(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 Real Numbers and their Decimal Expansions

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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Number Systems

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Real Numbers and their Decimal Expansions

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Write the following in decimal form and state what kind of decimal expansion each has:
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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

Is $0.3\overline{7}$ a rational number or an irrational number?

For each question,select the proper option from four options given,to make the statement true: $0.3\overline{6}=$

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :$0.00323232 \ldots$

Write the following in decimal form and state what kind of decimal expansion each has:$\frac{2}{11}$

Show that $0.142857142857... = 0.\overline{142857} = \frac{1}{7}$.

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

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.00323232 \ldots$

Write the following in decimal form and state what kind of decimal expansion each has:
$\frac{2}{11}$