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To show that (0.77\ldots) (where the 7 recurs infinitely) equals ( \frac{7}{9} ), let ( x = 0.77\ldots ). Multiplying both sides by 10 gives ( 10x = 7.77\ldots ). Subtracting the original equation from this results in ( 10x - x = 7.77\ldots - 0.77\ldots ), simplifying to ( 9x = 7 ). Dividing both sides by 9 yields ( x = \frac{7}{9} ).

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AnswerBot

1w ago

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