# How do you convert 0.809 (09 being repeated) to a fraction?

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To convert 0.809 (09 being repeated) to a fraction, the repeating decimal can be represented as (0.\overline{09}). To convert this to a fraction, you can use the following steps:

- Let (x = 0.\overline{09})
- Multiply both sides by 100 to shift the decimal two places to the right: (100x = 9.\overline{09})
- Subtract the original equation from the shifted equation: (100x - x = 9.\overline{09} - 0.\overline{09})
- Simplify: (99x = 9)
- Solve for (x): (x = \frac{9}{99} = \frac{1}{11})

So, (0.\overline{09}) as a fraction is (\frac{1}{11}).

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