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MathGroup Archive 2004

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Re: 34.123*89 = 3036.95 (3036.947)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg47916] Re: 34.123*89 = 3036.95 (3036.947)
  • From: "Christopher J. Henrich" <chenrich at monmouth.com>
  • Date: Fri, 30 Apr 2004 19:26:54 -0400 (EDT)
  • References: <c6s538$pkf$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <c6s538$pkf$1 at smc.vnet.net>, Thomas Schulz
<thomas-k-schulz at t-online.de> wrote:

> I am a NewBe - and i dont understand the Result.
> Mathematica says that 34.123*89 = 3036.94699999997 but its 3036.947...
> How can i change this?
> 
> i use a IBook (G4) with Mac OS X.
> THX
> Thomas
> 
Mathematica interprets decimal numbers like "34.123" in floating point. 
A floating-point number is, mathematically, an integer times a power of
two.  For different precisions, one has different restrictions on the
integer and the exponent.  

We are accustomed to think of "34.123" as an integer times a power of
10, specifically, 34123 * 10^-3.  Mathematica found the nearest
floating point number,and apparently it happened to be slightly less
that 34123/1000.

If you had asked for (34123/1000)*89 you would have ot an exact result. 
Indeed, if you give Mathematica exact input and do not request a
numerical approximation of the result, it will do its best to compute
an exact answer even if this involves ridiculously big numerators and
denominators.  Try (34123/1000)^89.

-- 
Chris Henrich
Yes, one can rant about the program designs, but generally things keep getting
more and more confused as time goes on. --Sea Wasp


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