You mapped the numbers between 0 and 1 that have a finite number of decimals, like 0.123123425736289

But there are many more real numbers between 0 and 1 that have an infinite number of decimals, like 0.1231234736876578632786278365782635879281987087420...

As jgreen says in a sibling comment, which number do you assign to 1/3 = 0.333333333333333333333333333333333333333333... ?

The result you got is well known but interesting, because it's unintuitive. Moreover with some tricks you can try to extend your method to all fractions, like 1/3, 5/7, 27/127, ...

The problem is that there are irrational numbers like pi, sqrt(2), ... and many other numbers that we have assigned no friendly name. Those "unfriendly" numbers are the actual problem.