Answer:
0.11616... = \(\frac{23}{198}\).
Step-by-step 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 = \(\frac{11.5}{99}\).
x= \(\frac{115}{990}\).
On dividing both number by 5
x = \(\frac{23}{198}\).
Therefore, 0.11616... = \(\frac{23}{198}\).
