Although the theory of continued fractions has attracted some of the most eminent mathematicians, the subject is rarely taught in undergraduate courses, and many competent mathematicians today are unfamiliar with the subject. In recent years, there has been some resurgence of interest in
the field. In addition, a number of problems have been found for which algorithms involving continued fractions lend themselves to high-speed computer operations. The efficiency of these techniques has led to investigations relating to numerical aspects, the chief concern of the present work. It will be the object here to introduce the more elementary properties of continued fractions and to show what they imply in numerical processes. Just as there are pitfalls in the use of other infinite processes, when fundamentals are neglected, it is also possible to misuse continued fractions. Some of the difficulties that may arise will be explored, and methods of overcoming them will be suggested.