Approximation for the infinite counting decimal

Question

Somewhere between the real number range, there exists a decimal that 'counts' natural numbers infinitely on its digits as:

$ 0.123456789101112131415161718192021......... $

It goes on 'counting' forever.

It is an irrational number, so

I'd like to find a close approximation of it (for about 30+ digits for example) like the PI approximation $(22/7)$

One last question for fun:

Is that number has been given a name before?

Answer 1

This number is called the Champernowne constant Some of it's approximation is $$\frac{10}{81}=0.\overline{123456790}$$ An even better approximation is $$\frac{60499999499}{490050000000}$$