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Re: String-to-Number Conversion Precision

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  • Subject: [mg112359] Re: String-to-Number Conversion Precision
  • From: Peter Breitfeld <phbrf at>
  • Date: Fri, 10 Sep 2010 06:13:34 -0400 (EDT)
  • References: <i6crfo$sa1$>

Ben wrote:

> I'm reading real numbers from a file and I'm trying to convert them
> from string format (with arbitrary precision) to real values with the
> same precision as given in the strings.
> For example, when I convert "1.867524468", I want the result to be set
> to precision 10.  Instead, I get the following.
> In[1]:=    string = "1.867524468"
> Out[1]:= "1.867524468"
> In[2]:=    x = ToExpression[string]
> Out[2]:= 1.86752
> The last 4-digits get cut off.  This is fine for when I do math with
> the number because the extra digits are still stored, but not when I
> want to rewrite the number to a different file.  When I convert the
> number back to a string for file output, the last 4-digits remain
> lost.
> In[3]:=    ToString[x]
> Out[3]:= "1.86752"
> Is there a function or formula I can use to automatically set the
> precision of these numbers to their precision in the string?  Thanks.

Mathematica treats numbers with less then $MachinePrecision digits
always as having MachinePrecision. It _displays_ them with 6 digits
after the decimal point, but knows all the digits. You can display them
using NumberForm or better (in this case) using InputForm. So 

In[3]:= ToString[InputForm[x]]

will give you all the original digits.

To set the precision for longer numbers according to the length of the
input string you may use something like this:

string = "1.867524468121212771299123312";
x = ToExpression[string]
SetPrecision[x, StringLength[string] - 1]
{Precision[x], Accuracy[x]}

Peter Breitfeld, Bad Saulgau, Germany --

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