Math class is tough!
This section provides a high-level overview of the issues involved when doing lots of floating-point arithmetic.98 The discussion applies to both hardware and arbitrary-precision floating-point arithmetic.
CAUTION: The material here is purposely general. If you need to do serious computer arithmetic, you should do some research first, and not rely just on what we tell you.
There is a very nice paper on floating-point arithmetic by David Goldberg, “What Every Computer Scientist Should Know About Floating-Point Arithmetic,” ACM Computing Surveys 23, 1 (1991-03): 5-48. This is worth reading if you are interested in the details, but it does require a background in computer science.