Question

5.111111111 in p/q form

Answer 1

Hope it may help u....!!!

Answer 2

Answer :

Given :

5.11111111 is a non - terminating repeating decimal .

Required to find :

1. P/q form of 5.11111

Solution :

Given number

5.11111111

Here , find the period and periodicity

( period = what digit is repeating )

(periodicity = Number of digits repeating ).

So,

period = 1

periodicity = 1

However,

Let x = 5.11111-------. ----> equation 1

Now let's multiply the equation 1 with 10

Therefore we get ,

10(x) = 10(5.11111-------)

10x = 51.11111--------. ------> equation 2

Now according to the problem ,

subtract equation 1 from equation 2

10x = 51.11111-------

1x = 5.11111-------

---------------------------

9x = 46.0000------

x = 46/9

Therefore ,

The p/q form of 5.1111 is 46/9 . ( where p and q are integers , q ≠ 0 , p and q are co-primes )