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Let's go through the problems one by one.

### 1. **Nickel Stack Height**
   - **Problem:** One nickel is \( \frac{39}{500} \) inch thick. Fifteen nickels are stacked vertically. How many inches tall is the stack?
   - **Solution:** Multiply the thickness of one nickel by the number of nickels.
   \[
   \text{Height} = 15 \times \frac{39}{500} = \frac{585}{500} = 1.17 \text{ inches}
   \]
   The stack is 1.17 inches tall.

### 2. **Line of Quarters Length**
   - **Problem:** One quarter is \( \frac{191}{200} \) inch in diameter. Eight quarters are placed side-by-side along a line. How many inches long is the line of quarters?
   - **Solution:** Multiply the diameter of one quarter by the number of quarters.
   \[
   \text{Length} = 8 \times \frac{191}{200} = \frac{1528}{200} = 7.64 \text{ inches}
   \]
   The line of quarters is 7.64 inches long.

### 3. **Closer to \( \frac{9}{11} \) or \( \frac{10}{11} \)?**
   - **Problem:** Is \( \frac{41}{50} \) closer to \( \frac{9}{11} \) or \( \frac{10}{11} \)? Verify your answer.
   - **Solution:** Convert each fraction to a decimal:
     - \( \frac{41}{50} = 0.82 \)
     - \( \frac{9}{11} \approx 0.8182 \)
     - \( \frac{10}{11} \approx 0.9091 \)
     - The difference between \( \frac{41}{50} \) and \( \frac{9}{11} \) is \( |0.82 - 0.8182| = 0.0018 \).
     - The difference between \( \frac{41}{50} \) and \( \frac{10}{11} \) is \( |0.82 - 0.9091| = 0.0891 \).
   \( \frac{41}{50} \) is closer to \( \frac{9}{11} \).

### 4. **Square Roots**
   - **Problem:** Find the two square roots of each number. Convert the decimal to a fraction.
     - \( \sqrt{0.25} = 0.5 \) or \( -0.5 \)
     - \( \sqrt{0.0625} = 0.25 \) or \( -0.25 \)
     - \( \sqrt{0.4} \approx 0.6325 \) or \( -0.6325 \)

### 7 & 8. **Approximate Irrational Numbers**
   - **Problem:** Approximate \( \sqrt{3} \) and \( \sqrt{18} \) to the nearest hundredth.
     - \( \sqrt{3} \approx 1.73 \)
     - \( \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} \approx 4.24 \)
   - **Solution:** Plot these on the number line provided.

### 9. **Between What Two Integers?**
   - **Problem:** Between what two integers does \( \sqrt{75} \) lie? To which is it closer?
   - **Solution:** Calculate \( \sqrt{75} \approx 8.66 \). It lies between 8 and 9, closer to 9.

### 10. **Photo Album Dimensions**
   - **Problem:** Calculate the dimensions of one page of the photo album.
   - **Solution:**
     - Each photo is \( 5 \times 5 \) cm because \( \text{Area} = 25 \text{ cm}^2 \).
     - Arrangement: 3 rows and 4 columns, so the total dimension without space and border is \( 3 \times 5 \) cm by \( 4 \times 5 \) cm.
     - Including spaces: 
       \[
       \text{Width} = 4 \times 5 + 3 \times 2 + 2 \times 3 = 20 + 6 + 6 = 32 \text{ cm}
       \]
       \[
       \text{Height} = 3 \times 5 + 2 \times 2 + 2 \times 3 = 15 + 4 + 6 = 25 \text{ cm}
       \]
       - The dimensions are 32 cm by 25 cm.

Would you like any further details on these problems? Here are some related questions:

1. How do you convert between decimals and fractions?
2. Why is \( \sqrt{18} \) equal to \( 3\sqrt{2} \)?
3. How do you calculate the length of a line of objects placed side by side?
4. What makes a number rational versus irrational?
5. How can you determine the approximate value of a square root without a calculator?

**Tip:** When comparing fractions, converting them to decimals can often simplify the process.

A worksheet containing math problems on rational and irrational numbers, including questions on nickels and quarters, finding square roots, comparing fractions, and calculating photo album dimensions.

This worksheet covers rational and irrational numbers, including calculating the height of a nickel stack, length of quarters in a row, comparing fractions, and solving for square roots. Suitable for Grades 6-8 with detailed examples.

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