Without performing long division,state whethe | vedclass

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

Question

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

Vedclass · Accepted Answer

Terminating

Vedclass · Answer

(A) To determine if the decimal expansion of a rational number $\frac{p}{q}$ is terminating,we examine 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 rational number $\frac{13}{3125}$,the denominator is $q = 3125$.Prime factorization of $3125 = 5 	imes 5 	imes 5 	imes 5 	imes 5 = 5^5$.This can be written as $2^0 	imes 5^5$.Since the denominator is in the form $2^n 	imes 5^m$ (where $n=0$ and $m=5$),the decimal expansion of $\frac{13}{3125}$ is terminating.

Without performing long division,state whether the decimal expansion of the rational number $\frac{13}{3125}$ is terminating or non-terminating repeating.

Similar Questions

Prove that the cube of any positive integer is of the form $9m$,$9m+1$,or $9m+8$,where $m$ is an integer.

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: $\frac{13}{3125}$.

Express $7429$ as a product of its prime factors.

Every composite number greater than $1$ can be expressed (factorized) as a product of primes,and this factorization is .........,apart from the order in which the prime factors occur.

When $(6k+1)^2$ is divided by $6$,the remainder is . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module