Check 11X11. Then look at 111X111. Then 1111X1111.
Do each on paper, using the multiplication methods we all learned in grade school. The answer to your question will quickly become apparent.
And it is not a "fallacy" of base 10 notation. A quirk, maybe, but certainly not a fallacy. Any base you use will give the same answer although the numerals used to write that answer will be different. Using hexadecimal or base 7 will still give the answer of 12 quadrillion, 345 trillion, 678billion, 987million, 654 thousand, three hundred twenty one.