(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

Rationalise the denominator of the following:
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Difficult

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Insert a rational number and an irrational number between the following:
$0$ and $0.1$

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Fill in the blanks to make the following statement true: The decimal expansion of $\frac{47}{50}$ is of $\ldots \ldots \ldots$ type.

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Rationalise the denominator of the following:
$\frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}}$

Difficult

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Simplify: $2^{-3} + (0.01)^{-\frac{1}{2}} - (27)^{\frac{2}{3}}$ (in $.125$)

Easy

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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

Rationalise the denominator of the following:$\frac{3 \sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$

Insert a rational number and an irrational number between the following:$0$ and $0.1$

Fill in the blanks to make the following statement true: The decimal expansion of $\frac{47}{50}$ is of $\ldots \ldots \ldots$ type.

Rationalise the denominator of the following:$\frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}}$

Simplify: $2^{-3} + (0.01)^{-\frac{1}{2}} - (27)^{\frac{2}{3}}$ (in $.125$)

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

Rationalise the denominator of the following:
$\frac{3 \sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$

Insert a rational number and an irrational number between the following:
$0$ and $0.1$

Rationalise the denominator of the following:
$\frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}}$