“I hope not. That could produce some unpleasant dimensional anomalies.”
Doctor Who: Logopolis
Now Rassilon found the Eye of Harmony, which balances all things, that they may neither flux nor wither nor change their state in any measure. And he caused the Eye to be brought to the world of Gallifrey wherein he sealed this beneficence with the Great Key. Then the people rejoiced. [The Deadly Assassin]
There’s a sign on my front door. You have been walking past it for seven hundred years. What does it say?
First Doctor - Never stated his age on screen.
Second Doctor - Told Victoria he was ‘Something like 450’
Third Doctor - Claimed to have been a scientist for ‘several thousand’ years
Fourth Doctor - At least 760 by the time he regenerated
Fifth Doctor - Never stated his age on screen
Sixth Doctor - Told Peri he was ‘More or less’ 900-years-old
Seventh Doctor - Claimed to be 953, same age as the Rani
Eight Doctor - Never stated his age on screen.
Ninth Doctor - Told Rose he was 900
Tenth Doctor - 906 when he regenerated
Eleventh Doctor - 1103 by the time he was ‘killed’ at Lake Silencio.
I truly believe he has no idea how old he is, certainly in Earth years, and Gallifreyan years obviously no longer exist so he just makes up a number.
All those facts and figures I saw of the Doctor’s life, you were never alone. All those bright and shining companions.

The 4th Doctor, Tom Baker. by tolkien-andthe-tardis
India ink, acrylic, graphite on light cardboard paper. 4.5x5 feet.