The decimal expansion of any irrational number $x>0$ is non-repeating. This is well known. So, we have a way of obtaining irrational numbers, such has$$x=0.101\,101\,110\,111\,101\,111\,101\ldots$$(after the decimal point, we have one $1$, one $0$, two $1$'s, one $0$, three $1$'s, one $0$, and so on).
My (admittedly vague) question is this: how to obtain a known irrational number whose decimal expansion (or, for that matter, whose expansion on some base) is easily shown to be non-repeating? Of course, when I write that that the decimal expansion “is easily shown to be non-repeating” what I mean is that it is easy to describe its decimal expansion (and to see that it is non-repeating); otherwise, one could just say that, since the number is irrational, its decimal expansion must be non-repeating. And by “known number” I mean something like, say, $\sqrt2$ or $\pi^e$.