Presented are the mathematical explanation of the algorithm for representing rational numbers in base two, paper-and-pencil methods for producing the representation, some patterns in these representations, and pseudocode for computer programs to explore these patterns. (MNS)

Mathematical methods are used to study certain related Logo procedures in detail. Simple procedures with known properties are then used to build the higher-level procedures which correspond to higher-level mathematical concepts. Examples are from introductory aspects of number theory. (MNS)

Why a computer error occurred is considered by analyzing the binary system and decimal fractions. How the computer stores numbers is then described. Knowledge of the mathematics behind computer operation is important if one wishes to understand and have confidence in the results of computer calculations. (MNS)

An example is given of how to help students who have obtained a correct answer by a wrong method. They are asked to suppose that a child has found an easy method for division, and eventually write a computer program to show the correct method. (MNS)

The NCTM curriculum states that students should be able to "compare and contrast the real number system and its various subsystems with regard to their structural characteristics." In evaluating overall conformity to the 1989 standard, the National Council of Teachers of Mathematics (NCTM) requires that "teachers must value and encourage the use…

Numerical inaccuracies, which occur in many ordinary computations, can create serious problems and render answers meaningless. Cancellation and accumulation errors are described, and suggestions for experimentation are discussed. (MNS)

The author presents two examples of lattice multiplication followed by a computer algorithm to perform this multiplication. The algorithm is given in psuedocode but could easily be given in Pascal. (PK)

Identifies and proves two theorems related to expressing rational numbers in decimal form for any natural base m>1. Includes two BASIC computer programs with sample runs. (MVL)