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in Real Numbers by (47.4k points)
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Convert \(\overline{0.9}\) to a rational number.

1 Answer

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by (47.8k points)
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Best answer

Let x = \(\overline{0.9}\). Then x = 0.99999…

Multiplying by 10 on both sides, we get

10x = 9.99999… = 9 + 0.9999… = 9 + x

9x = 9

x = 1. That is, \(\overline{0.9}\) = 1 (∵ 1 is rational number).

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