Integer outputs of $y=x^2$ , do their last digits form an irrational?

Integer outputs of $y=x^2$ , do their last digits form an irrational?

Let the domain of $y=x^2$ be the positive integers. I input consecutive
positive integers from $[1, \infty)$ their last digits are $a, b, c, ...$
respectively. If I then make the number $z=\frac {a}{10}+\frac{b}{100}
+\frac {c}{1000}+\cdot \cdot \cdot$ , is this number irrational? If not,
is there any other combination (such as $\frac {c}{10}+\frac{f}{100}
+\frac {q}{1000}+\cdot \cdot \cdot$, but still using all of $a, b, c,
\cdot \cdot \cdot$) that could result in an irrational number? I have no
idea how to solve this problem, it is just something I have wondered about
for a long time.