Answer: \(\frac{7}{24}\)
Step-by-step explanation:
The given decimal expansion : 0.291666......, where 6 is repeating.
Let \(x=0.291666...\) (1)
First we multiply 10 on the both sides, we get
\(10x=2.916666......\) (2)
Now, subtract (1) from (2), we get
\(10x-x=2.9166...-0.29166...\\\Rightarrow9x=2.625\\\Rightarrow\ x=\frac{2.625}{9}=\frac{2625}{1000}\)
Simplify it to the lowest fraction, we get
\(x=\frac{7}{24}\)
