Let ={0,1} be an alphabet. Now consider/interpret as the set of all possible real numbers

Let  Σ  ={0,1} be  an  alphabet.   Now  consider/interpret  Σ∗ as  the  set  of  all  possible  real numbers R contained  on  the  interval  [0,1]  represented  in  base  2.   Let L be  the  language defined by the set of strings contained in Q (the set of rational numbers).  Given a string in ω ∈Σ∗,  describe an algorithm that will determine if ω ∈L (i.e.  describe an procedure to either accept or reject ω).