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EDIT: I THINK I STAND CORRECTED
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I got tired of reading people saying that the infinite stack of hundreds is more money, so get this :
Both infinites are countable infinites, thus you can make a bijection between the 2 sets (this is literally the definition of same size sets). Now use the 1 dollar bills to make stacks of 100, you will have enough 1 bills to match the 100 bills with your 100 stacks of 1.
Both infinites are worth the same amount of money... Now paying anything with it, the 100 bills are probably more managable.
You could also just divide your infinite stack of $1 bills into 100 infinite stacks of $1 bills. And, obviously, an infinite stack of $100 bills is equivalent to 100 infinite stacks of $1 bills.
(I know this is only slightly different than what you're getting at, which is that infinitely many stacks of 100 $1 bills is equivalent to an infinite stack of $100 bills)