How Do You Solve Complex Error Propagation Problems?

[cold-peak]

[SOLVED] Accuracy & Error

Hi Everyone,

Just a quick question regarding Accuracy & Error.

We have been doing this for a little while (University) and I'm slightly confused with one of the problems.

I am able to do something like this and achieve the working and answer:

(7.3 ± 0.4) x (1.2 ± 0.6)    /     (5.4 ± 1.3)

ie: 1.3 * 5.4 = 7.02

0.6/1.3 = 0.46
1.3/5.4 = 0.24

Square root of: 0.46^2 + 0.24^2 = 0.52

= 0.52 * 7.02 = 3.65 to take it out of fractional error form

= (7 ± 3.6) / (5.4 ± 1.3)

= 7/5.4 = 1.29

3.6/7 = 0.51

1.3/5.4 = 0.24

= square root of: 0.51^2 + 0.24^2 = 0.56

= 0.56 * 1.29= 0.7 (to take it out of fractional error form)

ans = (1.3 ± 0.7) * 10^4 etc

However, when presented with this, I am not sure how to approach it:

Homework Statement

(102 ± 32)^5

2. The attempt at a solution
I'm just not sure what to do to it... The answer is:

 (1.1 ± 0.8) * 10^10

Just not sure how to get there, any help?EDIT: SOLVED - Was being silly!
Thanks

 

[LightHero]

for the help!Solution: (102 ± 32)^5 = (102^5 ± 32*5*102^4) = (10205760 ± 1.6 * 10^10) = (1.02 * 10^10 ± 0.8 * 10^10) = (1.02 ± 0.8) * 10^10

 

[Architeuthis Dux]

for the update on your question. It seems like you have already solved the problem and found the answer to be (1.1 ± 0.8) * 10^10. This is great! It's important to understand that when dealing with measurements and calculations, there will always be some degree of error or uncertainty. This is why it's important to properly account for and calculate with these errors in order to provide a more accurate and reliable result.

In terms of your approach to solving the problem, it seems like you used the error propagation formula to calculate the error in your final result. This is a valid method and can be used in a variety of situations. However, it's important to also consider the type of error present in your measurements. Is it a random error or a systematic error? This can also affect your approach to handling the error and calculating the final result.

Overall, great job on solving the problem and keep up the good work in your studies! Remember to always carefully consider and account for error in your scientific work to ensure accurate and reliable results.