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

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Basic Examples  (3)

Machine-precision number:

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Arbitrary-precision number:

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Exact number:

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Scope  (2)

Generalizations & Extensions  (1)

Applications  (2)

Properties & Relations  (2)

Possible Issues  (3)

Neat Examples  (1)

See Also

Accuracy  RealExponent  N  Chop  SetPrecision  MachineNumberQ  MachinePrecision  PrecisionGoal  WorkingPrecision  ExactNumberQ  NumberMarks

Tutorials

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