Which of the following rational numbers have the terminating decimal representation?
       (i) 3/5              (ii) 7/20                   (iii) 2/13
       (iv) 27/40        (v) 133/125            (vi) 23/7
       [Making use of the result that a rational number p/q where p and q have no common factor(s) will have a terminating representation if and only if the prime factors of q are 2's or 5's or both.]

(i) The prime factor of 5 is 5. Hence 3/5 has a terminating decimal representation.
(ii) 20 = 4 x 5 = 2² x 5.
    The prime factors of 20 are both 2's and 5's. Hence 7/20 has a terminating decimal.
(iii) The prime factor of 13 is 13. Hence 2/13 has non- terminating decimal.
(iv) 40 = 2³ x 5.
    The prime factors of 40 are both 2's and 5's. Hence 27/40 has a terminating decimal.
(v) 125 = 5³
    The prime factor of 125 is 5's. Hence 133/125 has a terminating decimal.
(vi) The prime factor of 7 is 7. Hence 23/7 has a non-terminating decimal representation.