TLDR: The largest number has 16 digits.
Ask an astronomer and we'll travel eons into the universe and beyond.
Ask a microbiologist and we'll fall into mystical quarks and preons, the building blocks of everything.
Ask my 5 year old and you'll get 643.
This is a question anyone can guess, but when you get down to the nitty-gritty, it's surprisingly personal.
Plenty
I discard it, like imaginary numbers, infinity is an alchemy, a symbol, rather than a practicable digit. It could never appear on a tape measure.
Here are the parameters:
1. Each individual digit must count:
It's amazing that the universe is estimated to be 93 billion light years from end to end, but it could be 93.4 or 93.5 and both would be fine. To get the most detail out of the hair, it would take an app to make sense. Traveling from one side of the universe to the other would be great, but…
“You're really not going to like it.”
— Hitchhiker's Guide to the Galaxy, Douglas Adams
Even if we felt the need, this is a number we know fluctuates. The size of the universe is useful, but the number of 93 billion light years is a piece of pure amazement: an example of what big means.
At best, it's simply a reference point for numbers that are much smaller, rather than something worth knowing with billions of digits of precision.
2. The number must have a practical application in the real world:
There are groups dedicated to determining long numbers for the sake of the number itself. At the time of writing, it is known that Pi 62.8 trillion digits.