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

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Question

let $x=5 . \overline{2}=5.2222 \ldots ....(1)$

Multiplying both sides by $10,$ we get

$10=52.222 \ldots=52 . \overline{2} ....(2)$

If we subt

Vedclass · Accepted Answer

$\frac{47}{9}$

Vedclass · Answer

let $x=5 . \overline{2}=5.2222 \ldots ....(1)$

Multiplying both sides by $10,$ we get

$10=52.222 \ldots=52 . \overline{2} ....(2)$

If we subtract $5 . \overline{2}$ from $52 . \overline{2}$, the repeating portion the decimal cancels out.

$	herefore$ Subtracting $(1)$ and $(2),$ we get $10 x-x=47 \Rightarrow 9 x=47 \Rightarrow x=\frac{47}{9}$

Hence, $5. \overline{2}=\frac{47}{9}$

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

$5. \overline{2}$

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Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ : $5. \overline{2}$