Overview
This lecture introduces scientific notation, explains why it's used for very large and small numbers, demonstrates how to convert between standard and scientific notation, and provides example problems.
What is Scientific Notation?
- Scientific notation is a compact way to write very large or very small numbers.
- It is useful in science to reduce errors and save time when dealing with many zeros.
Why Use Scientific Notation?
- Writing out all zeros in extremely large or small numbers is time-consuming and error-prone.
- Scientific notation makes calculations and reading numbers easier and less confusing.
How to Write Numbers in Scientific Notation
- Place the decimal so only one nonzero digit is to the left of it.
- Count how many places the decimal moves to reach this new position.
- Write the number as (digit) . (other digits) × 10^(number of places moved).
- Moving the decimal left gives a positive exponent; moving right gives a negative exponent.
Converting Examples to Scientific Notation
- Example: 2,530,000,000,000,0 → 2.53 × 10^13 (decimal moved 13 places left).
- Example: 0.0000000203 → 2.03 × 10^-8 (decimal moved 8 places right).
- For each movement left, exponent increases; for each movement right, exponent decreases.
How to Convert Back to Standard Notation
- To convert from scientific to decimal, move the decimal right for positive exponents, left for negative exponents.
- Fill in zeros as needed for each place you move the decimal.
- Example: 4.13 × 10^3 → 4,130
- Example: 8.2 × 10^-3 → 0.0082
Key Terms & Definitions
- Scientific notation — expressing a number as a product of a number (1–10) and a power of ten.
- Exponent — the small raised number in 10^n, showing how many times to multiply or divide by 10.
- Decimal notation — the "usual" way of writing numbers, without exponents.
Action Items / Next Steps
- Watch the video on "really understanding scientific notation" for deeper comprehension.
- Practice converting numbers to and from scientific notation with additional problems.