State whether the following rational number h | vedclass

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

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Non-terminating repeating,$0.3666...$

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(B) To determine if a rational number $\frac{p}{q}$ has a terminating decimal expansion,we check the prime factorization of the denominator $q$ after simplifying the fraction to its lowest terms.First,simplify $\frac{55}{150}$ by dividing both numerator and denominator by their greatest common divisor,which is $5$:$\frac{55 \div 5}{150 \div 5} = \frac{11}{30}$.Now,find the prime factorization of the denominator $30$:$30 = 2 	imes 3 	imes 5$.$A$ rational number has a terminating decimal expansion if and only if the prime factorization of the denominator contains only powers of $2$ and/or $5$.Since the denominator $30$ contains a factor of $3$ (which is not $2$ or $5$),the decimal expansion is non-terminating and repeating.Performing the division $11 \div 30$ gives $0.3666...$ or $0.3\overline{6}$.

State whether the following rational number has a terminating decimal expansion or not. If it has,then find it: $\frac{55}{150}$

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