Without actually performing the long division | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) To determine if a rational number $\frac{p}{q}$ has a terminating decimal expansion,we check the prime factorization of the denominator $q$.If $q$

Vedclass · Accepted Answer

Terminating decimal expansion

Vedclass · Answer

(A) To determine if a rational number $\frac{p}{q}$ has a terminating decimal expansion,we check the prime factorization of the denominator $q$.If $q$ is of the form $2^n 	imes 5^m$,where $n$ and $m$ are non-negative integers,then the decimal expansion is terminating.Given the fraction $\frac{13}{3125}$,the denominator is $3125$.Prime factorization of $3125 = 5 	imes 5 	imes 5 	imes 5 	imes 5 = 5^5$.This can be written as $2^0 	imes 5^5$,which is in the form $2^n 	imes 5^m$ (where $n=0$ and $m=5$).Since the denominator is of the form $2^n 	imes 5^m$,the decimal expansion of $\frac{13}{3125}$ is terminating.

Without actually performing the long division,state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion: $\frac{13}{3125}$.

Similar Questions

Without actually performing the long division,state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion: $\frac{35}{50}$.

Find the $HCF$ of $96$ and $404$ by the prime factorisation method. Hence,find their $LCM$.

Write down the decimal expansion of the rational number $\frac{15}{1600}$.

Without actually performing the long division,state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion: $\frac{29}{343}$.

Find the $LCM$ and $HCF$ of the following pairs of integers and verify that $LCM \times HCF =$ product of the two numbers $336$ and $54$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module