Divisibility tests for digits other than 7 are well known and rely on the base 10 representation of numbers. For example, a natural number is divisible by 4 if the last 2 digits are divisible by 4 because 4 divides 10[sup k] for all k equal to or greater than 2. Divisibility tests for 7, while not nearly as well known, do exist and are also…

Representation of integers in various bases is explored, with a proof. (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)

Discusses arithmetic during long-multiplications and long-division. Provides examples in decimal reciprocals for the numbers 1 through 20; connection with divisibility tests; repeating patterns; and a common fallacy on repeating decimals. (YP)

A student noticed an interesting fact about the base two numerals for perfect numbers. Mathematical explanations for some questions are given. (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…

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)