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Let's solve the problems one by one:

### First Section: Write each number in standard form

1. \( 5 \times 100 + 8 \times 10 + 6 \times 1 + 5 \times \frac{1}{10} + 4 \times \frac{1}{100} + 5 \times \frac{1}{1,000} \)

   - \( 5 \times 100 = 500 \)
   - \( 8 \times 10 = 80 \)
   - \( 6 \times 1 = 6 \)
   - \( 5 \times \frac{1}{10} = 0.5 \)
   - \( 4 \times \frac{1}{100} = 0.04 \)
   - \( 5 \times \frac{1}{1,000} = 0.005 \)

   So, adding these up:  
   \( 500 + 80 + 6 + 0.5 + 0.04 + 0.005 = 586.545 \)

   **Answer: 586.545**

2. \( 3 \times 100 + 7 \times 10 + 2 \times 1 + 8 \times \frac{1}{10} + 8 \times \frac{1}{100} + 4 \times \frac{1}{1,000} \)

   - \( 3 \times 100 = 300 \)
   - \( 7 \times 10 = 70 \)
   - \( 2 \times 1 = 2 \)
   - \( 8 \times \frac{1}{10} = 0.8 \)
   - \( 8 \times \frac{1}{100} = 0.08 \)
   - \( 4 \times \frac{1}{1,000} = 0.004 \)

   So, adding these up:  
   \( 300 + 70 + 2 + 0.8 + 0.08 + 0.004 = 372.884 \)

   **Answer: 372.884**

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### Second Section: Write each number in standard form

1. **Two and thirty-eight thousandths**  
   This means \( 2 + 0.038 = 2.038 \)  
   **Answer: 2.038**

2. **Three and fifty-three thousandths**  
   This means \( 3 + 0.053 = 3.053 \)  
   **Answer: 3.053**

3. **Five and twenty-nine hundredths**  
   This means \( 5 + 0.29 = 5.29 \)  
   **Answer: 5.29**

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### Third Section: Write a decimal that is equivalent to the given decimal

1. \( 4.90 = 4.9 \)
2. \( 7.5 = 7.50 \)
3. \( 2.700 = 2.7 \)
4. \( 34.30 = 34.3 \)
5. \( 19.5 = 19.50 \)
6. \( 25.200 = 25.2 \)
7. \( 7.50 = 7.5 \)
8. \( 21.40 = 21.4 \)
9. \( 12.300 = 12.3 \)

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Would you like any further explanation or details on any part? Here are five related questions to deepen understanding:

1. How do you convert between expanded form and standard form for decimals?
2. What is the difference between tenths, hundredths, and thousandths in decimal places?
3. Why is \( 4.90 \) equivalent to \( 4.9 \), and what does this reveal about trailing zeros in decimals?
4. How would you write a number like \( 7.025 \) in expanded form?
5. How do you compare two decimals to determine which one is larger?

**Tip:** When writing decimals, trailing zeros after the decimal point do not change the value of the number. For example, \( 7.5 \) is the same as \( 7.50 \).

Write each number in standard form and write a decimal that is equivalent to the given decimal.

Learn how to write numbers in standard form from expanded form and understand decimal equivalence. This worksheet is suitable for Grades 4-5 students, focusing on decimal place values and their equivalents.

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