All natural numbers (Base 10) can be converted to binary. No problem. But what about fractional numbers? All cannot be converted (finite expansion).
Example: $0.625$ can be converted but $0.11231$ cannot.
If I were to make a set of all those numbers which can be converted into binary, what condition should I impose on the set of all real numbers? This condition should be able to give an exhaustive list of all such numbers.
Would saying that a number reduced to it's $p/q$ form ($p$ and $q$ being coprime) should contains only powers of $2$ in the denominator be sufficient?