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Let F=0.841818181818181..... When F is written as a fraction in lowest terms,the denominator is exceeds the numerator by: a-13 b-14 c-29 d-87

Note by Mehdi Balti
2 years, 6 months ago

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@Mehdi Balti

let \(F=0.8418181818...\)

so \(100F=84.18181818...\)

\( \implies 100F-F=(84.18181818...)-(0.8418181818...) \implies 99F=83.34 \implies F=\frac{8334}{9900}=\frac{463}{550}\)

\(550-463=87\) so the answer is \(d-87\)

Kaito Einstein - 2 years, 6 months ago

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Thanks @Dedik KaitoKid Love you :)

Mehdi Balti - 2 years, 6 months ago

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\(F = 0.84\dot{1}\dot{8} = 0.84 + \dfrac{18}{9900} = \dfrac{0.84\times 9900+18}{9900} = \dfrac{8316+18}{9900} = \dfrac{8334}{9900} = \dfrac{463}{550}\)

\(\Rightarrow 550 - 463 = \boxed{87}\)

Chew-Seong Cheong - 2 years, 6 months ago

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