Question 1901

 Let the upper bar means the repeatitive decimals.
    _            _
 0.23 = 0.2 + 0.03 
                        _
      =  0.2 + 1/10 * 0.3

(since by geometric series: 0.3 = 0.3/(1-0.1) = 0.3/0.9 = 3/9)
                        
      = 0.2 + 1/10 * 3/9
       = 1/5 + 1/30
      = 7/30


 Kenny