Lesson 75: Multiplying 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

When multiplying numbers written in scientific notation, the process follows exponent rules. Multiply the coefficients (the numbers in front), add the exponents of 10, and then adjust the result so it is written in proper scientific notation form.

Learning Objectives

• Multiply coefficients correctly.
• Add exponents using exponent rules.
• Rewrite answers in proper scientific notation form.

Topics Covered

• Multiplying powers of ten
• Adding exponents
• Adjusting results to standard scientific notation form

Key Terms

• Coefficient: The number in front of the power of 10 in scientific notation.
• Power of Ten: A number written as 10 raised to an exponent.
• Exponent Rule (Product Rule): When multiplying powers with the same base, add the exponents.

Lesson Examples

Example 1: Basic Multiplication

1. Multiply (2 × 10³)(3 × 10⁴).
2. Multiply coefficients: 2 × 3 = 6.
3. Add exponents: 10³ × 10⁴ = 10⁷. Final answer: 6 × 10⁷.

Example 2: Adjusting the Result

1. Multiply (4 × 10²)(5 × 10³).
2. Multiply coefficients: 4 × 5 = 20.
3. Add exponents: 10² × 10³ = 10⁵. Since 20 is not between 1 and 10, rewrite as 2 × 10⁶.

Practice Problems

1. (3 × 10⁴)(2 × 10²)
2. (6 × 10⁻³)(5 × 10⁶)
3. (9 × 10¹)(8 × 10²)
4. (1.5 × 10³)(4 × 10⁻²)

Tips & Common Mistakes

• Always multiply coefficients first.
• Do not multiply exponents — add them.
• Rewrite the answer if the coefficient is not between 1 and 10.

Summary

To multiply numbers in scientific notation, multiply the coefficients and add the exponents. Afterward, ensure the final answer is written in proper scientific notation form with a coefficient between 1 and 10.

Challenge Problems

1. (7 × 10⁵)(8 × 10⁴)
2. (2.5 × 10⁻²)(4 × 10⁻³)
3. (9.8 × 10⁶)(3 × 10²)