# Accuracy

Accuracy[x]

gives the effective number of digits to the right of the decimal point in the number x.

# Details # Examples

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## Basic Examples(3)

Machine-precision number:

Arbitrary-precision number:

Exact number:

## Scope(4)

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:

## Generalizations & Extensions(1)

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

## Applications(2)

Check the quality of a result:

Track loss of accuracy in a repetitive calculation:

## Properties & Relations(3)

For normalized machineprecision numbers, Accuracy[x] is the same as \$MachinePrecision-Log[10,Abs[x]]:

No machine number has a higher accuracy than \$MinMachineNumber:

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

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

## Possible Issues(1)

Subnormal machine numbers violate the relationship Precision[x]==RealExponent[x]+Accuracy[x]: Instead, all subnormal numbers have the same uncertainty as \$MinMachineNumber:

## Neat Examples(1)

Accuracy and Precision in iterating the logistic map: