Write down the decimal expansion of the ratio | vedclass

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(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

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(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 $\frac{29}{343}$.

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