Determine whether the rational number frac{64 | vedclass

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

Question

(B) 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

Non-terminating repeating

Vedclass · Answer

(B) To determine if a rational number $\frac{p}{q}$ has a terminating decimal expansion,we check the prime factorization of the denominator $q$.If $q = 2^n 	imes 5^m$,where $n$ and $m$ are non-negative integers,the decimal expansion is terminating.Here,$q = 455$.Prime factorization of $455 = 5 	imes 7 	imes 13$.Since the prime factorization contains factors other than $2$ and $5$ (specifically $7$ and $13$),the decimal expansion of $\frac{64}{455}$ is non-terminating repeating.

Determine whether the rational number $\frac{64}{455}$ has a terminating or non-terminating repeating decimal expansion. If it is terminating,write down its decimal expansion.

Similar Questions

Determine whether the rational number $\frac{77}{210}$ has a terminating or non-terminating repeating decimal expansion. If it is terminating,write down its decimal expansion.

Use Euclid's algorithm to find the $HCF$ of $4052$ and $12576$.

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

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: $\frac{23}{2^{3} \times 5^{2}}$

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: $\frac{64}{455}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module