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Question 3. 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 you say about the prime factors of q?

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Question 3. 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 you say about the prime factors of q?

(i) 43.123456789
it has certain number of digits  so they can be represented in form of p/q . Hence they are rational number
As they have certain number of digit 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. . .
In this problem repetitions number are not same so it is not a irrational number
so prime factor of denominator Q will has a value which is not equal to 2 or 5. And irrational number is always none terminating
(iii) 43.123456789
In this number 0.123456789 repeating again and again so it is a rational number and it is none terminating so that the prime factor has a value which is not equal to 2 or 5

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How to check following real numbers are terminating or not, terminating or non terminating, ncert solutions for class 10 chapter 1 Exercise
Question 3. How to check following real numbers are terminating or not, terminating or non terminating, ncert solutions for class 10 chapter 1 Exercise 1.4 following real numbers have decimal expansions as given below. In each cas