] yields a version of expr in which all numbers have been set to have an accuracy of n digits.
When SetAccuracy is used to increase the accuracy of a number, the number is padded with zeros. The zeros are taken to be in base 2. In base 10, the additional digits are usually not zero.
SetAccuracy returns an arbitrary-precision number even if the number of signficant digits obtained will be less than $MachinePrecision.
When expr contains machine-precision numbers, SetAccuracy[
] can give results which differ from one computer system to another.
SetAccuracy will first expose any hidden extra digits in the internal binary representation of a number, and only after these are exhausted add trailing zeros.
0.004``25 generates a number with all trailing digits zero and accuracy 25 on any computer system.
] does not modify expr itself.
See the Mathematica book: Section 3.1.5.
See also: N, Accuracy, SetPrecision.
When an expression contains machine-precision real numbers, Mathematica tries to do all computations at machine-precision level.
This causes a loss of accuracy. One of the inputs had an accuracy of 30 digits but the result has an accuracy of only 16 digits.
By raising the accuracy of each subexpression, you can increase the accuracy of the overall result.
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