Question

7 What can you say about the prime factorisation of
the denominators?
(i) 34.12345
(ii) 34.5678​

Answer 1

Answer:

(i) 34.12345 = (3412345)/(100000)

This number is in the form of p/q

This is a rational number.

q = 100000 = (10)5 = (2 x 5)5 = 25 x 55

So, prime factor of q are in the form of = 2 or 5.

(ii) 43.12345¯678943.12345¯6789 = 43.123456789 123456789 123456789 …

The decimal expansion of this number is non terminating and recurring and it is possible to write in the form p/q.

This is a rational number.

So, besides 2 and 5 the prime factor of q, there are other prime positive integers possible. Hence, the given number is rational.