This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# WorkingPrecision

 WorkingPrecisionis an option for various numerical operations that specifies how many digits of precision should be maintained in internal computations.
• Setting WorkingPrecision->n causes all internal computations to be done to at most n-digit precision.
• Setting WorkingPrecision causes all internal computations to be done with machine numbers.
• Even if internal computations are done to n-digit precision, the final results you get may have much lower precision.
Find a root using 60-digit precision arithmetic:
Solve a differential equation using 24-digit precision arithmetic:
Find a root using 60-digit precision arithmetic:
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Solve a differential equation using 24-digit precision arithmetic:
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 Scope   (4)
Evaluate the function using 24-digit precision arithmetic:
Without higher precision you see mainly numerical roundoff error:
Approximate an integral using 24-digit precision arithmetic:
The PrecisionGoal is automatically increased to be 10 less than the working precision:
Find a minimum of a function, adaptively increasing the precision up to 50 digits:
The PrecisionGoal and AccuracyGoal are automatically set to be half the final precision:
Solve a differential equation with 32-digit precision arithmetic:
The PrecisionGoal and AccuracyGoal are set to be half of the working precision:
Using InterpolationOrder->All will reduce the errors between steps:
 Applications   (1)
Check the quality of a solution to Duffing's equation by using a sequence of solution precisions:
Make a sequence of solutions at successively higher working precision:
A plot shows that some of the solutions deviate toward the end:
Plot the solution as a function of working precision:
Convergence to the solution at the highest precision indicates about 6 digits can be trusted:
Low-precision parameters in functions may invalidate the use of higher-precision arithmetic:
The result is a poor approximation to :
Use of exact parameters allows comparison at different precisions:
Expect solution times to increase exponentially as a function of working precision:
A log plot of the computation time as a function of working precision: