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The problem asks you to compare three numbers: \(\pi\), \(\sqrt{7.29}\), and \(\frac{16}{7}\), using the given number line ranging from 0 to 4.

### Step 1: Calculate the approximate values of the numbers

- \(\pi \approx 3.1416\)
- \(\sqrt{7.29} = 2.7\) (since \(2.7^2 = 7.29\))
- \(\frac{16}{7} \approx 2.2857\) (since \(16 \div 7 \approx 2.2857\))

### Step 2: Place these values on the number line
- \(\pi \approx 3.1416\) is slightly above 3.
- \(\sqrt{7.29} = 2.7\) is located between 2 and 3, closer to 3.
- \(\frac{16}{7} \approx 2.2857\) is located between 2 and 3, but closer to 2.

### Step 3: Compare the numbers
We can now compare their positions:
- \(\frac{16}{7} \approx 2.2857\) is the smallest.
- Next is \(\sqrt{7.29} = 2.7\).
- Finally, \(\pi \approx 3.1416\) is the largest.

### Step 4: Analyze the answer choices
- **A. \(\pi < \sqrt{7.29}\)** — Incorrect, because \(\pi > \sqrt{7.29}\).
- **B. \(\frac{16}{7} < \pi\)** — Correct, because \(\frac{16}{7} \approx 2.2857\) and \(\pi \approx 3.1416\).
- **C. \(\pi < \frac{16}{7}\)** — Incorrect, because \(\pi > \frac{16}{7}\).
- **D. \(\sqrt{7.29} < \frac{16}{7}\)** — Incorrect, because \(\sqrt{7.29} > \frac{16}{7}\).

### Correct Answer: **B**

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you approximate square roots without a calculator?
2. Why is \(\pi\) an irrational number, and how is it represented on a number line?
3. Can \(\frac{16}{7}\) be expressed as a mixed fraction, and what would it be?
4. How does the number line help in comparing decimal approximations?
5. What are the common ways to estimate fractions like \(\frac{16}{7}\)?

**Tip:** When comparing fractions, convert them to decimals to easily position them on a number line.

Use the number line above to correctly compare the following numbers: π, √7.29, 16/7.

Learn how to compare numbers like π, √7.29, and 16/7 using a number line. This step-by-step solution explains how to calculate their decimal approximations and position them on the number line. Suitable for Grades 6-8 students.

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