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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

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