From: Florian Gross <flgr@...>
Date: 2004-10-28T05:09:02+09:00
Subject: Re: Rounding error, (100.0 * 9.95).to_i == 994

Jason DiCioccio wrote:

> I'm confused now..  100.0 * 9.95 is clearly 995.  So what exactly is the 
> issue with floating point numbers is making this come out to 
> 994.999999999983 (or wahtever ;))?  If every language is plagued by this 
> problem, then I'd be curious to know the history behind it..

Floating point numbers are expressed in base 2. 9.95 has an infinite 
number of digits in base 2 representation just like the result of 1/3 
has in base 10.

However floating point numbers clearly can't be stored with an infinite 
amount of bits which is why the above gets slightly imprecise.

You can have a look at all the digits of a float like this:

irb(main):172:0> "%.32f" % 9.95
=> "9.94999999999999930000000000000000"