The task is to place the given numbers on a number line between 4 and 5, rounding them to the nearest tick mark. Let’s analyze each number:

1. 4.08 – This is slightly above 4, but much closer to 4 than to 4.5. So, on the number line, it will be placed just a little bit after 4, rounded to 4.

2. 4 and 2/3 (4⅔) – To convert this to a decimal, divide 2 by 3: $4 + \frac{2}{3} = 4 + 0.6667 = 4.6667$ This is closer to 4.75 than 4.5, so it will be placed between 4.5 and 5, closer to 4.75.

3. 4 and 1/2 (4½) – This is exactly halfway between 4 and 5. So, it will be placed at 4.5 on the number line.

4. 4.75 – This is three-quarters of the way between 4 and 5, so it will be placed at 4.75 directly.

Summary of placements:

• 4.08 → Rounded to 4
• 4⅔ (4.6667) → Placed near 4.75
• 4½ (4.5) → Placed at 4.5
• 4.75 → Placed at 4.75

Would you like further clarification or more details?

Here are 5 related questions:

1. How do we convert fractions into decimals?
2. What is the significance of rounding to the nearest tick mark?
3. How would we place numbers if the number line extended beyond 5?
4. What are other common fractions that are close to 0.5 or 0.75?
5. How can we ensure accurate rounding on a number line?

Tip: Always visualize the placement of decimals or fractions on a number line to better understand their positions relative to whole numbers.