Write down the decimal expansion of the ratio | vedclass

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

Question

(D) To determine if the rational number $\frac{29}{343}$ has a terminating decimal expansion,we examine the prime factorization of the denominator.$1$

Vedclass · Accepted Answer

Non-terminating repeating

Vedclass · Answer

(D) To determine if the rational number $\frac{29}{343}$ has a terminating decimal expansion,we examine the prime factorization of the denominator.$1$. The denominator is $343 = 7^3$.$2$. $A$ rational number $\frac{p}{q}$ has a terminating decimal expansion if and only if the prime factorization of $q$ is of the form $2^n 	imes 5^m$,where $n$ and $m$ are non-negative integers.$3$. Since the prime factorization of $343$ is $7^3$,which does not contain factors of $2$ or $5$,the decimal expansion is non-terminating and repeating.$4$. Therefore,$\frac{29}{343}$ does not have a terminating decimal expansion.

Write down the decimal expansion of the rational number $\frac{29}{343}$.

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

Write down the decimal expansion of the rational number $\frac{17}{8}$.

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

Show that any positive odd integer is of the form $6q+1$,$6q+3$,or $6q+5$,where $q$ is some integer.

Vedclass Test Series

Exam Paper Generator

Online Exam Module