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To convert the repeating decimal (0.88888...) into a fraction, let (x = 0.88888...). By multiplying both sides of the equation by 10, we get (10x = 8.88888...). Subtracting the original equation from this gives (10x - x = 8.88888... - 0.88888...), which simplifies to (9x = 8). Therefore, (x = \frac{8}{9}), so (0.88888... = \frac{8}{9}).
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