The decimal form of frac{12}{35} is ldots ldo | vedclass

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Question

(B) For the fraction $\frac{12}{35}$,we first check the denominator $q = 35$.The prime factorization of the denominator is $q = 5 	imes 7$.$A$ ration

Vedclass · Accepted Answer

non-terminating recurring decimal expansion

Vedclass · Answer

(B) For the fraction $\frac{12}{35}$,we first check the denominator $q = 35$.The prime factorization of the denominator is $q = 5 	imes 7$.$A$ 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.Since the denominator $35$ contains a prime factor $7$ (which is not $2$ or $5$),the decimal expansion of $\frac{12}{35}$ is non-terminating and recurring.Therefore,the correct option is $B$.

The decimal form of $\frac{12}{35}$ is $\ldots \ldots \ldots \ldots$

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