What is 0.80 (80 being repeated) repeating converting multi-digit repeating decimals to fractions?

To convert the repeating decimal (0.80\overline{80}) to a fraction, let (x = 0.808080...). Multiplying both sides by 100 (to shift the decimal point two places to the right), we get (100x = 80.808080...). Now, subtract the original equation from this one: (100x - x = 80.808080... - 0.808080...), which simplifies to (99x = 80). Thus, (x = \frac{80}{99}), so (0.80\overline{80} = \frac{80}{99}).