Advanced measurement error: propagation of uncertainty

This is the video about propagation of error/uncertainty I wish had been out there when I was learning this stuff.
Note: I have glossed over some details in how EXACTLY significant figure rules are explained by the full treatment. Left as a proof to the reader!
Also, note that my intuitive geometric explanation only really makes sense when the operation being done is addition/subtraction or multiplication/division. If you're trying to get the uncertainty in a measurement being raised to the 4th power, for example, I have no obvious geometric reason that the error is 4 times the error of the measurement (though it does kind of make sense as an extension of this.)
*****Oct 31, 2022 update: At 4:32*****
I have made a mistake in my calculation of the uncertainty of the area. I have written 10%, but INCORRECTLY written the fraction as 0.01. The uncertainty should in the area should be sqrt(0.1^2+0.042^2) = 0.108 = 10.8%. Obviously, the hypotenuse of a triangle can't be smaller than either of its legs!

[@loodog555]

*****Oct 31, 2022 update: At **4:32*******
I have made a mistake in my calculation of the uncertainty of the area. I have written 10%, but INCORRECTLY written the fraction as 0.01 and messed up the calculation as a result. The uncertainty should in the area should be sqrt(0.1^2+0.042^2) = 0.108 = 10.8%. Obviously, the hypotenuse of a triangle can't be smaller than either of its legs! This is smaller than the original ROUGH WORST-CASE of 14%, but it is NOT 4.3%.

[@jankokokosar9976]

I noticed in a moment. Thank you for this correction.

[@bolton368]

This is a bit different
Your a teacher. Cool

[@loodog555]

Yeah, I was going to keep this in my separate private teaching space, but I was thinking that this was the video I wished someone had made for me when I was learning this stuff so I wanted it to be discoverable for random internet people trying to find it too.