(C) Let $x = 0.888 \ldots = 0.\overline{8} \quad \dots(1)$Multiplying both sides by $10$,we get:$10x = 8.888 \ldots = 8.\overline{8} \quad \dots(2)$Su

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(C) Let $x = 0.888 \ldots = 0.\overline{8} \quad \dots(1)$Multiplying both sides by $10$,we get:$10x = 8.888 \ldots = 8.\overline{8} \quad \dots(2)$Subtracting equation $(1)$ from equation $(2)$:$10x - x = 8.\overline{8} - 0.\overline{8}$$9x = 8$Therefore,$x = \frac{8}{9}$.

Class 9 Mathematics Number Systems Real Numbers and their Decimal Expansions

Easy

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

A
$\frac{8}{3}$
B
$\frac{5}{9}$
C
$\frac{8}{9}$
D
$\frac{8}{7}$

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Number Systems

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Real Numbers and their Decimal Expansions

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.2555 \ldots$

Medium

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Every rational number is

Easy

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Fill in the blanks to make the following statement true: The decimal expansion of $\frac{2}{3}$ is of $\ldots \ldots$ type.

Easy

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

Medium

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Calculate the sum: $0.\overline{35} + 0.\overline{28}$.

Medium

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

Similar Questions

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :$0.2555 \ldots$

Every rational number is

Fill in the blanks to make the following statement true: The decimal expansion of $\frac{2}{3}$ is of $\ldots \ldots$ type.

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

Calculate the sum: $0.\overline{35} + 0.\overline{28}$.

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

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.2555 \ldots$

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