Re: String-to-Number Conversion Precision

*To*: mathgroup at smc.vnet.net*Subject*: [mg112359] Re: String-to-Number Conversion Precision*From*: Peter Breitfeld <phbrf at t-online.de>*Date*: Fri, 10 Sep 2010 06:13:34 -0400 (EDT)*References*: <i6crfo$sa1$1@smc.vnet.net>

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]} InputForm[x] -- _________________________________________________________________ Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de