To determine whether the expression \(\dfrac{3}{14} \cdot \dfrac{7}{71}\) is rational or irrational, we should first understand the properties of rational and irrational numbers.
A number is considered rational if it can be expressed as the quotient of two integers (where the denominator is not zero). Both \(\dfrac{3}{14}\) and \(\dfrac{7}{71}\) are rational numbers, as they can be written as the ratio of integers.
When we multiply two rational numbers, the result is also a rational number. Specifically:
\[ \dfrac{3}{14} \cdot \dfrac{7}{71} = \dfrac{3 \cdot 7}{14 \cdot 71} = \dfrac{21}{994} \]
Since \(21\) and \(994\) are both integers, and \(994 \neq 0\), the product \(\dfrac{21}{994}\) is a rational number.
Thus, the answer is:
(Choice A) Rational
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