At the start of Portal 2, it’s clear that time has passed. You’ve been woken up every few months for physical and mental fitness tests, until something goes wrong and you’re left in stasis for much longer. How long is Chell, your character, in stasis? How much time has passed between the end of Portal and the start of Portal 2?
Assuming the announcer was reciting the number of days you had been in stasis, as with your earlier 50-day wake up call, “it has been 9 9 9 9 9..9 9…[static]“, it has been at least 273 years, or 27,300 assuming the pause wasn’t a broken-record effect.
In “The Final Hours of Portal 2” e-book, Keighley mentions that:
One way to further differentiate Portal and Half-Life was to set the game far in the future—at least 50,000 years.
It doesn’t explicitly say that Portal 2 was set in 52,000 AD, but the general point was that the events between the two series are so distant from one another as to not interfere.