Which of the following numbers are rational, and which are irrational? Express those which are rational in the form \(\frac{m}{n}\) with \(m, n \in \mathbb{Z}\).

(a) \(0 . a_{1} a_{2} a_{3} \ldots\), where for \(n=1,2,3, \ldots\), the value of \(a_{n}\) is the number \(0,1,2,3\) or 4 which is the remainder on dividing \(n\) by 5 .

(b) \(0.101001000100001000001 \ldots\)

(c) \(1 . b_{1} b_{2} b_{3} \ldots\), where \(b_{i}=1\) if \(i\) is a square, and \(b_{i}=0\) if \(i\) is not a square.