Question

use the drop-down menus to classify each number as rational or irrational. click the arrows to choose an answer from each menu. 4.\overline{79} is irrational \sqrt{24} is rational \frac{5}{2} is rational

Explanation:

Step1: Analyze \( 4.\overline{79} \)

A repeating decimal can be expressed as a fraction of two integers. Let \( x = 4.\overline{79} = 4.797979\ldots \). Then \( 100x = 479.7979\ldots \). Subtract \( x \) from \( 100x \): \( 100x - x = 479.7979\ldots - 4.7979\ldots \), so \( 99x = 475 \), and \( x=\frac{475}{99} \), which is a ratio of integers. So \( 4.\overline{79} \) is rational (the original classification as irrational is wrong).

Step2: Analyze \( \sqrt{24} \)

Simplify \( \sqrt{24}=\sqrt{4\times6} = 2\sqrt{6} \). \( \sqrt{6} \) is irrational (since 6 is not a perfect square), and multiplying an irrational number by a non - zero rational number (2) gives an irrational number. So \( \sqrt{24} \) is irrational (the original classification as rational is wrong).

Step3: Analyze \( \frac{5}{2} \)

\( \frac{5}{2}=2.5 \), which is a fraction of two integers (5 and 2, with 2≠0). By definition, a number that can be written as \( \frac{p}{q} \) where \( p,q\in\mathbb{Z}, q
eq0 \) is rational. So \( \frac{5}{2} \) is correctly classified as rational.

Answer:

• \( 4.\overline{79} \): rational
• \( \sqrt{24} \): irrational
• \( \frac{5}{2} \): rational