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 formp/q, what can you say about the prime factors of q?

(i) 43.123456789It has certain number of digits, so they can be represented in form ofpq.Hence they are rational number.As they have certain number of digits and the number which has certainnumber of digits is always terminating number and for terminating numberdenominator has prime factor2and5only (ii) 0.120120012000120000. . .Here the prime factor of denominator Q will has a value which is not equal to2or5.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 from2or5, some other factor also.So, it is an rational number,0.123456789repeating again and again. It is non- terminating.