In the E3 demo Codsworth comments that the protagonist is 200 years late for dinner. Robots in fiction tend to be comically precise. I'd be surprised if he were rounding off the elapsed time to the nearest century.

You did notice you had the option of asking Godsworth "200 years?" This is when he would have given you the "precise" answer to how many years.

Sorry, but Pete, Todd and Codsworth all say the same thing.
I'll put stock in that over a mini game with Vegas in it as evidence of when the game is set all day, every day.

Especially since the robot in Vault 112 (FO3), which was sealed a couple of years before the Great War, says you're 202.3 years late...