This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)
 Documentation / Mathematica / Built-in Functions / Numerical Computation / Numerical Precision  /
Precision

  • Precision[ x ] gives the number of digits of precision in the number x.
  • If x is not a number, Precision[ x ] gives the minimum value of Precision for all the numbers that appear in x.
  • Precision gives Infinity when applied to exact numbers, such as integers.
  • Precision gives $MachinePrecision for machine-precision numbers.
  • See the Mathematica book: Section 3.1.4.
  • See also: Accuracy, N, Chop, SetPrecision, MachineNumberQ.

    Further Examples

    Here is an approximate real number.

    In[1]:=

    This gives the total number of digits entered to specify the real number.

    In[2]:=

    Out[2]=

    This evaluates using numbers with 30 digits of precision.

    In[3]:=

    Out[3]=

    The result has 30 digits of precision.

    In[4]:=

    Out[4]=

    Mathematica treats 3.0 as a machine-precision number.

    In[5]:=

    Out[5]=

    In[6]:=

    Out[6]=

    Giving anything less than $MachinePrecision digits yields a machine-precision number.

    In[7]:=

    Out[7]=

    This evaluates using 30-digit precision numbers.

    In[8]:=

    Out[8]=

    In this case, the result has a precision of exactly 30 digits.

    In[9]:=

    Out[9]=

    If you give input only to a few digits of precision, Mathematica cannot give you high-precision output.

    In[10]:=

    Out[10]=

    If you want Mathematica to assume that 0.142 is exact, then you have to show this explicitly.

    In[11]:=

    Out[11]=