(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 Mix Examples - Number Systems

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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Mix Examples - Number Systems

Classify the following numbers as rational or irrational with justification:
$(i)$ $-\sqrt{0.4}$
$(ii)$ $\frac{\sqrt{12}}{\sqrt{75}}$

Medium

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For each question,select the proper option from four options given,to make the statement true: $(5^{-2})^{3} = \ldots \ldots \ldots$

Easy

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Find the value of $64^{\frac{2}{3}}$.

Easy

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Simplify:
$(\frac{3}{5})^4 \times (\frac{3}{5})^{-12} \times (\frac{3}{5})^{6}$

Difficult

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Find the value of $\frac{4}{(216)^{-\frac{2}{3}}} + \frac{1}{(256)^{-\frac{3}{4}}} + \frac{2}{(243)^{-\frac{1}{5}}}$

Medium

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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

Classify the following numbers as rational or irrational with justification:$(i)$ $-\sqrt{0.4}$$(ii)$ $\frac{\sqrt{12}}{\sqrt{75}}$

For each question,select the proper option from four options given,to make the statement true: $(5^{-2})^{3} = \ldots \ldots \ldots$

Find the value of $64^{\frac{2}{3}}$.

Simplify:$(\frac{3}{5})^4 \times (\frac{3}{5})^{-12} \times (\frac{3}{5})^{6}$

Find the value of $\frac{4}{(216)^{-\frac{2}{3}}} + \frac{1}{(256)^{-\frac{3}{4}}} + \frac{2}{(243)^{-\frac{1}{5}}}$

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Classify the following numbers as rational or irrational with justification:
$(i)$ $-\sqrt{0.4}$
$(ii)$ $\frac{\sqrt{12}}{\sqrt{75}}$

Simplify:
$(\frac{3}{5})^4 \times (\frac{3}{5})^{-12} \times (\frac{3}{5})^{6}$