Today, when I got my homework back from my Experimental Physics Class, I was marked off on this type of question.

X=3Y+Z+T

I said:
X=Y+Y+Y+Z+T

error(X)=(error(Y)^2+error(Y)^2+error(Y)^2+error(Z)^2+error(T)^2)^(1/2)
=(3(error(Y)^2)+error(Z)^2+error(T)^2)^(1/2)

But, the prof. was adamant that this was incorrect (even though it followed the traditional rules of algebra) and instead that this was correct:
=((3error(Y))^2+…)^(1/2)

The reason given by the prof was that the errors should not be added like regular terms but simply squared right away, although he himself had never fully understood the reason. He demonstrated another argument through derivatives that I was unable to follow, and he referred me to another professor who might be better able to explain it. Since I won’t have an opportunity to reach this prof. until Friday, Dopers?

Here’s a simple way of thinking about it logically: The error in 3Y logically has to be thrice the error in Y, so

[symbol]s[/symbol][sub]3y[/sub] = 3[symbol]s[/symbol][sub]y[/sub].