frac{p}{q} is a rational number and for non-n | vedclass

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Question

(A) According to the Fundamental Theorem of Arithmetic and the properties of rational numbers,a rational number $\frac{p}{q}$ (where $p$ and $q$ are c

Vedclass · Accepted Answer

a terminating decimal expansion

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(A) According to the Fundamental Theorem of Arithmetic and the properties of rational numbers,a rational number $\frac{p}{q}$ (where $p$ and $q$ are coprime) has a terminating decimal expansion if and only if the prime factorization of the denominator $q$ is of the form $2^{m} 5^{n}$,where $m$ and $n$ are non-negative integers.Therefore,the decimal form of $\frac{p}{q}$ is a terminating decimal expansion.

$\frac{p}{q}$ is a rational number and for non-negative integers $m$ and $n$,$q = 2^{m} 5^{n}$ if and only if the decimal form of $\frac{p}{q}$ is $\ldots \ldots \ldots \ldots$

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