(B) Let $x = 0.272727...$ (Equation $1$)Since there are two repeating digits, multiply both sides by $100$:$100x = 27.272727...$ (Equation $2$)Subtrac

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(B) Let $x = 0.272727...$ (Equation $1$)Since there are two repeating digits, multiply both sides by $100$:$100x = 27.272727...$ (Equation $2$)Subtract Equation $1$ from Equation $2$:$100x - x = 27.272727... - 0.272727...$$99x = 27$$x = \frac{27}{99}$Simplify the fraction by dividing both numerator and denominator by $9$:$x = \frac{3}{11}$

Class 9 Mathematics Number Systems Mix Examples - Number Systems

Easy

Express $0.\overline{27}$ in the $\frac{p}{q}$ form.

A
$\frac{27}{100}$
B
$\frac{3}{11}$
C
$\frac{27}{90}$
D
$\frac{27}{99}$

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Mix Examples - Number Systems

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

Easy

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State whether the following statement is true or false:
Every whole number is a rational number.

Easy

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Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.888 \ldots$

Easy

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Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0 .$
$0 . \overline{35}$

Medium

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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 $0.\overline{27}$ in the $\frac{p}{q}$ form.

Similar Questions

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

State whether the following statement is true or false:Every whole number is a rational number.

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :$0.888 \ldots$

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0 .$$0 . \overline{35}$

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

State whether the following statement is true or false:
Every whole number is a rational number.

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.888 \ldots$

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0 .$
$0 . \overline{35}$