Physics CH 0: General Introduction (9 of 20) Multiplying with Uncertainties in Measurements

In this video I will multiply 2 lengths when there are uncertainties in the measured length.

Next video in the series can be seen at:

[xLegiolx]

Thanks a lot professor, you came up with very specific examples and it helps a lot, keep doing this tutorials please. correct the mistake at the end of the video 3x10^1 instead 3 x 10^2

[alexgordon]

Thank you so much, i have looked around the internet for examples for this and all have come up with bad examples and don't give a detailed explanation. This really helped.

[jordanmwandila]

Professor you are the best in our Zambian language we say professor ULI Mu nyoli nyoli 💯🔥☑️

[umutesener]

Can you please explain how to determine the standard deviation of this multiplication? Great video btw, very simple and clear.

[patrickmutuku]

That definition of significant figures though. its a bit loose

[fardeenzaman]

Should've been +- 20 cm^2 at the end as 25 itself would round down to 20 with Sig dig rules. On top of that the real number was actually 24 so it definitely should've been rounded down. Otherwise, excellent explanation!

[MariusRenn]

I might be misunderstanding the method here, but there seems to be an important factor missing: Take the following example: (2±1)*(2±2) which outputs a range of [0, 12] (as the smallest result is 1*0 and the largest is 3*4). Using the proposed method you'd have (2±50%)*(2±100%) which would give you a result of (4±150%) or (4±6), which would NOT cover the range [0, 12]. The missing factor is that the uncertainties need to be multiplied as well. After all, having uncertainties p, q in (x+p)*(y+q) yields xy+py+qx+pq, where the uncertain portion is py+qx+pq. This could be rewritten to (p/x+q/y)*xy + pq. This shows that writing the uncertainties as ratios (as proposed in the video) is fine, but you still need to add the product of uncertainties pq at the end. This would also "fix" the above example equation as you would add another 1*2=2 to the uncertainty to obtain (4±8), which covers the actual range. I think the only reason it "works" in the video is because the uncertainties are small and so their product is even smaller. With the generous rounding, this mistake is then glossed over.

[kuesitithy]

How should I go about this question please
(123 +- 1%) (1.1 +- 1%)
Please tag me when you're done. Thank you again 🙏

[kritika]

wow this was so easy to follow and so quick as well thank you!

[sselinnnk]

How did he know how to round of the percentage uncertainties to those numbers?

[manmohanbisht]

Sir while rounding off 25 it won't become 30 right..
Since 2 is even so we don't change the digit..

e. g.
1245
Round of will be 124

[davidbobek]

(3*10^2)cm^2 = 300cm^2 and not 30cm^2, or am I wrong?

[ayushdubey]

sir I am an Indian and i preferred your channel, you rought very well i don't have even thanks alot and YOU GOT A NEW SUBSCRIBER

[blakenz]

'if you want to be absolutely certain' haha i see what u did there prof.

[anasalayad]

at 4:19 the final result is incorrect. the correct answer is 3×10 only without the power of 2

[elizabethleiva]

Good morning. Thanks for the videos. Could you please solve the problem # 1.16 Section 1.5 Uncertainties and significant figures. Young Freedman edition 12

[manojdimri]

Sir please tell me why you add percentage. Is this a rule, if it is so please explain it.

[Firster]

Sorry sir, could u please help me.I have to divide 4 to (6 +-0, 043).Are There any problems with the uncertainty in divison that has 2 significant numbers?

[aminabdelmaboud..]

I really love your simplicity :'( 🤍

[Ineedanaccountnow]

Okay but how do you know how many significant figures to put in your percentages?