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

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(B) Let $x = 0.2555 \ldots = 0.2\overline{5} \quad ....(1)$Multiply both sides by $10$:$10x = 2.555 \ldots = 2.\overline{5} \quad ....(2)$Multiply bot

Vedclass · Accepted Answer

$\frac{23}{90}$

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(B) Let $x = 0.2555 \ldots = 0.2\overline{5} \quad ....(1)$Multiply both sides by $10$:$10x = 2.555 \ldots = 2.\overline{5} \quad ....(2)$Multiply both sides by $100$:$100x = 25.555 \ldots = 25.\overline{5} \quad ....(3)$Subtracting equation $(2)$ from equation $(3)$:$100x - 10x = 25.\overline{5} - 2.\overline{5}$$90x = 23$Therefore,$x = \frac{23}{90}$.

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.2555 \ldots$

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Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :$0.2555 \ldots$