Legend3107 0 Posted October 22, 2017 Report Share Posted October 22, 2017 (edited) 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 12.54^{3} +/- 0.06%, then I would simply multiply 12.54^{3} * (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 October 22, 2017 by Legend3107 Reply Link to post Share on other sites

kw0573 1,252 Posted October 22, 2017 Report Share Posted October 22, 2017 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. Reply Link to post Share on other sites

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