The decimal form of some real numbers is given below. In each case, decide whether the number is rational or not. If it is rational, and expressed in form what can you say about the prime factors of q?

(i) 43.123456789

(ii) 0.120120012000120000….

(iii) 43.

(i) 43.123456789

43.123456789 is terminating.

So, it would be a rational number

Hence, 43.123456789 is now in the form of .

And the prime factors of q are in terms of 2 and 5.

(ii) 0.120120012000120000….

0.120120012000120000…. is non-terminating and non-repeating.

So, it is not a rational number.

(iii) 43.

43. is non- terminating but terminating.

So, it would be a rational number.

In a non-terminating, repeating expansion of

q will have factors other than 2 or 5.