(B) Let $x = 0.\overline{83}$.This can be written as $x = 0.838383...$ (Equation $1$).Since there are two repeating digits, multiply both sides by $10

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(B) Let $x = 0.\overline{83}$.This can be written as $x = 0.838383...$ (Equation $1$).Since there are two repeating digits, multiply both sides by $100$:$100x = 83.838383...$ (Equation $2$).Subtract Equation $1$ from Equation $2$:$100x - x = 83.838383... - 0.838383...$$99x = 83$.Therefore, $x = \frac{83}{99}$.Thus, $0.\overline{83} = \frac{83}{99}$.

Class 9 Mathematics Number Systems Real Numbers and their Decimal Expansions

Medium

Express $0.\overline{83}$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.

A
$83/100$
B
$83/99$
C
$83/90$
D
$8/9$

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Class 9

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Number Systems

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Real Numbers and their Decimal Expansions

Express $0.12 \overline{3}$ in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$.

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Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
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Express $0.\overline{83}$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.

Similar Questions

Express $0.12 \overline{3}$ in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$.

Express $1.23\overline{4}$ in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$.

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :$0 . \overline{001}$

Show that $0.3333... = 0.\overline{3}$ can be expressed in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \ne 0$.

Express $3.\overline{5}$ in the $\frac{p}{q}$ form.

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Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0 . \overline{001}$