Cyclic decimal periods.

• To: mathgroup at smc.vnet.net
• Subject: [mg21478] Cyclic decimal periods.
• From: "Alan W.Hopper" <awhopper at hermes.net.au>
• Date: Tue, 11 Jan 2000 04:17:56 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Greetings Mathworld people,

I would like to contribute my Mathematica notebook,
PeriodicDecimalCycles.nb ,
(located in the attachment file, I hope), and I would like to offer the
use of this
notebook or the code from it, to be a part of the
mathworld.wolfram.com/notebooks/
site, if you want it.

I used Mathematica 3.0  ;

In[1]:= \$Version

Out[2]=  Power Macintosh 3.0 (December 1, 1996)

The idea is to form all decimal cycles associated with the reciprocals
of all prime and
some some composite numbers into a pair of adjacent rows (folded for
long periods),
where the top row is the actual cycle and the bottom being the correct
decimal period.
When displayed you can then read off any decimal fraction for the
appropriate denominator
by starting with the digit immediately below the numerator.

Mathematica's list handling capabilities ensure that all the correct
periods within
individual cycles are displayed.

My congratulations to Eric and all the other contributers for this great
internet maths
encyclopedia project, keep up the good work!

Since Eric's comprehensive Mathematica notebooks are now on the Wolfram
site,
I hope that something like tutorial notebooks, can someday complement
the basic package files.

yours sincerely,

Alan W. Hopper.

Katoomba, Australia.

awhopper at hermes.net.au

filename="PeriodicDecimalCycles.nb"

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1/  Proceedings of the Cambridge Philosophical Society, Vol III \
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J.W.L. Glaisher - On Circulating Decimals, P. 185-204.

2/  Cycles of Recurring Decimals , Vol I (1950), Vol II (1953) , \
D.R.Kaprekar.
(Aryabhushan Press).

3/  Number Theory and its History ,  Oystein Ore,  Chapt. 13, Theory of \
Decimal Expansions,
(Dover publications).           \
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