classify each number below as a rational number or an irrational number.
$\frac{20}{14}$ $\quad$ $\circ$ $\quad$ $\circ$
$-24.\overline{10}$ $\quad$ $\circ$ $\quad$ $\circ$
$-2\sqrt{5}$ $\quad$ $\circ$ $\quad$ $\circ$
$-16\pi$ $\quad$ $\circ$ $\quad$ $\circ$
$-\sqrt{25}$ $\quad$ $\circ$ $\quad$ $\circ$

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Accepted Answer

# Explanation:
## Step1: Analyze $\frac{20}{14}$
Rational numbers are ratios of integers. $\frac{20}{14} = \frac{10}{7}$, a ratio of integers.
## Step2: Analyze $-24.\overline{10}$
Repeating decimals are rational. $-24.\overline{10}$ has a repeating decimal pattern.
## Step3: Analyze $-2\sqrt{5}$
$\sqrt{5}$ is non-integer, non-repeating/terminating. $-2\sqrt{5}$ inherits this property.
## Step4: Analyze $-16\pi$
$\pi$ is irrational; multiplying by integer $-16$ keeps it irrational.
## Step5: Analyze $-\sqrt{25}$
$\sqrt{25}=5$, so $-\sqrt{25}=-5$, an integer (rational).

# Answer:
| Number          | rational | irrational |
|-----------------|----------|------------|
| $\frac{20}{14}$ | $\bigcirc$ |            |
| $-24.\overline{10}$ | $\bigcirc$ |            |
| $-2\sqrt{5}$    |          | $\bigcirc$ |
| $-16\pi$        |          | $\bigcirc$ |
| $-\sqrt{25}$    | $\bigcirc$ |            |

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Question

Explanation:

Step1: Analyze $\frac{20}{14}$

Step2: Analyze $-24.\overline{10}$

Step3: Analyze $-2\sqrt{5}$

Step4: Analyze $-16\pi$

Step5: Analyze $-\sqrt{25}$

Answer:

Number	rational	irrational
$-24.\overline{10}$	$\bigcirc$
$-2\sqrt{5}$		$\bigcirc$
$-16\pi$		$\bigcirc$
$-\sqrt{25}$	$\bigcirc$