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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

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