From: Edgardo Hames <ehames@...>
Date: 2004-10-29T03:58:00+09:00
Subject: Re: Rounding error, (100.0 * 9.95).to_i == 994

On Fri, 29 Oct 2004 02:40:14 +0900, Guillaume Marcais <guslist@free.fr> wrote:
> On Thu, 2004-10-28 at 04:23, Mark Hubbart wrote:
> 
> Another funny failing of the notation is that not everything that looks
> like a number actually represents a number. The following is quite
> intriging:
> 
> x = 0.99999... (infinite serie of 9s)
> 10*x = 9.99999...
> 10*x - x = 9*x = 9
> So x = 1!

0.9999... (infinite serie of 9s) is the standard (not IEEE, but plain
math) of the real number 1. Do you remember how to transform a
periodic number to a quotient? That's the integer part of the number
plus (the periodical part divided by as many nines as the periodical
part's digits). For example:

1.333... = 1 + 3/9
8.577577577... = 8 + 577/999

So, 

0.99999... = 0 + 9/9 which is clearly 1.

Regards,
Ed

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