# Chapter P, Prerequisites - Section P.2 - Real Numbers - P.2 Exercises: 77

(a) 7/9 (b) 26/90=13/45 (c) 57/99=19/33

#### Work Step by Step

(a) $x=0.\bar7=0.77777...$ $10x=7.77777...$ $10x-x=9x=7.77777...-0.77777...=7$ $x=7/9$ (b) $x=0.2\bar8=0.288888...$ $100x=28.888....$ $10x=2.888...$ $100x-10x=90x=26$ $x=26/90=13/45$ (c) $x=\overline{57}=0.575757...$ $100x=57.575757....$ $100x-x=99x=57$ $x=57/99=19/33$

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