Let:
[
x = 0.363636\ldots
]
The repeating part is 36, so multiply by 100:
[
100x = 36.363636\ldots
]
Subtract the first equation:
[
100x-x=36.363636\ldots-0.363636\ldots
]
[
99x=36
]
[
x=\frac{36}{99}
]
Simplify:
[
x=\frac{4}{11}
]
Answer:
[
\boxed{\frac{4}{11}}
]
