(A) Let $x = 0.\overline{3} = 0.333\dots$ (Equation $1$).Multiply both sides by $10$:$10x = 3.333\dots$ (Equation $2$).Subtract Equation $1$ from Equa

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(A) Let $x = 0.\overline{3} = 0.333\dots$ (Equation $1$).Multiply both sides by $10$:$10x = 3.333\dots$ (Equation $2$).Subtract Equation $1$ from Equation $2$:$10x - x = 3.333\dots - 0.333\dots$$9x = 3$$x = \frac{3}{9} = \frac{1}{3}$.Therefore,$0.\overline{3} = \frac{1}{3}$.

Class 9 Mathematics Number Systems Mix Examples - Number Systems

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For each question,select the proper option from the four options given to make the statement true: $0.\overline{3} = \dots$

A
$\frac{1}{3}$
B
$\frac{3}{10}$
C
$\frac{2}{3}$
D
$\frac{3}{2}$

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Mix Examples - Number Systems

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For each question,select the proper option from the four options given to make the statement true: $0.\overline{3} = \dots$

Similar Questions

Insert a rational number and an irrational number between the following:$\frac{-2}{5}$ and $\frac{1}{2}$

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If $a = \frac{3+\sqrt{5}}{2}$,then find the value of $a^{2} + \frac{1}{a^{2}}$.

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Insert a rational number and an irrational number between the following:
$\frac{-2}{5}$ and $\frac{1}{2}$

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$\frac{3}{\sqrt{8}} + \frac{1}{\sqrt{2}}$