Dividing In Scientific Notation

🔑 Key Concepts

• When dividing numbers in scientific notation, divide the coefficients.
• Use the quotient rule for exponents: when dividing powers with the same base, subtract the exponents.
• The answer must be normalized so the coefficient is at least 1 and less than 10.
• If the coefficient is less than 1, move the decimal right and decrease the exponent.
• If the coefficient is 10 or greater, move the decimal left and increase the exponent.

✏️ 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 \(10^4\), \(10^0\), or \(10^{-3}\).
• Quotient Rule: when dividing powers with the same base, subtract the exponents.
• Normalize: to adjust an answer so the coefficient is between 1 and 10.
• Negative Exponent: an exponent that represents a value less than 1 when using powers of 10.

💡 Main Idea

To divide numbers in scientific notation, divide the coefficients and subtract the exponents on the powers of 10. After applying the exponent rules, always check whether the coefficient needs to be normalized so the final answer is written correctly in scientific notation.

📚 What You Should Already Know

Students should already know how to write numbers in scientific notation, divide decimals, subtract integers, and apply basic exponent rules with powers of 10.

🚀 What Comes Next

This lesson prepares students to multiply and divide numbers in scientific notation in real-world contexts, compare very large and very small values, and solve scientific notation word problems.

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