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Re: Precision in Mathematica 6
*To*: mathgroup at smc.vnet.net
*Subject*: [mg92286] Re: Precision in Mathematica 6
*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
*Date*: Fri, 26 Sep 2008 06:25:38 -0400 (EDT)
*Organization*: The Open University, Milton Keynes, UK
CaveSnow wrote:
*snip*
> this is the things I written in my notebook
>
> FindRoot[\!\(
> \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(t\)]
> FractionBox[\(Sin[x]\), \(x\)] \[DifferentialD]x\) == 1, {t, 1}]
>
> N[t, 10] /. %
*snip*
> In other words I used FindRoot to find the t that makes the definite
> integral from 0 to t of sinx/x be 1.
> As a result I got a certain rule, that had a small amount of digits
> (only 6 of them). Then I issued the second command ti get more digits
> from the result. But the result, even if I asked 10 digits remained
> the same 1.06484.
*snip*
Here, you are working with machine/hardware-precision numbers (aka
double-precision floating-point numbers), numbers that usually have up
to 16 decimal digits.
To control the number of decimal digits that are displayed, you can use
either *NumberForm* (see below) or goto menu "Preferences" ->
"Appearance" -> "Numbers" -> "Formating" -> "Displayed precision", there
change the field called "Number of digits displayed in output" from 6
(the "factory" default) to whatever you wish.
Note that the above setting does not affect the precision of
computations and you will not be able to display more that 16 decimal
digits for machine-precision numbers.
In[209]:= sol = FindRoot[Integrate[Sin[x]/x, {x, 0, t}] == 1, {t, 1}]
Precision[t /. sol]
$MachinePrecision
Do[Print[NumberForm[t, n] /. sol], {n, 20}]
Out[209]= {t -> 1.06484}
Out[210]= MachinePrecision
Out[211]= 15.9546
During evaluation of In[209]:= 1.
During evaluation of In[209]:= 1.1
During evaluation of In[209]:= 1.06
During evaluation of In[209]:= 1.065
During evaluation of In[209]:= 1.0648
During evaluation of In[209]:= 1.06484
During evaluation of In[209]:= 1.06484
During evaluation of In[209]:= 1.0648397
During evaluation of In[209]:= 1.06483973
During evaluation of In[209]:= 1.064839726
During evaluation of In[209]:= 1.0648397255
During evaluation of In[209]:= 1.06483972554
During evaluation of In[209]:= 1.064839725537
During evaluation of In[209]:= 1.0648397255366
During evaluation of In[209]:= 1.06483972553656
During evaluation of In[209]:= 1.064839725536558
During evaluation of In[209]:= 1.064839725536558
During evaluation of In[209]:= 1.064839725536558
During evaluation of In[209]:= 1.064839725536558
During evaluation of In[209]:= 1.064839725536558
Also, the tutorial "Machine-Precision Numbers" might be worth reading:
http://reference.wolfram.com/mathematica/tutorial/MachinePrecisionNumbers.html
Regards,
-- Jean-Marc
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