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RE: Re: Precision of output

  • To: mathgroup at
  • Subject: [mg48259] RE: [mg48236] Re: Precision of output
  • From: "DrBob" <drbob at>
  • Date: Wed, 19 May 2004 05:20:58 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

Kazimir's explanation is not quite right. 0.14 is machine-precision, not
2-digit precision, so 4209/0.14 is also machine-precision (53 binary digits,
or about 16 decimal digits, on my machine).

Otherwise, Kazimir's explanation is correct.

Machine precision is less than 100, so N[..,100] has no effect. The result
is machine precision, and default display for machine precision numbers is
six digits (on my machine), even though there are 16 that it could display.


-----Original Message-----
From: Per Rønne [mailto:spam at husumtoften.invalid] 
To: mathgroup at
Subject: [mg48259] [mg48236] Re: Precision of output

Kazimir <kazimir04 at> wrote:

> Mathematica thinks that only the first two digits are precise and
> knows nothing about the consecutive digits. In other words it's a
> standor notation for any number between 0.13500000(continue) and
> 0.1449999999(continue). Thus, it can not suppose that it will find a
> preciser answer. To get the desired answer you have to ask
> N[4209/SetPrecision[0.14, &#8734;], 100]
> or 
> 4209/(0.14``100)
> In the latest case you say that 0.14 is defined with 100 digits and it
> finds the result with this precision
> > But if I write N[420900/14,100] I get:
> > 30064.285714285714285714285714285714285714285714285714285714285714285714
> > 285714\
> > 28571428571428571428571
> Here, you don't put a digital point for 14, thus MATHEMATICA is sure
> that 14 is 14, and not 13.85 or 14.45 sumthing else, and it finds 100
> points. If you add only a digital point like this
> N[420900/14., 100]
> you will have the first result.

Thank you to all of you. This explains it.
Per Erik Rønne

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