(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

Easy

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

Rationalise the denominator of the following:$\frac{3+\sqrt{2}}{4 \sqrt{2}}$

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

Classify the following numbers as rational or irrational with justification:$(i)$ $\sqrt{\frac{9}{27}}$$(ii)$ $\frac{\sqrt{28}}{\sqrt{343}}$

Find the value of $\left(\frac{125}{64}\right)^{-\frac{2}{3}}$.

Convert the following rational number into decimal form and state the kind of its decimal expansion:$\frac{4}{13}$

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Rationalise the denominator of the following:
$\frac{3+\sqrt{2}}{4 \sqrt{2}}$

Classify the following numbers as rational or irrational with justification:
$(i)$ $\sqrt{\frac{9}{27}}$
$(ii)$ $\frac{\sqrt{28}}{\sqrt{343}}$

Convert the following rational number into decimal form and state the kind of its decimal expansion:
$\frac{4}{13}$