{tex}let \: x = 0.12 \bar{5} \bar{4} \\ \\ or \: x = 0.12545454... \\ \\ 100x = 12.545454... \\ \\ 10000x = 1254.545454... \\ \\subtract : \\ 10000x - 100x = 1254.5454... - 12.5454... \\ \\ 9900x = 1242 \\ \\ x = \frac{9900}{1242} \\ \\ x = \frac{550}{69} \\ \\ thus \: \: \: 0.12 \bar{5} \bar{4} = \frac{550}{69} \:{/tex}

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