![Trending Articles on Technical and Non Technical topics](/images/trending_categories.jpeg)
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Express each of the following decimals in the form $\frac{p}{q}$:$ 0 . \overline{54} $
Given:
The given decimal number is \( 0 . \overline{54} \).
To do:
We have to express the given decimal in $\frac{p}{q}$ form.
Solution:
$0. \overline{54}$
Let $x = 0.5454....$
Multiply both sides by 10.
$10x = 10(0.5454....)$
$10x = 5.454......$
Multiply both sides by 100.
$100x = 100(0.5454....)$
$100x = 54.5454.....$
Therefore,
$100x-x = 54.5454.... - 0.5454.....$
$99x = 54$
$x = \frac{54}{99}$
$x=\frac{9\times6}{9\times11}$
$x=\frac{6}{11}$
Therefore,
$0. \overline{54}$ in $\frac{p}{q}$ form is $\frac{6}{11}$.
Advertisements