when you write down the number one hundred do yo really write down 100 digits, or the three digits 1,0 and 0? When you write down 1 billion, do you draw 1 billion symbols or simply write the text "1 billion".
Infinity has a symbol, a sideways 8.
Problem solved.
You are writing down "take 1 and add 1 for 9 iterations, then multiple that by 10". The only information in there is "1", the rest is instructions on what to do with it. You can add "infinite" zeros on the end but really it is just a function saying "multiple the number by the sum of ten 1s and loop".