# Why does SetPrecision drop “unknown” digits if precision requested is Infinity but retain them if it's finite?

I was trying to reset the imprecision record of a number like 0.00760222661227556321.025 by calling SetPrecision with second argument of Infinity. But then I was very surprised to see the following counterintuitive behavior:

SetPrecision[0.00760222661227556321.025, 30]
SetPrecision[0.00760222661227556321.025, Infinity]
N@%


0.00760222661227556321733231370352

1/128

0.0078125

I.e., when asked to set finite precision, SetPrecision just resets the precision marker, but when asked for infinite precision, it rounds the number to remove actual "extra" digits.

Is this inconsistency intended? How is it justified?

Both are correct because they are elements of Interval[0.0076022266122755632´1.025]`, which is the only thing that makes sense to expect.