Actually, theapproximationtakes no time at all; it's just ignoring the Y, right?

And thedecision whether to do thatis not hard; but it depends oncontext. If a 1% error in your answer is acceptable, and Y is less than 1% of Z (actually, of their sum), then it's acceptable to ignore it. Unfortunately, you haven't told us the context of the video, so we have no idea what conditions led to the statement that Y can be ignored.

As for X, the idea is thatmultiplication does not change the relative error. The relative (percent) error in Z relative to Z+Y is the same as the relative error in XZ relative to X(Z+Y), because relative error is proportional; the X can be canceled. So, again, the decision whether to ignore a small number is easy: you only need to compareto the other addend, and don't have to consider any other parts of the calculation.

But by not clearly showing the specific problem you are asking about, you have complicated things. What was actually said in that video? What were they doing? How did they know that Y was negligible?

It was given that Y was negligible ..Actually, theapproximationtakes no time at all; it's just ignoring the Y, right?

And thedecision whether to do thatis not hard; but it depends oncontext. If a 1% error in your answer is acceptable, and Y is less than 1% of Z (actually, of their sum), then it's acceptable to ignore it. Unfortunately, you haven't told us the context of the video, so we have no idea what conditions led to the statement that Y can be ignored.

As for X, the idea is thatmultiplication does not change the relative error. The relative (percent) error in Z relative to Z+Y is the same as the relative error in XZ relative to X(Z+Y), because relative error is proportional; the X can be canceled. So, again, the decision whether to ignore a small number is easy: you only need to compareto the other addend, and don't have to consider any other parts of the calculation.

But by not clearly showing the specific problem you are asking about, you have complicated things. What was actually said in that video? What were they doing? How did they know that Y was negligible?

my problem is that .. who said that relative error wouldn't change if we continue with other operands/elements?(in my case multiplication .. ) ?! ..may please gimme an example for that? thanks alot! exactly that's my problem, why wouldn't relative error change if we continue to other elements/operands ?!