Question

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 \(\frac{p}{q}\), what can you say about the prime factors of q ? 

(i) 43.123456789 

(ii) 0.120120012000120000……….. 

(iii) 43.123456789

Answer 1

(i) 43.123456789 

\(\frac{p}{q}\)is a rational number 

Prime factor of q: 

q = 10⁹= 2⁹ × 5⁹

(ii) 0.120120012000120000………… 

This is an irrational number 

(iii) 43.123456789

This is a rational number. 

Because, Prime factors of ‘q’ are contrinued in non-terminating decimal expansion.