The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form p , q you say about the prime factors of q?
(i) 43.123456789
(ii) 0.120120012000120000...
(iii) 
(i) Since this number has a terminating decimal expansion, it is a rational number of the form p/q, and q is of the form 2m × 5n.
(ii) The decimal expansion is neither terminating nor recurring. Therefore, the given number is an irrational number.
(iii) Since the decimal expansion is non-terminating recurring, the given number is a rational number of the form p/q, and q is not of the form 2m × 5n.
