(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 Mix Examples - Number Systems

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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Mix Examples - Number Systems

If $\sqrt{2}=1.414$ and $\sqrt{3}=1.732,$ find the value of $\frac{4}{3\sqrt{3}-2\sqrt{2}}+\frac{3}{3\sqrt{3}+2\sqrt{2}}.$

Medium

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Multiply $3 \sqrt{7}$ and $5 \sqrt{7}$.

Easy

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Express $0.7\overline{39}$ in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$.

Medium

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Write the number in short form: $3.8232323 \ldots$

Easy

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State whether the following statement is true:
There is a number $x$ such that $x^{2}$ is irrational but $x^{4}$ is rational. Justify your answer by an example.

Easy

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

Similar Questions

If $\sqrt{2}=1.414$ and $\sqrt{3}=1.732,$ find the value of $\frac{4}{3\sqrt{3}-2\sqrt{2}}+\frac{3}{3\sqrt{3}+2\sqrt{2}}.$

Multiply $3 \sqrt{7}$ and $5 \sqrt{7}$.

Express $0.7\overline{39}$ in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$.

Write the number in short form: $3.8232323 \ldots$

State whether the following statement is true:There is a number $x$ such that $x^{2}$ is irrational but $x^{4}$ is rational. Justify your answer by an example.

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

State whether the following statement is true:
There is a number $x$ such that $x^{2}$ is irrational but $x^{4}$ is rational. Justify your answer by an example.