Homework help: Uncertainty with negative power

In summary: That's where the 4E-4 comes from, and the 3E-4 was due to rounding. I forget what the exact rule is for rounding, but I believe that is approximately right.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. That's where the 4E-4 comes from, and the 3E-4 was due to rounding. I forget what the exact rule is for rounding, but I believe
  • #1
Jerry Z
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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:
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  • #2
Jerry Z said:
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
SammyS said:
Hello @Jerry Z . Welcome to PF !

What's your question?
i cannot get the right answer for the question stated
 
  • #4
Jerry Z said:
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
SammyS said:
Perhaps there is a problem with significant figures and/or rounding off in intermediate steps.
So I'm solving it correctly?
 
  • #6
Jerry Z said:
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.
 
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  • #7
SammyS said:
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
Jerry Z said:
Thank you so much! It is indeed the rounding in the end that made the difference.
Great !

So, what was the acceptable answer?
 
  • #9
SammyS said:
Great !

So, what was the acceptable answer?

Answer is edited in the original text. Thanks again!
 
  • #10
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.
 
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1. What is uncertainty with negative power?

Uncertainty with negative power refers to the level of uncertainty or error associated with a measurement or calculation that involves a number raised to a negative power. This can often occur when dealing with scientific notation, where the exponent is negative.

2. How do I calculate uncertainty with negative power?

To calculate uncertainty with negative power, you will need to use a formula called the power rule for uncertainty. This involves multiplying the absolute uncertainty of the number by the absolute value of the power. The resulting product is the uncertainty with negative power.

3. Why is uncertainty with negative power important?

Uncertainty with negative power is important because it helps us understand the level of error or inaccuracy in a measurement or calculation. By knowing the uncertainty, we can determine the reliability and validity of our results and make informed decisions about their use in further experiments or studies.

4. How does uncertainty with negative power affect scientific research?

Uncertainty with negative power can significantly impact scientific research as it can affect the accuracy and precision of data and results. It is crucial for scientists to consider and accurately calculate uncertainty to ensure the validity of their findings and avoid drawing incorrect conclusions.

5. What are some common sources of uncertainty with negative power?

Some common sources of uncertainty with negative power include measurement errors, limitations of instruments, and human error in recording or calculating data. It can also occur when dealing with data that has been rounded or estimated, or when using complex equations or functions in calculations.

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