(*(Subscript[x, 0]) is the input,  
      i . e .  
          the first several digits of a number believed to be rational.*) 
(Subscript[x, 0]) =  .7419354838709677

    (Subscript[a, 0]) = IntegerPart[(Subscript[x, 0])]

    n = 0
 (*It is possible that the bound on (Subscript[a, n]) will need to be adjusted depending on the number of digits of information we are given.*) 

    While[(Subscript[a, n]) < 10000 || n < 2, n = n + 1; 
      (Subscript[x, n]) = (1/((Subscript[x, n - 1]) - IntegerPart[(Subscript[x, n - 1])])); 
      (Subscript[a, n]) = IntegerPart[(Subscript[x, n])]]

    v = Table[(Subscript[a, i - 1]), {i, n}]

    FromContinuedFraction[v]