If you have an exact number (like) Pi, then N can only give an approximation. And note that evaluate something with numerical precision x is the same as giving an approximation, that is the same.
As Gianluca says, this:
721134999999
is a worse approximation than:
721135000000
If you want to be sure to get non-rounded numbers, get a bunch more:
First[RealDigits[N[Pi, 800]]][[762 ;;]]
