Write 0.(17 repeated) as a fraction

Answer 1

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