Question

Whats 0.116, 16 is repeating as a simplified fraction right answer plz

Answer 1

`x=0.1\overline{16}\\ 10x=1.\overline{16}\\ 1000x=116.\overline{16}\\\\ 1000x-10x=116.\overline{16}-1.\overline{16}\\ 990x=115\\ x=(115)/(990)=(23)/(198)`

Answer 2

0.11616... =
`(23)/(198)`.

Explanation:

Given : 0.116 , 16 is repeating .

To find : simplified fraction.

Solution : We have given 0.11616.....

Let x = 0.11616.....

On multiplying the both sides by 100 because there are two numbers which are repeating.

100x = 100 * 0.11616.....

100 x = 11.616....

We can write 11.616.... in terms of x

100 x = 11. 5 + 0.11616....

100x = 11.5+ x .

On subtracting both sides by x

99 x = 11.5

On dividing both sides by 99

x =
`(11.5)/(99)`.

x=
`(115)/(990)`.

On dividing both number by 5

x =
`(23)/(198)`.

Therefore, 0.11616... =
`(23)/(198)`.