Metric SI Unit Conversions: Metric SI Area - Free Printable

It looks like you've uploaded an answer key for a worksheet titled *"Metric/SI Unit Conversion - Sheet 1"*, which focuses on converting between square meters (m²) and square centimeters (cm²) using cross-multiplication.

Let me walk through the problem-solving method and explain how each conversion works.

---

🔍 Understanding the Concept

We are converting area units:
- 1 meter (m) = 100 centimeters (cm)
- Therefore, 1 square meter (m²) = 100 cm × 100 cm = 10,000 cm²

So:
> ✔ 1 m² = 10,000 cm²

This is crucial for all conversions.

---

🧮 Method: Cross-Multiplication

The worksheet uses proportions to solve conversions. The general setup is:

$$
\frac{1 \text{ m}^2}{10,000 \text{ cm}^2} = \frac{x \text{ m}^2}{y \text{ cm}^2}
$$

Then cross-multiply to solve for the unknown.

---

✔ Let's Go Through Each Problem

#### 1. Convert 5 m² to cm²
$$
\frac{1 \text{ m}^2}{10,000 \text{ cm}^2} = \frac{5 \text{ m}^2}{x \text{ cm}^2}
$$
Cross-multiply:
$$
1 \cdot x = 5 \cdot 10,000 \Rightarrow x = 50,000 \text{ cm}^2
$$
✔ Answer: 50,000 cm²

---

#### 2. Convert 7 m² to cm²
$$
\frac{1}{10,000} = \frac{7}{x} \Rightarrow x = 7 \times 10,000 = 70,000
$$
✔ Answer: 70,000 cm²

---

#### 3. Convert 600 cm² to m²
Now we're going from smaller to larger unit.
$$
\frac{1 \text{ m}^2}{10,000 \text{ cm}^2} = \frac{x \text{ m}^2}{600 \text{ cm}^2}
$$
Cross-multiply:
$$
10,000x = 600 \Rightarrow x = \frac{600}{10,000} = 0.06
$$
✔ Answer: 0.06 m²

---

#### 4. Convert 8 m² to cm²
$$
x = 8 \times 10,000 = 80,000 \text{ cm}^2
$$
✔ Answer: 80,000 cm²

---

#### 5. Convert 900 cm² to m²
$$
x = \frac{900}{10,000} = 0.09 \text{ m}^2
$$
✔ Answer: 0.09 m²

---

#### 6. Convert 2 m² to cm²
$$
x = 2 \times 10,000 = 20,000 \text{ cm}^2
$$
✔ Answer: 20,000 cm²

---

#### 7. Convert 300 cm² to m²
$$
x = \frac{300}{10,000} = 0.03 \text{ m}^2
$$
✔ Answer: 0.03 m²

---

#### 8. Convert 1000 cm² to m²
$$
x = \frac{1000}{10,000} = 0.1 \text{ m}^2
$$
✔ Answer: 0.1 m²

---

#### 9. Convert 10 m² to cm²
$$
x = 10 \times 10,000 = 100,000 \text{ cm}^2
$$
✔ Answer: 100,000 cm²

---

#### 10. Convert 3000 cm² to m²
$$
x = \frac{3000}{10,000} = 0.3 \text{ m}^2
$$
✔ Answer: 0.3 m²

---

📌 Summary of Key Steps

1. Know the conversion factor:
$$
1 \text{ m}^2 = 10,000 \text{ cm}^2
$$

2. Use proportion and cross-multiply:
$$
\frac{1 \text{ m}^2}{10,000 \text{ cm}^2} = \frac{\text{given value}}{\text{unknown}}
$$

3. Convert large → small (m² → cm²): Multiply by 10,000
4. Convert small → large (cm² → m²): Divide by 10,000

---

💡 Tips for Students

- Always write down the conversion factor clearly.
- Use units in your equations to avoid confusion.
- Check if your answer makes sense:
- If converting m² to cm², expect a larger number.
- If converting cm² to m², expect a smaller number, possibly decimal.

---

✔ Final Answer Key Recap:

| Problem | Question | Answer |
|--------|---------|--------|
| 1 | 5 m² → ? cm² | 50,000 cm² |
| 2 | 7 m² → ? cm² | 70,000 cm² |
| 3 | 600 cm² → ? m² | 0.06 m² |
| 4 | 8 m² → ? cm² | 80,000 cm² |
| 5 | 900 cm² → ? m² | 0.09 m² |
| 6 | 2 m² → ? cm² | 20,000 cm² |
| 7 | 300 cm² → ? m² | 0.03 m² |
| 8 | 1000 cm² → ? m² | 0.1 m² |
| 9 | 10 m² → ? cm² | 100,000 cm² |
| 10 | 3000 cm² → ? m² | 0.3 m² |

All answers match the provided answer key.

---

Let me know if you'd like a printable version or want help creating similar problems!