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Cell[CellGroupData[{
Cell["About N (Version 4 only)", "Title",
  TextAlignment->Center,
  Background->RGBColor[0, 1, 1]],

Cell["\<\
This notebook is by Steven Amgott.  Please send any questions or\
\[NonBreakingSpace]comments to samgott1@swarthmore.edu.  Feel free to use and \
distribute this notebook, but keep this author information in any copy you \
use or distribute.\
\>", "SmallText"],

Cell[TextData[{
  "In versions of ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " ",
  StyleBox["other than 4",
    FontColor->RGBColor[1, 0.501961, 0]],
  ", the function ",
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    FontColor->RGBColor[1, 0.501961, 0]],
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  ", this doesn't always happen.  For instance,"
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Cell[TextData[{
  "only displays six significant digits on my office computer.  (The actual \
number depends on the settings of machine variables in the copy of ",
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    FontSlant->"Italic"],
  " you are using and on the computer you are using.  The default after \
installation is usually six.)  However,"
}], "Text"],

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Cell["does produce the 20 digits.  What is going on?", "Text"],

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  " used the argument ",
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  "to both choose the precision of the computation of expression and the \
number of digits to display.  Now it uses it for the precision of the \
computation, but the number of displayed digits depends on whether the result \
is a \"machine-precision\" number or an \"arbitrary precision\" number.  On \
my computer, when there are 16 or fewer digits, ",
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Cell["\<\
To see what numbers on your machine are treated as machine-precision numbers, \
you can evaluate\
\>", "Text"],

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Cell[TextData[{
  "For more details, see the sections ",
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  " in the ",
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  " book.  Clicking on one of those section numbers in this cell should open \
the relevant section in the Help Browser (provided the main book is installed \
on the computer you are using).  Another source of information is the \
Technical Support pages at Wolfram Research.  The article where I originally \
found some of this information is (as of 11/2/2001) located at:"
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  "In that article, they suggest using ",
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digits of \[Pi], you could use"
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Cell[TextData[{
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Cell[TextData[{
  "(The ",
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  " command gives the number of significant decimal digits.  A similar \
command, ",
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    FontColor->RGBColor[1, 0, 0]],
  ", gives the number of significant decimal digits to the right of the \
decimal point.) "
}], "Text"],

Cell["\<\
The reason it does not work is that the number 1.0 is a machine-precision \
number, and only has precision 16. \
\>", "Text"],

Cell[BoxData[
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Cell[TextData[{
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  " will only try to match the precision of the input.  In the following \
cell, the input only has precision 20, so even though we ask for 30 digits we \
only get 20 in the output."
}], "Text"],

Cell[BoxData[{
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    \(N[Sin[1.00000000000000000000], 30]\), "\n", 
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Cell["If we have 30 digits in the input, then it works.", "Text"],

Cell[BoxData[{
    \(N[Sin[1.000000000000000000000000000000], 30]\), "\[IndentingNewLine]", 
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Cell["\<\
Typing in a large number of zeros is tiresome, so there is a way around it.\
\>", "Text"],

Cell[BoxData[{
    \(SetPrecision[N[Sin[1.0]], 30]\), "\[IndentingNewLine]", 
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Cell[TextData[{
  "(There is also a similar ",
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    FontColor->RGBColor[1, 0, 0]],
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