Write 0.(17 repeated) as a fraction
The repeating decimal 0.(17) can be written as a fraction by setting the repeated part as x:
Let x = 0.171717...
Then, 100x = 17.1717...
Subtracting the two equations:
100x - x = 17.1717... - 0.1717...
99x = 17
x = 17/99
Therefore, 0.(17) = 17/99