(i) 43.123456789It has certain number of digits, so they can be represented in form of qp​.Hence they are rational number. As they have certain number of digits and the number which has certain number of digits is always terminating number and for terminating number denominator has prime factor 2 and 5 only.(ii) 0.120120012000120000. . .Here the prime factor of denominator Q will has a value which is not equal to 2 or 5.So, it is an irrational number as it is non-terminating and non-repeating.(iii) 43.123456789Here the prime factor of denominator Q will has a value which is apart from 2 or 5, some other factor also.So, it is an rational number, 0.123456789 repeating again and again. It is non- terminating.