(D) Let $x = 5. \overline{2} = 5.2222 \ldots \quad \dots(1)$Multiplying both sides by $10,$ we get$10x = 52.2222 \ldots = 52. \overline{2} \quad \dots

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(D) Let $x = 5. \overline{2} = 5.2222 \ldots \quad \dots(1)$Multiplying both sides by $10,$ we get$10x = 52.2222 \ldots = 52. \overline{2} \quad \dots(2)$Subtracting equation $(1)$ from equation $(2)$:$10x - x = 52.2222 \ldots - 5.2222 \ldots$$9x = 47$$x = \frac{47}{9}$Hence,$5. \overline{2} = \frac{47}{9}$.

Class 9 Mathematics Number Systems Mix Examples - Number Systems

Medium

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

A
$\frac{57}{2}$
B
$\frac{46}{9}$
C
$\frac{47}{3}$
D
$\frac{47}{9}$

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Mix Examples - Number Systems

Prove that,$\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}=1$.

Medium

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Express $0.6 + 0.\overline{7} + 0.4\overline{7}$ in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$.

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$\frac{1}{\sqrt{9}-\sqrt{8}}$ is equal to

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Multiply $5 \sqrt{3}$ and $4 \sqrt{12}$.

Easy

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Simplify the following:
$\sqrt{45}-3 \sqrt{20}+4 \sqrt{5}$

Medium

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

Similar Questions

Prove that,$\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}=1$.

Express $0.6 + 0.\overline{7} + 0.4\overline{7}$ in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$.

$\frac{1}{\sqrt{9}-\sqrt{8}}$ is equal to

Multiply $5 \sqrt{3}$ and $4 \sqrt{12}$.

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

Simplify the following:
$\sqrt{45}-3 \sqrt{20}+4 \sqrt{5}$