Did you learn how to subtract?Level pending
The decimal parts of two irrational numbers in \((0,1)\) taken at random are found to \(2014\) places. The probability that the smaller one can be subtracted from the other without borrowing can be expressed as \(p^k\), where \(p\) is a rational number and \(k > 1000\) is a positive integer. Find the last three digits of \(\lfloor 100(p+k+1) \rfloor\).
Assume for this question that the digit in first decimal place of the larger number is greater than the digit in that of the other. (As a follow up, can you say what would the probability be, without this assumption?)