If I have the number $x$ in binary:
$x=.1101001$
Would the following be correct, when rounding to...
Three decimal places: $x=.111$
Four decimal places: $x=.1101$
Five decimal places: $x=.11010$
2026-03-29 01:33:42.1774748022
Rounding in binary
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Yes, it would be correct. Because each position in binary is half the previous you can just chop off the unwanted bits and increment by $1$ if the first bit you discarded is a $1$. That works perfectly if you round up on exactly half. Otherwise you have to figure out what to do if you are chopping off a $1$ with nothing at all behind it.