Express the following in the form frac{p}{q}, | vedclass

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Question

(A) Let $x = 0.404040 \ldots = 0.\overline{40} \quad \dots(1)$Since there are two repeating digits,multiply both sides by $100$:$100x = 40.404040 \ldo

Vedclass · Accepted Answer

$\frac{40}{99}$

Vedclass · Answer

(A) Let $x = 0.404040 \ldots = 0.\overline{40} \quad \dots(1)$Since there are two repeating digits,multiply both sides by $100$:$100x = 40.404040 \ldots = 40.\overline{40} \quad \dots(2)$Subtracting equation $(1)$ from equation $(2)$:$100x - x = 40.\overline{40} - 0.\overline{40}$$99x = 40$$x = \frac{40}{99}$Thus,the number $0.404040 \ldots$ expressed in the form $\frac{p}{q}$ is $\frac{40}{99}$.

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.404040 \ldots$

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Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :$0.404040 \ldots$