Virgil
Posts:
8,833
Registered:
1/6/11


Re: Wikipedia and fractions in other base then decimal
Posted:
Feb 11, 2013 5:28 PM


In article <3c4b196b1998412f94aabe6b71bd8477@k14g2000vbv.googlegroups.com>, JT <jonas.thornvall@gmail.com> wrote:
> On 11 Feb, 09:00, Virgil <vir...@ligriv.com> wrote: > > In article > > <03a59b131fbd409891d7f093d7cf5...@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 onehalf 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/(1r) so r + r^2 + r^3 + ... = r/(1r)
So 0.111... base three = 1/3 + 1/3^2 + 1/3^3. + ... = (1/3)/(11/3) = (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! 

