(A) Let $x = 0.\overline{4} = 0.4444...$ (Equation $1$).Since there is one repeating digit after the decimal point, multiply both sides by $10$:$10x =

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(A) Let $x = 0.\overline{4} = 0.4444...$ (Equation $1$).Since there is one repeating digit after the decimal point, multiply both sides by $10$:$10x = 4.4444...$ (Equation $2$).Subtract Equation $1$ from Equation $2$:$10x - x = 4.4444... - 0.4444...$$9x = 4$$x = \frac{4}{9}$.Thus, $0.\overline{4}$ expressed in the form $\frac{p}{q}$ is $\frac{4}{9}$.

Class 9 Mathematics Number Systems Real Numbers and their Decimal Expansions

Medium

Express $0.\overline{4}$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.

A
$\frac{4}{9}$
B
$\frac{4}{10}$
C
$\frac{4}{90}$
D
$\frac{4}{99}$

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Number Systems

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Real Numbers and their Decimal Expansions

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Express $0.\overline{4}$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.

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Show that $0.2353535 \ldots = 0.2 \overline{35}$ can be expressed in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$.

Convert the following rational number into decimal form and state the kind of its decimal expansion: $\frac{25}{8}$

For each question,select the proper option from four options given,to make the statement true: The decimal expansion of $-\frac{11}{4}$ is..........

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