Is 0.01011011101111011111 rational or irrational

Answer 1

All numbers with a finite number of decimal digits are rational. Some that infinitely many decimal digits are rational as well. If you mean to repeat the pattern, adding one more "1" every time, then no, it is not rational - rational numbers repeat the SAME sequence of digits over and over (for example, 0.1515151515...), at least eventually (they may start with some digits that are not part of the repeating part, such as 3.87112112112...).