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Let's break down and solve the questions from the image:

### 20. Vocabulary
- **Question**: Write the rules for the patterns used to multiply by 0.1 and by 0.01.
- **Answer**:
  - When you multiply a number by **0.1**, the decimal point moves one place to the left.
  - When you multiply a number by **0.01**, the decimal point moves two places to the left.

### 21. Higher Order Thinking
- **Question**: The product of a factor and 0.1 is 8.35. What is the factor? What is the product of the factor and 0.01?
- **Answer**:
  - To find the factor, you divide 8.35 by 0.1:
    \[
    \text{Factor} = \frac{8.35}{0.1} = 83.5
    \]
  - Now, find the product of the factor (83.5) and 0.01:
    \[
    83.5 \times 0.01 = 0.835
    \]

### 22. Select all the multiplication problems that have a product of 4.86.
- **Question**: Choose from:
  - \( 48.6 \times 0.01 \)
  - \( 486 \times 0.01 \)
  - \( 4.86 \times 0.1 \)
  - \( 486 \times 0.1 \)

- **Answers**:
  - \( 48.6 \times 0.1 = 4.86 \)
  - \( 486 \times 0.01 = 4.86 \)
  - \( 4.86 \times 0.1 = 0.486 \) (incorrect)
  - \( 486 \times 0.1 = 48.6 \) (incorrect)

  Therefore, the correct answers are:
  - \( 48.6 \times 0.1 \)
  - \( 486 \times 0.01 \)

### 23. Which multiplication problem's product will have a decimal point two places to the left compared to the factor 35.1?
- **Options**:
  - A: \( 35.1 \times 0.01 \)
  - B: \( 35.1 \times 10 \)
  - C: \( 35.1 \times 0.1 \)
  - D: \( 35.1 \times 100 \)

- **Answer**: 
  - Multiplying \( 35.1 \) by **0.01** moves the decimal two places to the left, making it **0.351**.
  - Therefore, the correct answer is **A: \( 35.1 \times 0.01 \)**.

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Would you like more detailed explanations for any of these answers or help with additional questions? Here are some related questions:

1. How do you determine the number of decimal places in a product when multiplying decimals?
2. What happens when multiplying by powers of 10 (like 0.1, 0.01, 10, 100)?
3. Can you find a general pattern for multiplying any number by small decimals (like 0.001, 0.0001)?
4. What is the rule for moving decimal points when dividing by 0.1 or 0.01?
5. How would you approach multiplication problems with multiple decimals?

**Tip**: When multiplying by powers of 10, just focus on moving the decimal point left or right by the corresponding number of places—left for smaller values (e.g., 0.1, 0.01) and right for larger values (e.g., 10, 100).

Questions from a math worksheet involving multiplying by decimals and interpreting multiplication results.

Explore how to multiply decimals such as 0.1 and 0.01, and learn to determine the movement of decimal places. Practice problems for Grade 5-6 involving multiplication patterns and identifying correct solutions.

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