(C) Let $x = 0.3\overline{6} = 0.3666...$ (Equation $1$)Multiply both sides by $10$: $10x = 3.666...$ (Equation $2$)Multiply Equation $1$ by $100$: $1

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(C) Let $x = 0.3\overline{6} = 0.3666...$ (Equation $1$)Multiply both sides by $10$: $10x = 3.666...$ (Equation $2$)Multiply Equation $1$ by $100$: $100x = 36.666...$ (Equation $3$)Subtract Equation $2$ from Equation $3$:$100x - 10x = 36.666... - 3.666...$$90x = 33$$x = \frac{33}{90}$Simplify the fraction by dividing both numerator and denominator by $3$:$x = \frac{11}{30}$

Class 9 Mathematics Number Systems Mix Examples - Number Systems

Easy

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

A
$\frac{36}{100}$
B
$\frac{4}{11}$
C
$\frac{11}{30}$
D
$\frac{2}{5}$

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Class 9

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Number Systems

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Mix Examples - Number Systems

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0.$
$0.5 \overline{7}$

Medium

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Find the value of $a$ :
$\frac{3-\sqrt{5}}{3+2 \sqrt{5}}=a \sqrt{5}-\frac{19}{11}$

Difficult

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Find three different irrational numbers between the rational numbers $\frac{3}{4}$ and $\frac{4}{5}$.

Medium

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For each question,select the proper option from four options given,to make the statement true: $\sqrt{5} + \sqrt{5}$ is a / an $\ldots \ldots \ldots$ number.

Easy

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Insert a rational number and an irrational number between the following:
$0.0001$ and $0.001$

Medium

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

Similar Questions

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0.$$0.5 \overline{7}$

Find the value of $a$ : $\frac{3-\sqrt{5}}{3+2 \sqrt{5}}=a \sqrt{5}-\frac{19}{11}$

Find three different irrational numbers between the rational numbers $\frac{3}{4}$ and $\frac{4}{5}$.

For each question,select the proper option from four options given,to make the statement true: $\sqrt{5} + \sqrt{5}$ is a / an $\ldots \ldots \ldots$ number.

Insert a rational number and an irrational number between the following:$0.0001$ and $0.001$

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Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0.$
$0.5 \overline{7}$

Find the value of $a$ :
$\frac{3-\sqrt{5}}{3+2 \sqrt{5}}=a \sqrt{5}-\frac{19}{11}$

Insert a rational number and an irrational number between the following:
$0.0001$ and $0.001$