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Physics Calculating Uncertainty Question (urgent)


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This is related to calculating uncertainties. If I have 12.5400 +/- 0.0025 and I need to do the following: 

(4/3) * 3.14 * (12.5400 +/- 0.0025)3, what is my new uncertainty?

I've read that I need to multiply the uncertainty by the power, ie .0025 * 3 and then I would multiply this by the constant 3.14 and (4/3) which would give me: +/- 0.0314

But I've also read that first you convert the uncertainty to a percentage, then add them, ie 12.543 +/- 0.06%, then I would simply multiply 12.543 * (4/3) * 3.14 and my uncertainty would stay the same at +/- 0.06% but this would give me an absolute uncertainty of like 495 which is completely different to method 1

I'm really confused on what to do and if somebody could help me out that would be amazing

Edited by Legend3107
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Method I: Multiple percentage (decimal) uncertainty by 3, then multiply by the volume. %unc = 0.0025 / 12.54 = 0.0002. Multiply by 3, 0.0006. Then multiply by volume to get 8255.83 ± 4.95, which when reducing number of significant digits in uncertainty become 8256 ± 5. Remember to not multiply number by percent, but by the decimal. So for example if you find 75% of 100, you don't multiply 100 by 75.

Method II. Just a more general way than Method I. Treat the volume as (4/3) (3/14) (12.5400 ± 0.0025)(12.5400 ± 0.0025)(12.5400 ± 0.0025), sum the percentage uncertainties. 0.0002 + 0.0002 + 0.0002 = 0.0006 and the rest is same, you get 8256 ± 5.

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