Floating-Point Arithmetic Precision and Accuracy Summary: Floating-Point Arithmetic Precision and Accuracy With Mathematica Alkis Akritas University of Kansas Dept of Computer Science 415 Snow Hall Lawrence KS 66045 USA akritas@eecs.ukans.edu Introduction In performing numerical computations on a computer, we are faced with the problem of representing the infinite set of real numbers within a computer of finite memory and of given word length; therefore, certain compromises have to be made. For example, Sqrt[2] represents some number which is approximately 1.41421. If we want to represent it exactly there is little choice but to leave it as Sqrt[2]. For arithme- tic purposes this is rather useless, but to say that Sqrt[2] is equal to 1.41421 (or, any other finite decimal expansion) is simply wrong. What is usually done is to work with approximations and accept the fact that the end result is also an approximation. The most widely implemented solution in Numerical Analysis is to approximate the real numbers using the finite set of floating-point numbers. Mathematica has two kinds of floating-point numbers: machine- Collections: Computer Technologies and Information Sciences