The Wolfram Language has sophisticated built-in automatic numerical precision and accuracy control. But for special-purpose optimization of numerical computations, or for studying numerical analysis, the Wolfram Language also allows detailed control over precision and accuracy.

N — numerical evaluation to specified precision and accuracy

PrecisionGoal, AccuracyGoal — precision and accuracy goals for computations

WorkingPrecision — precision to use inside algorithms

Precision — find the precision of a number

Accuracy — find the accuracy of a number

Chop — set sufficiently small numbers or imaginary parts to zero

SetPrecision, SetAccuracy — reset precision or accuracy of a number

$MinPrecision, $MaxPrecision — settable global precision bounds

$MaxExtraPrecision — maximum extra precision to use inside exact algorithms

Machine Numbers

MachinePrecision — symbol representing machine precision

MachineNumberQ — test if a number is a machine number

$MachinePrecision  ▪  $MachineEpsilon  ▪  $MinMachineNumber  ▪  $MaxMachineNumber