Scientific Notation Multiplication

🔑 Key Concepts

• When multiplying numbers in scientific notation, multiply the coefficients first.
• Use the product rule for powers of 10: \( 10^a \cdot 10^b = 10^{a+b} \).
• If the coefficient is 10 or greater, rewrite it so the coefficient is at least 1 but less than 10.
• Scientific notation answers should be written in the form \( a \times 10^n \), where \( 1 \le a < 10 \).
• Standard form shows the full value without scientific notation.

✏️ Worked Examples

🧠 Math Vocabulary

• Scientific notation: A way to write very large or very small numbers using a coefficient and a power of 10.
• Standard form: The regular decimal notation of a number without powers of 10.
• Coefficient: The decimal factor in scientific notation, such as \( 3.762 \) in \( 3.762 \times 10^3 \).
• Power of 10: A number written as \( 10^n \), where the exponent tells how many places the decimal point moves.
• Product rule: When multiplying powers with the same base, add the exponents.
• Quotient rule: When dividing powers with the same base, subtract the exponents.
• Normalization: Rewriting a scientific notation answer so the coefficient is at least 1 but less than 10.

💡 Main Idea

To multiply numbers in scientific notation, multiply the coefficients and then add the exponents on the powers of 10. If the coefficient is not between 1 and 10, normalize the answer before writing it in scientific notation.

📚 What You Should Already Know

Students should already know how to multiply decimals, use exponents, apply the product rule, and move between powers of 10 and standard form.

🚀 What Comes Next

After multiplying in scientific notation, students can extend the same exponent rules to division, real-world measurement problems, speed of light problems, and mixed operations with scientific notation.

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