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.
From: Per R�nne [mailto:email@example.com]
Subject: Re: Precision of output
Kazimir <firstname.lastname@example.org> 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, ∞], 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 R�nne