Lesson 74: Dividing Numbers in Scientific Notation

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• Lesson Description
• Learning Objectives
• Topics Covered
• Key Terms
• Lesson Examples
• Practice Problems
• Tips & Common Mistakes
• Summary
• Challenge Problems
• Unit Navigation

Lesson Description

Dividing numbers written in scientific notation follows the quotient rule of exponents. Divide the coefficients, subtract the exponents of 10, and then rewrite the answer so it is in proper scientific notation form.

Learning Objectives

• Divide coefficients accurately.
• Subtract exponents using exponent rules.
• Express answers in proper scientific notation.

Topics Covered

• Dividing powers of ten
• Subtracting exponents (Quotient Rule)
• Adjusting the coefficient to proper form

Key Terms

• Quotient Rule: When dividing powers with the same base, subtract the exponents.
• Coefficient: The number multiplied by the power of 10.
• Scientific Notation: A number written as a value between 1 and 10 multiplied by a power of 10.

Lesson Examples

Example 1: Basic Division

1. Divide (6 × 10⁷) ÷ (3 × 10²).
2. Divide coefficients: 6 ÷ 3 = 2.
3. Subtract exponents: 10⁷ ÷ 10² = 10⁵. Final answer: 2 × 10⁵.

Example 2: Adjusting the Result

1. Divide (8 × 10³) ÷ (4 × 10⁵).
2. Divide coefficients: 8 ÷ 4 = 2.
3. Subtract exponents: 10³ ÷ 10⁵ = 10⁻². Final answer: 2 × 10⁻².

Practice Problems

1. (9 × 10⁶) ÷ (3 × 10²)
2. (5 × 10⁴) ÷ (2 × 10¹)
3. (7 × 10⁻³) ÷ (7 × 10²)
4. (4.5 × 10⁵) ÷ (9 × 10³)

Tips & Common Mistakes

• Always divide coefficients first.
• Subtract exponents — do not divide them.
• Ensure the final coefficient is between 1 and 10.

Summary

To divide numbers in scientific notation, divide the coefficients and subtract the exponents. Afterward, confirm that the result is written in proper scientific notation form with a coefficient between 1 and 10.

Challenge Problems

1. (1.2 × 10⁸) ÷ (3 × 10³)
2. (6.4 × 10⁻²) ÷ (8 × 10⁻⁵)
3. (9 × 10⁷) ÷ (1.5 × 10²)