2013/10/12 by Simone Ugolini, Ugolini, Simone
Computer Science · Mathematics · #History and Theory of Mathematics #Mathematical and Theoretical Analysis #Numerical Methods and Algorithms #math.DS #math.NT
paper · pdf · doi:10.48550/arxiv.1310.3395
12 pages. Exposition improved. Added a section on base-$B$ representation, with $B$ not necessarily equal to 10
arxiv created 2013/10/21 · arxiv updated 2013/10/22
In this paper we deal with a classical problem in elementary number theory, namely repeating decimals. We show how the digits of the period of the decimal representation of any fraction (k)/(m), where k and m are positive integers arbitrarily chosen, can be obtained relying upon the graphs associated with the iteration of a certain map over the finite set \0, 1, …, 10n-2 \ for a suitable integer n, which depends on m. In the last section of the paper we generalize the results to any arbitrary choice of the base B ≥ 2 for the representation of the fraction (k)/(m).