Question

Decide whether the real numbers are rational or not. If they are rational ,then write its p/q form.What can you say about the prime factors of q?

i)24.1352436789

ii).12346783940564543……

iii)41.2¯

Answer 1

(i) 43.123456789 

Since this number has a terminating decimal expansion, it is a rational number of the form /
and q is of the form 2×5 i.e., the prime factors of q will be either 2 or 5 or both. 

(ii) 0.120120012000120000 … 

The decimal expansion is neither terminating nor recurring. Therefore, the given number is an irrational number.

iii) 41.2¯

Since, it has non-terminating but repeating decimal expansion, it is a rational number and q has factors other than 2 and 5 .