Cyclical Decimal Expansion

*To*: mathgroup at smc.vnet.net*Subject*: [mg114405] Cyclical Decimal Expansion*From*: "Harvey P. Dale" <hpd1 at nyu.edu>*Date*: Fri, 3 Dec 2010 05:21:57 -0500 (EST)

What's the easiest way to determine the length of the repeating cycle for decimal expansions of fractions? For example, 1/7 = 0.14285714285714285714 . . . so the length of its repeating cycle (142857) is 6. For 1/3 the length of the cycle is obviously 1. For some fractions, e.g., 1/4, the decimal expansion is not cyclical (in base 10). Thanks. Harvey ______________________________________________________________________ This email has been scanned by the MessageLabs Email Security System. For more information please visit http://www.messagelabs.com/email ______________________________________________________________________