This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.

# PrecisionGoal

 PrecisionGoalis an option for various numerical operations which specifies how many effective digits of precision should be sought in the final result.
• PrecisionGoal->Infinity specifies that precision should not be used as the criterion for terminating the numerical procedure. AccuracyGoal is typically used in this case.
• Even though you may specify PrecisionGoal->n, the results you get may sometimes have much less than n-digit precision.
• PrecisionGoal effectively specifies the relative error allowed in a numerical procedure.
• With PrecisionGoal->p and AccuracyGoal->a, Mathematica attempts to make the numerical error in a result of size x be less than .
Approximate an integral to at least 10 digits of precision:
 Out[1]=

Use accuracy (absolute error) as the basis for error control in solving an ODE:
 Out[1]=
The error is small:
 Out[3]=
Without specifying the PrecisionGoal, the error is much larger:
 Out[4]=
 Scope   (2)