Mathematica can handle numbers of essentially unlimited length, in any base, using state-of-the-art platform-optimized algorithms, including several developed at Wolfram Research. For rational numbers, it uses number theoretic methods to efficiently find the exact forms of repeating digit sequences.
IntegerDigits — digits of an integer
RealDigits — digits of a real number
FromDigits — reconstruct a number from its digits
IntegerLength — total number of digits in an integer
DigitCount — count the number of occurrences of given digits
IntegerString — digits of an integer as a string
BaseForm — display a number in base b