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Topic: Wikipedia and fractions in other base then decimal
Replies: 16   Last Post: Feb 11, 2013 9:43 PM

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Virgil

Posts: 9,012
Registered: 1/6/11
Re: Wikipedia and fractions in other base then decimal
Posted: Feb 11, 2013 5:28 PM
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In article
<3c4b196b-1998-412f-94aa-be6b71bd8477@k14g2000vbv.googlegroups.com>,
JT <jonas.thornvall@gmail.com> wrote:

> On 11 Feb, 09:00, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <03a59b13-1fbd-4098-91d7-f093d7cf5...@w4g2000vbk.googlegroups.com>,
> >
> >  JT <jonas.thornv...@gmail.com> wrote:

> > > Wikipedia claims that 1/2 decimal 0,5 is 0,1 in ternary... and also
> > > 0,1 in binary.....

> >
> > > In reality it is 0.12 in ternary and 0.101 in binary
> >
> > Shouldn't 0.12 in base three be the same as
> >    1/3 + 2/3^2 = 3/9 + 2/9 = 5/9?
> >
> > I make one-half expressed in base 3 to be 0.1111...
> > --

>
> No both you ,wikipedia 0,5 decimal= 0,1 ternary and William Elliot and
> you are wrong 0.111..., while i am correct.



How is 0.12 base three =  1/3 + 2/3^2 = 3/9 + 2/9 = 5/9 wrong?


Also, for |r| < 1, the infinite series 1 + r + r^2 + r^3 + ...
converges to 1/(1-r) so
r + r^2 + r^3 + ... = r/(1-r)

So 0.111... base three = 1/3 + 1/3^2 + 1/3^3. + ...
= (1/3)/(1-1/3)
= (1/3)/(2)3) = 1/2

So it appears that, at least for those who can work it out for
themselves, you are the one who is wrong!
--





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