Lesson 70: Powers of 10

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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

Powers of 10 are expressions like 10², 10³, and 10⁻⁴ that use exponents to represent repeated multiplication or division by 10. Understanding how these powers affect place value is essential for working with large and small numbers and forms the foundation of scientific notation.

Learning Objectives

• Evaluate positive and negative powers of 10.
• Explain how powers of 10 shift decimal places.
• Connect powers of 10 to place value and scientific notation.

Topics Covered

• Positive exponents of 10
• Negative exponents of 10
• Decimal movement and place value patterns

Key Terms

• Exponent: A number that tells how many times a base is multiplied by itself.
• Power of 10: An expression of the form 10ⁿ, where n is an integer.
• Negative Exponent: Indicates repeated division by the base.

Lesson Examples

Example 1: Positive Exponents

1. 10¹ = 10
2. 10² = 10 × 10 = 100
3. 10³ = 10 × 10 × 10 = 1,000 (decimal moves 3 places right)

Example 2: Negative Exponents

1. 10⁻¹ = 1 ÷ 10 = 0.1
2. 10⁻² = 1 ÷ 100 = 0.01
3. 10⁻³ = 1 ÷ 1,000 = 0.001 (decimal moves 3 places left)

Practice Problems

1. Evaluate 10⁴.
2. Evaluate 10⁻³.
3. Write 0.0001 as a power of 10.
4. How many decimal places does 10⁵ move the decimal?

Tips & Common Mistakes

• Positive exponents move the decimal to the right.
• Negative exponents move the decimal to the left.
• Do not confuse 10⁻² with −100. It equals 0.01.

Summary

Powers of 10 create predictable patterns in place value. Positive exponents produce large numbers by multiplying by 10 repeatedly. Negative exponents produce small decimals by dividing by 10 repeatedly. Mastering these patterns prepares you for scientific notation.

Challenge Problems

1. Write 1,000,000 as a power of 10.
2. Write 0.0000001 as a power of 10.
3. Explain why 10⁰ = 1.