Overview
This lesson introduces scientific notation, explaining how to convert large and small numbers between standard and scientific notation formats.
Introduction to Scientific Notation
- Scientific notation is a way to represent very large or very small numbers concisely.
- The format is: a number between 1 and 10 multiplied by 10 raised to an exponent (n × 10^x).
Converting Large Numbers to Scientific Notation
- Move the decimal to create a number between 1 and 10; count decimal places moved for the exponent.
- If you move the decimal left, the exponent is positive and indicates a large number.
- Examples:
- 45,000 → 4.5 × 10^4
- 3,750 → 3.75 × 10^3
- 580,000 → 5.8 × 10^5
- 72,000,000 → 7.2 × 10^7
- 9,300,000,000 → 9.3 × 10^9
Converting Small Numbers to Scientific Notation
- Move the decimal to create a number between 1 and 10; count decimal places moved for the exponent.
- If you move the decimal right, the exponent is negative and indicates a small number.
- Examples:
- 0.0023 → 2.3 × 10^-3
- 0.00076 → 7.6 × 10^-4
- 0.049 → 4.9 × 10^-2
- 0.00000541 → 5.41 × 10^-6
- 0.000000000835 → 8.35 × 10^-10
Converting Scientific Notation to Standard Notation
- With a positive exponent, move the decimal right to make a large number.
- With a negative exponent, move the decimal left to make a small number.
- Examples:
- 2.4 × 10^2 = 240
- 3.56 × 10^3 = 3,560
- 4.27 × 10^5 = 427,000
- 3.96 × 10^7 = 39,600,000
- 3.7 × 10^-3 = 0.0037
- 4.16 × 10^-5 = 0.0000416
Mixed Review & Practice
- Negative exponents create small numbers (move decimal left); positive exponents create large numbers (move decimal right).
- Practice examples:
- 7.35 × 10^-3 = 0.00735
- 3.64 × 10^5 = 364,000
- 1.5 × 10^-2 = 0.015
- 2.8 × 10^3 = 2,800
Key Terms & Definitions
- Scientific Notation — A way to express numbers as a product of a number between 1 and 10 and a power of 10.
- Exponent — Shows how many places to move the decimal point; positive for large numbers, negative for small numbers.
- Standard Notation — The usual way to write numbers without exponents.
Action Items / Next Steps
- Practice converting numbers between scientific and standard notation.
- Review examples and try additional practice problems to reinforce the concepts.