How to determine which formula is subject to which type of error

Question

Y = 3396.2341542
F=(4pi(Y+x)^2)-(4piY^2)
G=8*pi*(Y*x)

If x is generally a small number (<0.00001) Which of these formulas would be subject to round-off error and which would be subject to truncation error?

I think the first one is round-off error but what is the second?

Answer 1

Your question is not a programming question, so I would highly recommmend you to post it on a different forum, e.g. Physics Stackexchange since it seems to be a physics-related question. Just a few hints to help you on your way: - the first line is not a formula, it is a parameter declaration, so it is probably wrong to say this first 'formula' would be subject to round-off error. - a truncation error is the error made by truncating an infinite sum and approximating it by a finite sum

A good way would now be to just think about how the outcomes of F and G are affected if the input variable Y is subject to one of these errors.

Good luck!