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Let's work through this exercise step by step.

### 1. **Plot these numbers on the number line:**
- Numbers to plot: \(0.1\), \(1.2\), \( \frac{3}{10} \), \( \frac{1}{2} \), \( \frac{3}{4} \), \(0.5\), \(0.9\), \( \frac{1}{4} \), \(1.8\), \( \frac{2}{5} \).

We have a number line from 0 to 2. Let's estimate where each number goes:
- **\(0.1\)**: This is between 0 and 0.2.
- **\(1.2\)**: This is between 1 and 1.5.
- **\(\frac{3}{10}\) or 0.3**: This is just after 0.25.
- **\(\frac{1}{2}\)** or 0.5: This is in the middle of 0 and 1.
- **\(\frac{3}{4}\)** or 0.75: This is three-quarters of the way between 0 and 1.
- **\(0.5\)**: This is in the middle (same as \(\frac{1}{2}\)).
- **\(0.9\)**: This is just before 1.
- **\(\frac{1}{4}\)** or 0.25: This is halfway between 0 and 0.5.
- **\(1.8\)**: This is close to 2.
- **\(\frac{2}{5}\)** or 0.4: This is slightly less than 0.5.

### 2. **Write the numbers for the points on the ruler:**
- **a = \( \frac{1}{16} \)** (already given)
- **b = \( \frac{2}{16} \) or \(\frac{1}{8}\)**
- **c = \( \frac{3}{16} \)**
- **d = \( \frac{4}{16} \) or \( \frac{1}{4} \)**
- **e = \( \frac{5}{16} \)**
- **f = \( \frac{6}{16} \) or \( \frac{3}{8} \)**
- **g = \( \frac{7}{16} \)**
- **h = \( \frac{8}{16} \) or \( \frac{1}{2} \)**

### 3. **Compare the fractions:**
   - **\( \frac{7}{8} \) vs \( \frac{7}{9} \)**: \( \frac{7}{8} > \frac{7}{9} \)
   - **\( \frac{11}{12} \) vs \( \frac{13}{12} \)**: \( \frac{11}{12} < \frac{13}{12} \)
   - **\( \frac{4}{5} \) vs \( \frac{5}{4} \)**: \( \frac{4}{5} < \frac{5}{4} \)
   - **\( \frac{9}{14} \) vs \( \frac{8}{13} \)**: \( \frac{9}{14} < \frac{8}{13} \)

Would you like more details on any of these steps?

Here are 5 related questions:
1. How can you easily find equivalent fractions on a number line?
2. What is the difference between plotting decimals and fractions on a number line?
3. How can you convert fractions to decimals when comparing them?
4. Why is \( \frac{7}{8} \) larger than \( \frac{7}{9} \) even though both numerators are the same?
5. Can you show how to find decimal equivalents for fractions like \( \frac{3}{4} \) or \( \frac{1}{5} \)?

**Tip:** Always simplify fractions to their lowest terms for easier comparisons!

Plot the given numbers on the number line, label the fractions on the ruler, and compare fractions using <, >, or =.

Learn how to plot decimals and fractions on a number line and compare fractions with different numerators and denominators. This exercise focuses on understanding fractions, converting between fractions and decimals, and comparing fractions using inequality symbols.

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