(B) To determine the decimal expansion of $\frac{1}{7}$,we perform long division of $1$ by $7$.Dividing $1$ by $7$ gives $0.142857142857...$Since the

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(B) To determine the decimal expansion of $\frac{1}{7}$,we perform long division of $1$ by $7$.Dividing $1$ by $7$ gives $0.142857142857...$Since the remainder never becomes $0$ and the sequence of digits $142857$ repeats indefinitely,the decimal expansion is non-terminating and recurring.