I've been puzzling over a question I've posed for myself involving floating point operations. My specific question was originally: given the number PI, if I plan to raise it to some power y, how many digits to the right of the decimal point would I need to ensure an answer that was correct to the least significant integer?
Given small y, this is easy to play with in Excel, but I'm looking for the more general area of knowledge and how one would attack this problem for other numerical data and criteria. I am sure there is some branch of mathematics devoted to this type of analysis, but I don't even know what to search for. I've browsed a few of the large math web sites, but other than the extremely broad area of numerical analysis, I'm at a loss as to where else to head.