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Built-in Mathematica Symbol

$MinPrecision

$MinPrecision
gives the minimum number of digits of precision to be allowed in arbitrary-precision numbers.

Positive values of $MinPrecision make Mathematica pad arbitrary-precision numbers with zero digits to achieve the specified nominal precision. The zero digits are taken to be in base 2, and may not correspond to zeros in base 10.

$MaxPrecision=$MinPrecision=n makes Mathematica do fixed-precision arithmetic.

Make sure precision is kept at or above machine precision in a calculation:

Do a computation with fixed 20-digit precision:

Make sure precision is kept at or above machine precision in a calculation:

Do a computation with fixed 20-digit precision:

Power method for the largest eigenvalue using fixed precision:

Find the largest eigenvalue of the 4×4 Hilbert matrix to 47 digits:

Without fixed precision the result indicates lost precision:

The fixed precision is correct to 47 digits since the iteration is self-correcting:

$MinPrecision does not affect parts of computations with machine numbers:

If needed, use SetPrecision to eliminate machine numbers from the input: