Guide to Multiplying & Dividing Scientific Notation: Rules and Examples

📚 Quick Study Guide

🔢 Scientific Notation: A way to express very large or very small numbers as a number between 1 and 10 multiplied by a power of 10 (e.g., $a \times 10^b$). ➗ Multiplying Scientific Notation: Multiply the numbers ($a$ values) and add the exponents ($b$ values). $(a \times 10^b) \times (c \times 10^d) = (a \times c) \times 10^{(b+d)}$. ➗ Dividing Scientific Notation: Divide the numbers ($a$ values) and subtract the exponents ($b$ values). $(a \times 10^b) / (c \times 10^d) = (a / c) \times 10^{(b-d)}$. 💡 Adjusting the Result: Ensure the number is in proper scientific notation (i.e., the number $a$ is between 1 and 10). If it's not, adjust the exponent accordingly.

🧪 Practice Quiz

1. What is the result of $(2 \times 10^3) \times (3 \times 10^4)$?
• A) $5 \times 10^7$
• B) $6 \times 10^7$
• C) $5 \times 10^12$
• D) $6 \times 10^12$
2. What is the result of $(8 \times 10^6) / (2 \times 10^2)$?
• A) $4 \times 10^4$
• B) $4 \times 10^3$
• C) $1.6 \times 10^4$
• D) $1.6 \times 10^3$
3. Simplify: $(5 \times 10^{-2}) \times (4 \times 10^5)$
• A) $9 \times 10^3$
• B) $20 \times 10^3$
• C) $2 \times 10^4$
• D) $2 \times 10^3$
4. What is the result of $(9 \times 10^9) / (3 \times 10^{-3})$?
• A) $3 \times 10^6$
• B) $3 \times 10^{12}$
• C) $2.7 \times 10^{12}$
• D) $2.7 \times 10^6$
5. Evaluate: $(1.2 \times 10^{-5}) \times (5 \times 10^{-3})$
• A) $6 \times 10^{-8}$
• B) $6 \times 10^{-2}$
• C) $6 \times 10^{-15}$
• D) $6 \times 10^{-9}$
6. What is $(4.8 \times 10^7) / (1.6 \times 10^{-1})$?
• A) $3 \times 10^6$
• B) $3 \times 10^8$
• C) $3 \times 10^9$
• D) $3 \times 10^7$
7. Calculate: $(7 \times 10^{-4}) \times (8 \times 10^{-6})$
• A) $5.6 \times 10^{-24}$
• B) $56 \times 10^{-10}$
• C) $5.6 \times 10^{-9}$
• D) $5.6 \times 10^{-10}$