Write down the decimal expansion of the ratio | vedclass

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Question

(C) rational number $\frac{p}{q}$ has a terminating decimal expansion if the prime factorization of the denominator $q$ is of the form $2^n 5^m$,where

Vedclass · Accepted Answer

Non-terminating

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(C) rational number $\frac{p}{q}$ has a terminating decimal expansion if the prime factorization of the denominator $q$ is of the form $2^n 5^m$,where $n$ and $m$ are non-negative integers.In the given rational number $\frac{129}{2^{2} 5^{7} 7^{5}}$,the denominator contains a factor of $7^5$ in addition to $2$ and $5$.Since the prime factorization of the denominator includes a prime factor other than $2$ or $5$ (which is $7$),the decimal expansion of this rational number is non-terminating and repeating.Therefore,it does not have a terminating decimal expansion.

Write down the decimal expansion of the rational number $\frac{129}{2^{2} 5^{7} 7^{5}}$.

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