Precision

Precision[x]

gives the effective number of digits of precision in the number x.

Details

  • Precision[x] gives a measure of the relative uncertainty in the value of x.
  • With absolute uncertainty dx, Precision[x] is -Log[10,dx/x].
  • For exact numbers such as integers, Precision[x] is Infinity.
  • Precision[x] does not normally yield an integer result.
  • For any approximate number x, Precision[x] is equal to RealExponent[x]+Accuracy[x].
  • For machineprecision numbers, Precision[x] yields MachinePrecision.
  • Numbers entered in the form digits`p are taken to have precision p.
  • Numbers such as 0``a whose overall scale cannot be determined are treated as having zero precision.
  • Numbers with zero precision are output in StandardForm as 0.10-a, where a is their accuracy.
  • If x is not a number, Precision[x] gives the minimum value of Precision for all the numbers that appear in x. MachinePrecision is considered smaller than any explicit precision.

Examples

open all close all

Basic Examples  (3)

Machine-precision number:

In[1]:=
Click for copyable input
Out[1]=

Arbitrary-precision number:

In[1]:=
Click for copyable input
Out[1]=

Exact number:

In[1]:=
Click for copyable input
Out[1]=

Scope  (2)

Generalizations & Extensions  (1)

Applications  (2)

Properties & Relations  (2)

Possible Issues  (4)

Neat Examples  (1)

Introduced in 1988
(1.0)
|
Updated in 2003
(5.0)