Let L be any language over the binary alphabet {0,1}. Let 1L be the language obtained by concatenating 1 with every string of L. That is, L contains w if and only if 1L contains 1w.
Now, define the real number x_L to be the sum of all terms of the form 10^-i where the binary numeral for i is a member of 1L.
For example, if L = {epsilon, 1, 10, 00} then L = {1, 11, 110, 100} and x_L = 0.101101.