Machine-precision number:

Arbitrary-precision number:

Exact number:

Accuracy is the effective number of digits known to the right of the decimal point:

A zero known to accuracy 20:

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

Accuracy of a machine zero:

The uncertainty in 0. equals the uncertainty in the smallest positive normalized machine number:

Specify accuracy as the goal for N:

The accuracy of a symbolic expression is the minimum of the accuracies of its numbers:

Check the quality of a result:

Track loss of accuracy in a repetitive calculation:

For normalized machine‐precision numbers, Accuracy[x] is the same as $MachinePrecision-Log[10,Abs[x]]:

No machine number has a higher accuracy than $MinMachineNumber:

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

Arithmetic operations will typically mix them:

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

The accuracy of the whole number is always less than or equal to either of these two accuracies:

For machine numbers, accuracy generally increases with decreasing magnitude, with a maximum at $MinMachineNumber:

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

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

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

Accuracy and Precision in iterating the logistic map: