The eighty(one) digit number 1080 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 109 years or less than 1017 seconds. So if you had to wait 1080 seconds, you'd be 1/1063rd 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: 1080 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.