(B) Let $x = 0.2555 \ldots = 0.2\overline{5} \quad ....(1)$Multiply both sides by $10$:$10x = 2.555 \ldots = 2.\overline{5} \quad ....(2)$Multiply bot

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(B) Let $x = 0.2555 \ldots = 0.2\overline{5} \quad ....(1)$Multiply both sides by $10$:$10x = 2.555 \ldots = 2.\overline{5} \quad ....(2)$Multiply both sides by $100$:$100x = 25.555 \ldots = 25.\overline{5} \quad ....(3)$Subtracting equation $(2)$ from equation $(3)$:$100x - 10x = 25.\overline{5} - 2.\overline{5}$$90x = 23$Therefore,$x = \frac{23}{90}$.

Class 9 Mathematics Number Systems Real Numbers and their Decimal Expansions

Medium

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

A
$\frac{33}{90}$
B
$\frac{23}{90}$
C
$\frac{44}{90}$
D
$\frac{23}{45}$

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Class 9

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Number Systems

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Real Numbers and their Decimal Expansions

Visualize the representation of $5.3\overline{7}$ on the number line up to $5$ decimal places,that is,up to $5.37777$.

Medium

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Show that $1.272727 \ldots = 1.\overline{27}$ can be expressed in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$.

Medium

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Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.00323232 \ldots$

Difficult

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Represent $5.4949$ on the number line,using successive magnification,up to $4$ decimal places.

Medium

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Express $0.12 \overline{3}$ in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$.

Medium

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

Similar Questions

Visualize the representation of $5.3\overline{7}$ on the number line up to $5$ decimal places,that is,up to $5.37777$.

Show that $1.272727 \ldots = 1.\overline{27}$ can be expressed in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$.

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :$0.00323232 \ldots$

Represent $5.4949$ on the number line,using successive magnification,up to $4$ decimal places.

Express $0.12 \overline{3}$ in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$.

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

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.00323232 \ldots$