**Solution:**

(i) 43.123456789

Since this number has a terminating decimal expansion, it is a rational number of the form /

and q is of the form 2^{}×5^{} i.e., the prime factors of q will be either 2 or 5 or both.

(ii) 0.120120012000120000 …

The decimal expansion is neither terminating nor recurring. Therefore, the given number is an irrational number.

iii) 41.2¯

Since, it has non-terminating but repeating decimal expansion, it is a rational number and q has factors other than 2 and 5 .