And to correctly write down this number would require even more atoms (let alone making a transaction or handling it in some way, lol)...
You can write this number (its lower and higher estimate) quite easily. But you can not write
all numbers from 1 to this number (without exhausting matter and energy in the universe).
I specifically mentioned 'correctly' which, I guess, is something different from the number's lower and higher estimates. The number of atoms in the universe is about 10^80 (if I'm not mistaken), so that to completely (read exactly) write down an arbitrary number with such division you would need about 10^80 digits, right?
It depends on the base

. I can write number 1234 using only 4 digits in base 10. I do not need 1234 digits.
to completely (read exactly) write down an arbitrary number with such division you would need about... 80 digits. Right?
I meant decimal notation indeed. And no, it would require 10^80 digits. As I got it, when people say that Bitcoin is divisible, they usually mean a number of decimal places (the number of digits following the decimal point). So the number of decimal places in this context should be considered as equal to the number of atoms in the universe, i.e. 10^80 decimal places
Otherwise, it is not even figuratively close to infinity, just some trivial 80 digits after the point, lol...