Binary expansion of reciprocals
J. Astin · International Journal of Mathematical Education in Science and Technology · 1984
This article looks at the problem of expressing a reciprocal in binary form. Since reciprocals of even numbers can be obtained from those of odd numbers by moving the ‘binary’ point, the article deals only with expansions of the reciprocals of odd numbers. The expansions consist of a pattern of zeros and ones repeated indefinitely; the shortest pattern for a given reciprocal is called its period. Using modular arithmetic it is shown how to find both the period and the expansion by a simple calculation by hand.