And...what would he use as a reference point? Kinda hard to keep track of the passage of time when you're travelling through time. Plus, which planet's years?
I like to think that a year on Gallifrey equals roughly nine months on Earth; hence the Doctor in Tomb Of The Cybermen
would have been about 600 Gallifrey years old, and by the time of Nuwho about 1200 (900 Gallifrey years travelling and 900 Earth years old).
He would surely know his age or have access to some kind of time-telling device
. In NuWho the Master even kew the Doctor's approximate age, so presumably there is some kind of synchronicity.