Question

question 1
order the following numbers from greatest to least.
$8.overline{4}, \frac{25}{3}, \sqrt{72}, \frac{35}{4}$
$\circ \sqrt{72}, \frac{25}{3}, \frac{35}{4}, 8.overline{4}$
$\circ \frac{25}{3}, \sqrt{72}, \frac{35}{4}, 8.overline{4}$
$\circ \frac{35}{4}, \sqrt{72}, 8.overline{4}, \frac{25}{3}$
$\circ \frac{35}{4}, \frac{25}{3}, 8.overline{4}, \sqrt{72}$

Explanation:

Step1: Convert each number to decimal

• \( 8.\overline{4} = 8.444\cdots \)
• \( \frac{25}{3} \approx 8.333\cdots \)
• \( \sqrt{72} \approx 8.485 \)
• \( \frac{35}{4} = 8.75 \)

Step2: Compare the decimals

• \( 8.75 > 8.485 > 8.444\cdots > 8.333\cdots \)
• So, \( \frac{35}{4} > \sqrt{72} > 8.\overline{4} > \frac{25}{3} \)

Answer:

\(\frac{35}{4},\sqrt{72},8.\overline{4},\frac{25}{3}\) (corresponding to the third option: \(\boldsymbol{\frac{35}{4},\sqrt{72},8.\overline{4},\frac{25}{3}}\))