Re: Cyclical Decimal Expansion

*To*: mathgroup at smc.vnet.net*Subject*: [mg114418] Re: Cyclical Decimal Expansion*From*: Ingolf Dahl <Ingolf.Dahl at physics.gu.se>*Date*: Sat, 4 Dec 2010 06:11:16 -0500 (EST)

This is connected to the fact that 7 is a divisor of 999999, so that we can write 1/7 == 999999/(7*10^6) + 999999/(7*10^12) + 999999/(7*10^18)+... I leave the fun of generalizing this to you Best regards Ingolf Dahl -----Ursprungligt meddelande----- Fr=E5n: Harvey P. Dale [mailto:hpd1 at nyu.edu] Skickat: den 3 december 2010 11:22 Till: mathgroup at smc.vnet.net =C4mne: [mg114405] Cyclical Decimal Expansion 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 ______________________________________________________________________