Lesson 46 — Multiplying and Dividing Scientific Notation

🎯 Goal

Apply multiplication and division rules with numbers in scientific notation.

📖 Lesson Description

• Multiplication: Multiply coefficients, add exponents: \( (a \times 10^m) \cdot (b \times 10^n) = (a \cdot b) \times 10^{m+n} \)
• Division: Divide coefficients, subtract exponents: \( \frac{a \times 10^m}{b \times 10^n} = \frac{a}{b} \times 10^{m-n} \)
• Adjust result to proper scientific notation if needed (coefficient between 1–10)

🔎 Examples

• \( (3 \times 10^4) \cdot (2 \times 10^3) = 6 \times 10^7 \)
• \( \frac{6 \times 10^5}{2 \times 10^2} = 3 \times 10^3 \)

✏️ Practice

1. \( (4 \times 10^6) \cdot (5 \times 10^2) \)
2. \( \frac{8 \times 10^9}{4 \times 10^3} \)
3. \( (7 \times 10^3) \cdot (3 \times 10^4) \)