How Should Uncertainty Be Reported for the Square Root of a Measurement?

[arierreF]

Homework Statement

Book: Introduction to error analysis, Taylor

In page 66, quick check 3.8

If you measure x = 100$\pm$ 6, what should you report for $\sqrt{x}$with its uncertainty.

Homework Equations

Rule for uncertainty as power:
$\frac{∂q}{|q|}$ = |n|$\frac{∂x}{|x|}$where $q = x^{n}$

3. Attempt

So our function is q = $x^{\frac{1}{2}}$

then σq = 0,3. (as in solution)The problem that is killing me is if i decide to use the general rule for error propagation, the result is different.

Using that rule:

|σq| = |$\frac{∂q}{|x|}| Δx = | \frac{1}{2\sqrt{x}} |Δx$
That gives:

|σq| ≈ 0,3After all, the problem is correct. It was just bad calculations.

I do not to know how to delete topics. :/

 

[anathema]

Thank you for your post. As a fellow scientist, I can understand your frustration with the discrepancy in the results obtained using different methods for error propagation. However, it is important to note that both methods are valid and can be used depending on the context and the specific problem at hand.

When it comes to reporting uncertainties, it is always best to follow the rules and guidelines set by your institution or field of study. In this case, since you are using the book "Introduction to error analysis" by Taylor, it is best to follow the method presented in the book. This will ensure consistency and accuracy in your reporting.

In the future, if you encounter any doubts or difficulties in your calculations, I would suggest seeking assistance from your professor or colleagues. Sometimes a fresh pair of eyes can help identify any errors in calculations.

As for deleting topics, unfortunately, as a forum user, you do not have the authority to delete topics. However, you can always edit your posts to correct any errors or misunderstandings.

I hope this helps, and best of luck with your studies.