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 what can you say about the prime factors of q? (i) 43.123456789 (ii) 0.120120012000120000. . .

(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 x 5^n
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.

Explanation 👇