🔑 Key Concepts
- When multiplying numbers in scientific notation, multiply the coefficients.
- Use the product rule for exponents: when multiplying powers with the same base, add the exponents.
- The answer must be normalized so the coefficient is at least 1 and less than 10.
- If the coefficient is 10 or greater, move the decimal left and increase the exponent.
- An exponent of 1 may be written as \(10^1\), but it is also common to write the factor as \(10\).
✏️ Worked Examples
🧠 Math Vocabulary
- Scientific Notation: a number written as a coefficient multiplied by a power of 10.
- Coefficient: the number in front of the power of 10. In scientific notation, it must be at least 1 and less than 10.
- Power of 10: an expression such as \(10^4\), \(10^1\), or \(10^{-3}\).
- Product Rule: when multiplying powers with the same base, add the exponents.
- Normalize: to adjust an answer so the coefficient is between 1 and 10.
- Exponent: the raised number that tells how many times a base is used as a factor.
💡 Main Idea
To multiply numbers in scientific notation, multiply the coefficients and add the exponents on the powers of 10. After using the product rule, check whether the coefficient needs to be normalized so the final answer is in proper scientific notation.
📚 What You Should Already Know
Students should already know how to write numbers in scientific notation, multiply decimals, add integers, and use powers of 10 with positive and negative exponents.
🚀 What Comes Next
This lesson prepares students to divide numbers in scientific notation, solve scientific notation word problems, compare very large and very small numbers, and apply exponent rules in more advanced expressions.
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