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Prove that : \(0.3\overline{56}\) = \(\frac{353}{990}\) |
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Answer» We have, \(0.0.3\overline{56}\) = 0.3 + 0.056 + 0.00056 + 0.0000056 + ⋯ ∞ ⇒ \(0.3\overline{56}\) = 0.3 + \(\big[\frac{56}{10^3} + \frac{56}{10^5} + \frac{56}{10^7} + ⋯ ∞\big]\) ⇒ \(0.3\overline{56}\) = \(\frac{3}{10}\) + \(\frac{\frac{56}{10^3}}{1-\frac{1}{10^2}}\) = \(\frac{3}{10}\) + \(\frac{56}{990}\) = \(\frac{353}{990}\) |
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