Thinking about my own question, I had another question that came to my mind. Take any real number and write its binary representation. With probability $1$ the proportion of zeroes and ones is the same and is equal to $1/2$. We can say that for its 3-representation and the representation in any system the proportion of numbers used is equal with probability $1$. So almost any number has this property.

But can we find any concrete number and prove this property for it?...