Let x equal the repeating decimal.
x = 0.363636...
Since there are two repeating digits, 36, we multiply the equation above by 100 on both sides, and write it above the equation. Then we subtract the equations.
100x = 36.363636...
- x = 0.363636...
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99x = 36
Divide both sides by 99.
x = 36/99
Divide both the numerator and denominator by 9.
x = 4/11
Answer: 0.363636... = 4/11