classify each number below as a rational number or an irrational number.

\begin{tabular}{|c|c|c|}
\hline
& rational & irrational \\
\hline
$-\frac{9}{19}$ & \bigcirc & \bigcirc \\
\hline
$-\sqrt{19}$ & \bigcirc & \bigcirc \\
\hline
$\sqrt{49}$ & \bigcirc & \bigcirc \\
\hline
$16\pi$ & \bigcirc & \bigcirc \\
\hline
$82.\overline{80}$ & \bigcirc & \bigcirc \\
\hline
\end{tabular}

Question

classify each number below as a rational number or an irrational number.

\begin{tabular}{|c|c|c|}
\hline
& rational & irrational \\
\hline
$-\frac{9}{19}$ & \bigcirc & \bigcirc \\
\hline
$-\sqrt{19}$ & \bigcirc & \bigcirc \\
\hline
$\sqrt{49}$ & \bigcirc & \bigcirc \\
\hline
$16\pi$ & \bigcirc & \bigcirc \\
\hline
$82.\overline{80}$ & \bigcirc & \bigcirc \\
\hline
\end{tabular}

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Rational Numbers", "Irrational Numbers" ], "current_concepts": [ "Rational Numbers", "Irrational Numbers" ] } ## Classify each number based on definition $$ \begin{aligned} &-\frac{9}{19} \in \mathbb{Q} \quad \text{(Ratio of integers)} \ &-\sqrt{19} otin \mathbb{Q} \quad \text{(19 is not a perfect square)} \ &\sqrt{49} = 7 \in \mathbb{Q} \quad \text{(Integer)} \ &16\pi otin \mathbb{Q} \quad \text{($\pi$ is transcendental)} \ &82.\overline{80} \in \mathbb{Q} \quad \text{(Repeating decimal)} \end{aligned} $$ | Number | Rational | Irrational | |---|---|---| | $-\frac{9}{19}$ | Rational | | | $-\sqrt{19}$ | | Irrational | | $\sqrt{49}$ | Rational | | | $16\pi$ | | Irrational | | $82.\overline{80}$ | Rational | | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Rational and Irrational Numbers" ] }

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QUESTION IMAGE

Question

Explanation:

Classify each number based on definition

Answer:

Number	Rational	Irrational
\(-\sqrt{19}\)		Irrational
\(\sqrt{49}\)	Rational
\(16\pi\)		Irrational
\(82.\overline{80}\)	Rational