[?] Get the Feynman Point of Pi with N?

Questions
1

A sequence of six 9s occurs in the decimal representation of ?, starting at the 762nd decimal place. These six 9s have come to be called the Feynman point.

N[Pi, 769] ends with …7211349999998

but

N[Pi, 768] ends with …721135000000

What gives?

2

If you allow just 768 digits,the one ending in 721135000000 is a better approximation of Pi than the one ending in 721134999999.

3

From the documentation:

“Pi can be evaluated to any numerical precision using N.”

Doesn’t seem like approximation is used.

4

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 ;;]]