Overview
This lecture introduces powers of 10, explains patterns in their expanded values, and teaches exponential form, expanded form, and standard form.
Understanding Powers of 10
- A power of 10 is the result of multiplying 10 by itself a certain number of times.
- Example: 10 × 10 = 100; 10 × 10 × 10 = 1,000.
Recognizing Patterns
- Each time you add another 10, you add another zero to the standard form result.
- The number of tens multiplied equals the number of zeros in the answer (e.g., four tens = 10,000 with four zeros).
- This pattern continues as more tens are multiplied together.
Different Forms of Powers of 10
- Expanded Form: Writing out each 10 being multiplied (e.g., 10 × 10 × 10 × 10 × 10).
- Standard Form: Writing the value as a number (e.g., 100,000).
- Exponential Form: Writing as a base and exponent (e.g., 10⁵).
Exponents and Terminology
- In exponential form, the larger number (10) is the base, and the small raised number is the exponent.
- The exponent tells how many times the base (10) is multiplied by itself.
- 10² means 10 × 10 = 100, not 10 × 2.
- 10¹ = 10, 10² = 100, 10³ = 1,000, etc.
Key Terms & Definitions
- Power of 10 — A number made by multiplying 10 by itself one or more times.
- Exponent — Small raised number indicating how many times the base is used as a factor.
- Base — The main number (here, 10) in exponential form.
- Expanded Form — Showing all factors being multiplied.
- Standard Form — Writing the numerical value without exponents.
- Exponential Form — Using a base and exponent notation (e.g., 10⁴).
Action Items / Next Steps
- Watch the linked mastery check video to practice finding powers of 10 on your own.