Machine-precision number:

Arbitrary-precision number:

Exact number:

A zero known to accuracy 20:

The precision is 0.:

The precision of z+1 is the same as the accuracy of z:

N attempts to get a result correct to the given precision:

This cannot always be achieved:

This is because relative error cannot be measured at zero and :

The precision of a symbolic expression is the minimum of the precisions of its numbers:

Check the quality of a result:

Track precision loss in a repetitive calculation:

All machine numbers have the same precision, MachinePrecision:

This is 53 bits or about 16 digits:

Real and imaginary parts of complex numbers can have different precisions:

Arithmetic operations will typically mix them:

But note that real and imaginary parts may still have different precisions:

The precision of the whole number lies in between these two precisions:

For approximate numbers, Precision[x]==RealExponent[x]+Accuracy[x]:

MachinePrecision is always considered effectively smaller than any explicit precision:

Numbers with sufficiently low precision are displayed with zero mantissa:

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:

Subnormal machine numbers violate the relationship Precision[x]==RealExponent[x]+Accuracy[x]:

Instead, all subnormal numbers have the same uncertainty as $MinMachineNumber:

Precision and Accuracy in iterating the tent map: