Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0 .$
$0 . \overline{35}$
$0 . \overline{35}$
(A) Let $x = 0 . \overline{35}$.
$\therefore x = 0.353535 \ldots$ $(1)$
Since there are two repeating digits,multiply both sides by $100$:
$100x = 35.353535 \ldots$ $(2)$
Subtract equation $(1)$ from equation $(2)$:
$100x - x = 35.353535 \ldots - 0.353535 \ldots$
$99x = 35$
$\therefore x = \frac{35}{99}$
Thus,$0 . \overline{35} = \frac{35}{99}$.
$\therefore x = 0.353535 \ldots$ $(1)$
Since there are two repeating digits,multiply both sides by $100$:
$100x = 35.353535 \ldots$ $(2)$
Subtract equation $(1)$ from equation $(2)$:
$100x - x = 35.353535 \ldots - 0.353535 \ldots$
$99x = 35$
$\therefore x = \frac{35}{99}$
Thus,$0 . \overline{35} = \frac{35}{99}$.
Explore More
Similar Questions
Find three different irrational numbers between the irrational numbers $\sqrt{2}$ and $\sqrt{5}$.
Medium
View SolutionExpress the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.2555 \ldots$
$0.2555 \ldots$
Medium
View SolutionFind the value of $a$ :
$\frac{5+2 \sqrt{3}}{7+4 \sqrt{3}}=a-6 \sqrt{3}$
$\frac{5+2 \sqrt{3}}{7+4 \sqrt{3}}=a-6 \sqrt{3}$
Difficult
View SolutionRationalise the denominator of the following expression and evaluate it by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$,and $\sqrt{5}=2.236$ up to three decimal places:
$\frac{\sqrt{2}}{2+\sqrt{2}}$
$\frac{\sqrt{2}}{2+\sqrt{2}}$
Medium
View SolutionThe value of $1.999...$ in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0,$ is
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo