Question

Which of the following rational numbers possesses continuous recurring in its decimal expansion 17\8,15\1600,29\343,13\3125,

Answer 1

(i)  17/8         
      Factorize the denominator we get
                        8 =2 x 2 x 2 = 2³
      So denominator is in form of 2ⁿ so 17/8 is terminating .

(ii) 15/1600   
      Factorize the denominator we get
                        1600 =2 x 2 x 2 x2 x 2 x 2 x 5 x 5  = 2⁶ x 5²
      so denominator is in form of 2ⁿ x5^m
      Hence 15/1600 is terminating.

(iii)  29/343     
      Factorize the denominator we get
                        343 = 7 x 7 x 7 = 7³
            There are 7 also in denominator so denominator is not in form of 2ⁿx5^m
            Hence it is none - terminating.

(iv)    13/3125

      Factorize the denominator we get

      3125 =5 x 5 x 5 x 5 x  5 = 5⁵

      So denominator is in form of 5^m so 13/3125 is terminating .