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(B) To determine if a rational number $\frac{p}{q}$ has a terminating decimal expansion,we check if the prime factorization of the denominator $q$ is

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Non-terminating repeating decimal expansion

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(B) To determine if a rational number $\frac{p}{q}$ has a terminating decimal expansion,we check if the prime factorization of the denominator $q$ is of the form $2^n 	imes 5^m$,where $n$ and $m$ are non-negative integers.First,simplify the fraction $\frac{77}{210}$ by dividing both numerator and denominator by their greatest common divisor,which is $7$:$\frac{77 \div 7}{210 \div 7} = \frac{11}{30}$.Now,find the prime factorization of the denominator $30$:$30 = 2 	imes 3 	imes 5$.Since the prime factorization of the denominator contains a factor $3$ (other than $2$ and $5$),the rational number $\frac{11}{30}$ has a non-terminating repeating decimal expansion.

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: $\frac{77}{210}$.

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