(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

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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

For each question,select the proper option from four options given,to make the statement true: The rationalising factor of $4-\sqrt{5}$ is...........

Construct the square root spiral up to $\sqrt{6}$.

Multiply $3 \sqrt{7}$ and $5 \sqrt{7}$.

Fill in the blanks to make the following statement true:$\sqrt{1 \frac{25}{144}} = \ldots$

Find three rational numbers between $-1$ and $-2$.

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

Fill in the blanks to make the following statement true:
$\sqrt{1 \frac{25}{144}} = \ldots$