To determine the correct order of the numbers from greatest to least, we'll first convert each number to its decimal form for comparison. Here are the four numbers we need to compare:
1. \( 7 \frac{1}{3} \)
2. \( \frac{221}{30} \)
3. \( 7 . \overline{36} \)
4. \( 2.4 \sqrt{3 \pi} \)
Let's convert these to decimals:
1. \( 7 \frac{1}{3} = 7 + \frac{1}{3} \approx 7.3333... \)
2. \( \frac{221}{30} \approx 7.3666... \)
3. \( 7 . \overline{36} = 7.366666... \)
4. \( 2.4 \sqrt{3 \pi} \approx 2.4 \times \sqrt{3 \times 3.14159} \approx 2.4 \times 3.143 \approx 7.3636... \)
Next, we'll arrange these numbers in descending order:
- \( 7 . \overline{36} \approx 7.3666 \)
- \( \frac{221}{30} \approx 7.3666 \)
- \( 2.4 \sqrt{3 \pi} \approx 7.3636 \)
- \( 7 \frac{1}{3} \approx 7.3333 \)
Now we need to match this order with the given sets of numbers:
1. \( 7 \frac{1}{3}, \frac{221}{30}, 7 . \overline{36}, 2.4 \sqrt{3 \pi} \)
- Order: \( 7.3333, 7.3666, 7.3666, 7.3636 \) (Not correct)
2. \( 7 \frac{1}{3}, 7 . \overline{36}, \frac{221}{30}, 2.4 \sqrt{3 \pi} \)
- Order: \( 7.3333, 7.3666, 7.3666, 7.3636 \) (Not correct)
3. \( 2.4 \sqrt{3 \pi}, 7 . \overline{36}, \frac{221}{30}, 7 \frac{1}{3} \)
- Order: \( 7.3636, 7.3666, 7.3666, 7.3333 \) (Not correct)
4. \( 2.4 \sqrt{3 \pi}, \frac{221}{30}, 7 . \overline{36}, 7 \frac{1}{3} \)
- Order: \( 7.3636, 7.3666, 7.3666, 7.3333 \) (Correct)
The correct set of numbers ordered from greatest to least is:
[tex]\[ 2.4 \sqrt{3 \pi}, \frac{221}{30}, 7 . \overline{36}, 7 \frac{1}{3} \][/tex]
