Numbers aren't lists of digits. They're abstract concepts that are referred to by lists of digits for the purpose of convenience. You can even have numbers without having invented digits. It's just annoying to write out one million, two hundred thirty-four thousand, five hundred sixty-seven and eighty-nine hundredths. So, we say 1,234,567.89 (or 1.234.567,89 for countries that use the comma for decimals).

0.5 in base 10 is the same as 0.1 in base 2, which is the same as 0.11111... in base 3. And the choice of base is completely arbitrary, with some societies using others, like base 12 or base 60.