The following real numbers have decimal expansions as given below. In each case,

(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^m×5ⁿ
That is, the prime factor of q will be 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) 43.123456789
Since the decimal expansion is non-terminating recurring, the given number is a rational number of the form  and q is not of the form 2^m×5ⁿ that is, the prime factors of q will also have a factor other than 2 or 5.