State whether the following rational number has a terminating decimal expansion or not. If it has a terminating decimal expansion,find it: $\frac{13}{125}$

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(D) rational number $\frac{p}{q}$ has a terminating decimal expansion if the prime factorization of the denominator $q$ is of the form $2^n \times 5^m$,where $n$ and $m$ are non-negative integers.
Given the fraction $\frac{13}{125}$:
$1$. Prime factorization of the denominator: $125 = 5^3 = 2^0 \times 5^3$.
$2$. Since the denominator is in the form $2^n \times 5^m$ (where $n=0, m=3$),the rational number has a terminating decimal expansion.
$3$. To find the decimal expansion,we make the denominator a power of $10$:
$\frac{13}{125} = \frac{13 \times 2^3}{5^3 \times 2^3} = \frac{13 \times 8}{10^3} = \frac{104}{1000} = 0.104$.

Explore More

Similar Questions

Write whether every positive integer can be of the form $4q + 2$,where $q$ is an integer. Justify your answer.

Find the $G$.$C$.$D$. of $(28, 35, 91)$.

$0.123123123...$ is

Why is $7 \times 11 \times 13 + 13$ a composite number? Explain.

The value of $\text{g.c.d.}(18, 24) \times \text{l.c.m.}(18, 24) = \dots$

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