It allows us to represent numbers using log symbols. Symbols required = O(log10(N)). Or put another way, the max number we can represent with S symbols is exponential in S. N = O(exp(S)).
You can represent any arbitrarily large number with a single symbol without positional notation, though. Let's use *. The number 3 is ***. The number 9 is *********. That interpretation of GP's comment (which, on re-read, is probably correct) makes it even more trivially false. Another comment by the same poster clarifies that I was actually responding to what he meant.
It allows us to represent numbers using log symbols. Symbols required = O(log10(N)). Or put another way, the max number we can represent with S symbols is exponential in S. N = O(exp(S)).