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The activity requires comparing two rational numbers, writing the correct inequality sign (either `<` or `>`), and placing the numbers on the number line. Let's go through each problem step-by-step:

### 1. **4.5 vs. \(\frac{1}{3}\)**
   - **Convert to decimals**:
     - \(4.5 = 4.5\)
     - \(\frac{1}{3} \approx 0.333\)
   - **Comparison**: \(4.5 > \frac{1}{3}\)
   - **Placement on Number Line**: \(4.5\) is much greater than \(\frac{1}{3}\), so \(4.5\) would be on the right side of the number line closer to 5, and \(\frac{1}{3}\) is close to 0.

### 2. **0.9 vs. 1.9**
   - **Convert to decimals**:
     - Both are already in decimal form.
   - **Comparison**: \(0.9 < 1.9\)
   - **Placement on Number Line**: \(0.9\) is between 0 and 1, and \(1.9\) is just before 2.

### 3. **3 vs. \(\frac{17}{5}\)**
   - **Convert to decimals**:
     - \(\frac{17}{5} = 3.4\)
   - **Comparison**: \(3 < \frac{17}{5}\)
   - **Placement on Number Line**: \(3\) is on the left, and \(3.4\) (or \(\frac{17}{5}\)) is to the right of 3 but before 4.

### 4. **\(\frac{5}{6}\) vs. 3**
   - **Convert to decimals**:
     - \(\frac{5}{6} \approx 0.833\)
   - **Comparison**: \(\frac{5}{6} < 3\)
   - **Placement on Number Line**: \(\frac{5}{6}\) is between 0 and 1, while 3 is farther right on the number line.

### 5. **5.3 vs. \(\frac{28}{5}\)**
   - **Convert to decimals**:
     - \(\frac{28}{5} = 5.6\)
   - **Comparison**: \(5.3 < \frac{28}{5}\)
   - **Placement on Number Line**: \(5.3\) is just past 5, while \(5.6\) is slightly farther right, between 5 and 6.

### 6. **0.2 vs. \(\frac{3}{5}\)**
   - **Convert to decimals**:
     - \(\frac{3}{5} = 0.6\)
   - **Comparison**: \(0.2 < \frac{3}{5}\)
   - **Placement on Number Line**: \(0.2\) is closer to 0, while \(0.6\) is between 0 and 1, but closer to 1.

### 7. **\(6 \frac{1}{7}\) vs. 6.69**
   - **Convert to decimals**:
     - \(6 \frac{1}{7} \approx 6.14\)
   - **Comparison**: \(6 \frac{1}{7} < 6.69\)
   - **Placement on Number Line**: \(6 \frac{1}{7}\) is between 6 and 7, closer to 6, while \(6.69\) is closer to 7.

### 8. **1 vs. 0**
   - **Convert to decimals**:
     - Both are already in decimal form.
   - **Comparison**: \(1 > 0\)
   - **Placement on Number Line**: \(1\) is on the right, and \(0\) is on the left.

### 9. **10.78 vs. \(\frac{120}{10}\)**
   - **Convert to decimals**:
     - \(\frac{120}{10} = 12\)
   - **Comparison**: \(10.78 < 12\)
   - **Placement on Number Line**: \(10.78\) is between 10 and 12, but closer to 11, while \(12\) is exactly at 12.

### 10. **\(5 \frac{5}{9}\) vs. \(5 \frac{13}{15}\)**
   - **Convert to decimals**:
     - \(5 \frac{5}{9} \approx 5.56\)
     - \(5 \frac{13}{15} \approx 5.87\)
   - **Comparison**: \(5 \frac{5}{9} < 5 \frac{13}{15}\)
   - **Placement on Number Line**: \(5 \frac{5}{9}\) is closer to 5, while \(5 \frac{13}{15}\) is nearer to 6.

Would you like more details, or have any specific questions about these problems?

### Related Questions:
1. How do you convert fractions into decimal form?
2. Why is comparing decimals important when placing them on a number line?
3. What are some strategies for understanding the relative sizes of fractions?
4. How can you use a number line to visualize operations like addition or subtraction?
5. What are some common mistakes to avoid when comparing rational numbers?

### Tip:
When comparing fractions, converting them to decimals can make it easier to understand their relative sizes!

Order of Rational Numbers on a Number Line: Compare two rational numbers and arrange them in order, placing them on a number line.

Learn how to compare rational numbers and arrange them on a number line. This worksheet covers key concepts such as converting fractions to decimals and understanding rational number placement. Suitable for Grade 7 students.

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