The following real number is expressed in decimal form. Determine whether it is rational or not. If it is rational,express it in the form of $\frac{p}{q}$. $18.484848 \ldots$

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(A) Let $x = 18.484848 \ldots$ (Equation $1$).
Since the repeating part is $48$,multiply both sides by $100$:
$100x = 1848.484848 \ldots$ (Equation $2$).
Subtract Equation $1$ from Equation $2$:
$100x - x = 1848.484848 \ldots - 18.484848 \ldots$
$99x = 1830$.
$x = \frac{1830}{99}$.
Dividing both numerator and denominator by $3$,we get $x = \frac{610}{33}$.
Since the number can be expressed in the form $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$,it is a rational number.

Explore More

Similar Questions

Prove that $3+2 \sqrt{5}$ is an irrational number.

Prove that the number $\sqrt{3}+\sqrt{7}$ is irrational.

Prove that the square of every integer is of the form $3m$ or $3m+1$,where $m \in \mathbb{Z}$.

Find the $g.c.d.$ of $240$ and $6552$ using Euclid's division algorithm.

Prove that the following number is irrational: $3+2\sqrt{5}$

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo