The eighty(one) digit number 10^{80} is approximately the number
of particles in the universe: protons, electrons, photons, etc.
(If this estimate is a factor of 10 too small due to "dark matter",
what would the revised estimate be?)

If it's been 10 billion years since the big bang,
that's 10^{9} years or less than 10^{17} seconds.
So if you had to wait 10^{80} seconds, you'd be 1/10^{63}rd
of the way done (which is
a billionth of
a billionth of
a billionth of
a billionth of
a billionth of
a billionth of
a billionth).
Upshot: 10^{80} is a large number, whether of seconds
or of particles.

For comparison, can you get a rough estimate of how many positions are possible in chess? What does this imply about devising the following strategy for playing chess: make a brute-force list of all possible chess positions, and what the single best possible move to make is. (Is there such a concept?) Then, when playing a game, just consult your list for each move!

Of course, larger numbers may still be of very real interest, even though they don't correspond to counting or measuring anything: 200-digit numbers are routinely used to encrypt data. Saying that the magnitude of a 200-digit number is "astronomical" is really an injustice.