Return-Path: X-Original-To: python-list@python.org Delivered-To: python-list@mail.python.org X-Spam-Status: OK 0.001 X-Spam-Evidence: '*H*': 1.00; '*S*': 0.00; 'subject:Python': 0.05; 'received:verizon.net': 0.07; 'terry': 0.07; 'received:80.91': 0.09; 'received:80.91.229': 0.09; 'received:gmane.org': 0.09; 'received:list': 0.09; 'substitute': 0.09; 'binary': 0.13; 'ranges.': 0.16; 'reedy': 0.16; 'wrote:': 0.18; 'example.': 0.18; 'jan': 0.19; 'seems': 0.20; 'header:In-Reply-To:1': 0.22; 'similarly': 0.23; 'subject: .': 0.29; 'pm,': 0.29; 'there': 0.33; 'header:User-Agent:1': 0.33; 'header:X-Complaints-To:1': 0.34; 'certain': 0.34; 'fraction': 0.34; 'integer': 0.34; 'numbers.': 0.34; 'to:addr:python-list': 0.35; 'received:org': 0.36; 'represent': 0.37; 'point': 0.40; 'to:addr:python.org': 0.40; 'more': 0.61; '12:56': 0.84 X-Injected-Via-Gmane: http://gmane.org/ To: python-list@python.org From: Terry Reedy Subject: Re: Python math is off by .000000000000045 Date: Sat, 25 Feb 2012 16:05:05 -0500 References: Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit X-Gmane-NNTP-Posting-Host: pool-74-109-121-73.phlapa.fios.verizon.net User-Agent: Mozilla/5.0 (Windows NT 6.1; WOW64; rv:8.0) Gecko/20111105 Thunderbird/8.0 In-Reply-To: X-BeenThere: python-list@python.org X-Mailman-Version: 2.1.12 Precedence: list List-Id: General discussion list for the Python programming language List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Newsgroups: comp.lang.python Message-ID: Lines: 14 NNTP-Posting-Host: 2001:888:2000:d::a6 X-Trace: 1330203944 news.xs4all.nl 6962 [2001:888:2000:d::a6]:47430 X-Complaints-To: abuse@xs4all.nl Path: csiph.com!x330-a1.tempe.blueboxinc.net!usenet.pasdenom.info!bete-des-vosges.org!feed.ac-versailles.fr!usenet-fr.net!de-l.enfer-du-nord.net!feeder2.enfer-du-nord.net!cs.uu.nl!news.stack.nl!newsfeed.xs4all.nl!newsfeed5.news.xs4all.nl!xs4all!post.news.xs4all.nl!not-for-mail Xref: x330-a1.tempe.blueboxinc.net comp.lang.python:20865 On 2/25/2012 12:56 PM, Tobiah wrote: > It seems to me that there are a great many real numbers that can be > represented exactly by floating point numbers. The number 1 is an > example. Binary floats can represent and integer and any fraction with a denominator of 2**n within certain ranges. For decimal floats, substitute 10**n or more exactly, 2**j * 5**k since if J < k, n / (2**j * 5**k) = (n * 2**(k-j)) / 10**k and similarly if j > k. -- Terry Jan Reedy