SetPrecision[expr, n] yields a version of expr in which all numbers have been set to have a precision of n digits.
When SetPrecision is used to increase the precision 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.
SetPrecision returns an arbitrary-precision number, even if the precision requested is less than $MachinePrecision.
When expr contains machine-precision numbers, SetPrecision[expr, n] can give results which differ from one computer system to another.
SetPrecision 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 precision 25 on any computer system.
SetPrecision[expr, n] does not modify expr itself.
See The Mathematica Book: Section 3.1.5.
See also: N, Precision, Chop, SetAccuracy, $MinPrecision, $NumberMarks.