gives the effective number of digits of precision in the number x.
- 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 machine‐precision 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.
Examplesopen allclose all
N attempts to get a result correct to the given precision:
Generalizations & Extensions (1)
Properties & Relations (2)
Possible Issues (4)
MachinePrecision is always considered effectively smaller than any explicit precision:
Since Precision is based on relative error, it is not measurable for zero:
You can measure the absolute size of the error with Accuracy:
If you expect the result to be near zero, you can specify accuracy as a goal for N:
Instead, all subnormal numbers have the same uncertainty as $MinMachineNumber: