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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

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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Comments

@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 $d-87$

Abdeslem Smahi - 5 years, 11 months ago

Thanks @Dedik KaitoKid Love you :)

Mehdi Balti - 5 years, 11 months ago

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

$\Rightarrow 550 - 463 = \boxed{87}$

Chew-Seong Cheong - 5 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$