Question

Please answer question no. 3(iii)​

Answer 1

Answer:

since 43.5678...... is a non terminating decimal expansion.so it's denominator has factors other than 2 or 5

Answer 2

3.

(¡¡¡)43.123456789123456789123456789........

=> It is a rational number, as prime fators of q will also have a factor other than 2 or 5.

Let x = 43.12345678912345.. a

10000000x = 43123456789.12345678912345..

b

Now subtracting a from b, we have

10000000x - x = 43123456789.1234567891234.. - 43.1234567891234

9999999x = 43123456746

x = 43123456746 / 9999999

x = 14374485583 / 3333333

Hence, given number is a rational number with factors other than 2 or 5.

Hope you got it