Multiply and Divide math worksheet with a caterpillar theme, showing number operations.

Problem Overview:

The task involves matching numbers on the left column to their corresponding results in the right column after multiplying or dividing by 10, 100, or 1000. The goal is to determine how each number was transformed and explain the calculation.

Solution Approach:

1. Understand the Transformation:
- Multiplying a number by 10, 100, or 1000 shifts the decimal point to the right by 1, 2, or 3 places, respectively.
- Dividing a number by 10, 100, or 1000 shifts the decimal point to the left by 1, 2, or 3 places, respectively.

2. Match Each Number:
- Compare the numbers on the left with those in the right column to identify the transformation.
- Use the provided example as a guide: \( 29 \div 100 = 0.29 \).

3. Explain Each Calculation:
- For each match, describe whether the number was multiplied or divided and by what factor (10, 100, or 1000).

---

Step-by-Step Solution:

#### 1. 29
- Matched with 0.29.
- Calculation: \( 29 \div 100 = 0.29 \).
- Explanation: Dividing by 100 moves the decimal point two places to the left.

#### 2. 9.3
- Matched with 9300.
- Calculation: \( 9.3 \times 1000 = 9300 \).
- Explanation: Multiplying by 1000 moves the decimal point three places to the right.

#### 3. 186
- Matched with 0.186.
- Calculation: \( 186 \div 1000 = 0.186 \).
- Explanation: Dividing by 1000 moves the decimal point three places to the left.

#### 4. 20.4
- Matched with 2040.
- Calculation: \( 20.4 \times 100 = 2040 \).
- Explanation: Multiplying by 100 moves the decimal point two places to the right.

#### 5. 734
- Matched with 7.34.
- Calculation: \( 734 \div 100 = 7.34 \).
- Explanation: Dividing by 100 moves the decimal point two places to the left.

#### 6. 63
- Matched with 63000.
- Calculation: \( 63 \times 1000 = 63000 \).
- Explanation: Multiplying by 1000 moves the decimal point three places to the right.

#### 7. 78.2
- Matched with 0.0782.
- Calculation: \( 78.2 \div 1000 = 0.0782 \).
- Explanation: Dividing by 1000 moves the decimal point three places to the left.

#### 8. 1.5
- Matched with 150.
- Calculation: \( 1.5 \times 100 = 150 \).
- Explanation: Multiplying by 100 moves the decimal point two places to the right.

---

Final Matches and Explanations:

| Left Column | Right Column | Calculation | Explanation |
|-------------|--------------|----------------------------------|--------------------------------------|
| 29 | 0.29 | \( 29 \div 100 = 0.29 \) | Divide by 100 (shift decimal left 2) |
| 9.3 | 9300 | \( 9.3 \times 1000 = 9300 \) | Multiply by 1000 (shift decimal right 3) |
| 186 | 0.186 | \( 186 \div 1000 = 0.186 \) | Divide by 1000 (shift decimal left 3) |
| 20.4 | 2040 | \( 20.4 \times 100 = 2040 \) | Multiply by 100 (shift decimal right 2) |
| 734 | 7.34 | \( 734 \div 100 = 7.34 \) | Divide by 100 (shift decimal left 2) |
| 63 | 63000 | \( 63 \times 1000 = 63000 \) | Multiply by 1000 (shift decimal right 3) |
| 78.2 | 0.0782 | \( 78.2 \div 1000 = 0.0782 \) | Divide by 1000 (shift decimal left 3) |
| 1.5 | 150 | \( 1.5 \times 100 = 150 \) | Multiply by 100 (shift decimal right 2) |

---

Final Answer:

\[
\boxed{
\begin{array}{lll}
29 & \rightarrow 0.29 & (29 \div 100) \\
9.3 & \rightarrow 9300 & (9.3 \times 1000) \\
186 & \rightarrow 0.186 & (186 \div 1000) \\
20.4 & \rightarrow 2040 & (20.4 \times 100) \\
734 & \rightarrow 7.34 & (734 \div 100) \\
63 & \rightarrow 63000 & (63 \times 1000) \\
78.2 & \rightarrow 0.0782 & (78.2 \div 1000) \\
1.5 & \rightarrow 150 & (1.5 \times 100)
\end{array}
}
\]