 
Summary: FloatingPoint 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 floatingpoint numbers. Mathematica has two kinds of floatingpoint numbers: machine
