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Topic: 1/3 partitioned expansion in different bases
Replies: 28   Last Post: Feb 3, 2013 11:57 PM

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 JT Posts: 1,448 Registered: 4/7/12
Re: 1/3 partitioned expansion in different bases
Posted: Feb 2, 2013 12:06 AM
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On 2 Feb, 03:54, forbisga...@gmail.com wrote:
> On Friday, February 1, 2013 1:10:12 PM UTC-8, JT wrote:
> > You are confused the zeros in 1/2 1/4 etc etc is imaginary not real.
> > And for the endless expansion of digits in 1/3, 1/7 i offered a
> > solution using bases without zero.

>
> And what of x in
>   x = 1 - 1
>
> Now construct 1/9th in base 3.
>
> 0.[9] in base 10(given 9 is followed by 10)
> 0.[2] in base 3 is the same.
>
>  x = 0.[2]
>  10x = 2.[2]
>  10x - x = 2
>  2x = 2
>  x = 1
>
> I can disagree with Frederik Williams about
>   .3 base 3 = 1 base 3 in your numbering system
> Now what was the benefit again?  Why do I want a
> 3 in base 3?

In base 3
1/81=(4)1
1/243=(5)1

You get terminating digits and no rounding errors.

Date Subject Author
2/1/13 JT
2/1/13 JT
2/1/13 JT
2/1/13 JT
2/1/13 JT
2/1/13 JT
2/1/13 JT
2/1/13 forbisgaryg@gmail.com
2/1/13 JT
2/1/13 forbisgaryg@gmail.com
2/1/13 JT
2/2/13 JT
2/1/13 Frederick Williams
2/1/13 JT
2/1/13 JT
2/1/13 JT
2/1/13 JT
2/2/13 JT
2/2/13 JT
2/2/13 JT
2/2/13 JT
2/2/13 JT
2/2/13 JT
2/2/13 JT
2/2/13 JT
2/2/13 JT
2/3/13 JT
2/3/13 Virgil
2/3/13 JT

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