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Topic: Can a fraction have none noneending and nonerepeating decimal representation?
Replies: 108   Last Post: Aug 16, 2013 5:22 PM

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 JT Posts: 1,448 Registered: 4/7/12
Re: Can a fraction have none noneending and nonerepeating decimal representation?
Posted: Jul 31, 2013 5:46 PM

Den onsdagen den 31:e juli 2013 kl. 23:29:08 UTC+2 skrev Virgil:
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> jonas.thornvall@gmail.com wrote:
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> > Den onsdagen den 31:e juli 2013 kl. 22:22:28 UTC+2 skrev Virgil:
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> > > In article <396e3715-0ca7-4dcf-8962-29fa30a5eda8@googlegroups.com>,
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> > > jonas.thornvall@gmail.com wrote:
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> > > > Den tisdagen den 30:e juli 2013 kl. 21:39:04 UTC+2 skrev Virgil:
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> > > > > In article <3ef71a1a-0168-4f56-bc9e-f4af3d5f9fe0@googlegroups.com>,
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> > > > > jonas.thornvall@gmail.com wrote:
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> > > > > > Den tisdagen den 30:e juli 2013 kl. 17:12:38 UTC+2 skrev
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> > > > > > jonas.t...@gmail.com:
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> > > > > > > Can a fraction have none noneending and nonerepeating decimal
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> > > > > > > representation?
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> > > > > > I was thinking that is seem that the choice of base to represent
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> > > > > > fractions,
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> > > > > > can lead to nonending repetive patterns, but can they also be none
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> > > > > > repetive?
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> > > > > In any natural number base, not only base ten decimals, rationals are
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> > > > > either terminating or repeating (all rationals are repeating if one
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> > > > > includes eventually repeating only zeroes) and all irrationals are
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> > > > > non-repeating.
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> > > > > > I guess not, but a rounding error calculating Pi could easily
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> > > > > > transform a
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> > > > > > perfectly rational fraction to irrational, isn't that true?
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> > > > > > A *SLIGHT* flaw in the arithmetic
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> > > > > --
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> > > > Well what i said was that a slight error doing arithmetics could prevent
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> > > > Pi
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> > > > from becoming rational.
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> > > A rounding error in calculating pi is much more likely to make pi seem
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> > > rational, since in calculating pi without error it is not.
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> > > --
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> > Or your arithmetic is not upto it, who knows
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> Those who know pi is irrational all know!
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> --

Yes Pi is considered to be irrational until proven differently, using another base, maybe a bijective base or written out as fraction.

I hope you do also realise that 1/3 have none terminating decimal expansion in decimal base. But have no problem terminating in bijective base 3.

Date Subject Author
7/30/13 JT
7/30/13 JT
7/30/13 Virgil
7/31/13 JT
7/31/13 Virgil
7/31/13 JT
7/31/13 Tucsondrew@me.com
7/31/13 JT
7/31/13 Tucsondrew@me.com
7/31/13 JT
7/31/13 Tucsondrew@me.com
7/31/13 JT
7/31/13 Virgil
7/31/13 Virgil
7/31/13 JT
7/31/13 Tucsondrew@me.com
7/31/13 JT
7/31/13 Tucsondrew@me.com
7/31/13 JT
7/31/13 JT
7/31/13 JT
7/31/13 JT
7/31/13 JT
7/31/13 LudovicoVan
7/31/13 JT
7/31/13 LudovicoVan
7/31/13 JT
7/31/13 JT
7/31/13 JT
7/31/13 Virgil
8/1/13 JT
8/1/13 JT
8/1/13 Virgil
8/1/13 Virgil
8/1/13 JT
8/1/13 Virgil
8/1/13 Virgil
8/3/13 grei
7/31/13 JT
8/4/13 Brian Q. Hutchings
8/4/13 Brian Q. Hutchings
7/31/13 Tucsondrew@me.com
7/31/13 Virgil
8/1/13 magidin@math.berkeley.edu
8/1/13 JT
8/1/13 Peter Percival
8/1/13 JT
8/1/13 Peter Percival
8/1/13 JT
8/1/13 Peter Percival
8/1/13 JT
8/1/13 Virgil
8/1/13 Virgil
8/1/13 Virgil
8/1/13 Virgil
8/1/13 magidin@math.berkeley.edu
8/1/13 JT
8/1/13 JT
8/1/13 Virgil
8/1/13 Peter Percival
8/1/13 JT
8/1/13 Virgil
8/1/13 JT
8/1/13 Virgil
8/1/13 Virgil
8/1/13 magidin@math.berkeley.edu
8/1/13 Richard Tobin
8/2/13 David Bernier
8/2/13 JT
8/2/13 Richard Tobin
8/2/13 JT
8/2/13 Peter Percival
8/2/13 Richard Tobin
8/2/13 JT
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8/16/13 Earle Jones
8/2/13 Virgil
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8/2/13 FredJeffries@gmail.com
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7/31/13 JT
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7/30/13 Earle Jones