InterviewSolution
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Write the following numbers p/q in formi. 9.315315….. ii. 357.417417….. |
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Answer» i. Let x = 9.315315 … = \(9.\overline{315}\) …(i) Since, three numbers i.e. 3, 1 and 5 are repeating after the decimal point. Thus, multiplying both sides by 1000, 1000x = 9315.315315… ∴ 1000x =\(9315.\overline{315}\)...(ii) Subtracting (i) from (ii) ∴ 1000x - x =\(9315.\overline{315}\) - \(9.\overline{315}\) ∴ 999x = 9306 ∴ \(x=\frac{9306}{999}\) = \(\frac{9\times1034}{9\times111}\) = \(\frac{1034}{111}\) ∴ 9.315315... = \(\frac{1034}{111}\) ii. Let x = 357.417417…= \(357.\overline{417}\) ...(i) Since, three numbers i.e. 4, 1 and 7 are repeating after the decimal point. Thus, multiplying both sides by 1000, 1000x = 357417.417417… ∴ 1000x = 357417.417 …(ii) Subtracting (i) from (ii), 1000x – x =\(357417.\overline{417}\) - \(357.\overline{417}\) ∴ 999x = 357060 ∴ \(x=\frac{357060}{999}\) = \(\frac{3\times119020}{3\times333}\) ∴ 357.417417... = \(\frac{119020}{333}\) |
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