entire calculation at one time with no intermediate steps. (Be especially careful of Order of Operations.)


Do final rounding at the end to whatever decimal place is required in your situation.
 
  • #7
5
0
What you did looks reasonable.

The details of getting uncertainties and applying rules for significant figures vary somewhat from book to book, instructor to instructor, discipline to discipline .

I suggest keeping two extra digits (over what's required for sig. figs.) .

OR

Do the entire calculation at one time with no intermediate steps. (Be especially careful of Order of Operations.)


Do final rounding at the end to whatever decimal place is required in your situation.
Thank you so much! It is indeed the rounding in the end that made the difference.
 
  • #8
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,252
970
Thank you so much! It is indeed the rounding in the end that made the difference.
Great !

So, what was the acceptable answer?
 
  • #9
5
0
Great !

So, what was the acceptable answer?
Answer is edited in the original text. Thanks again!
 
  • #10
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
32,721
5,029
This is an example of the merits of keeping everything algebraic as long as possible, only plugging in values at the end. In the present case, when at last plugging in numbers, you would have had 2*0.007/3.43. Putting that into my calculator gives 0.000356.
 

Related Threads on Homework help: Uncertainty with negative power

Replies
2
Views
3K
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
6
Views
12K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
7
Views
1K
Replies
2
Views
2K
  • Last Post
Replies
1
Views
464
  • Last Post
Replies
1
Views
82
  • Last Post
Replies
1
Views
8K
  • Last Post
Replies
1
Views
3K
Top