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!