It's O(10 billion), so your intuition is good regardless :) passwords with ten 10-digits: 10x10x... = 10^10 = 10 billion, passwords with nine digits = 10^9, etc etc down to 11,111,111,110 (I don't think we should count the empty password). The full length password dominates the size of the keyspace so much that you more or less get truncations for free.