Understanding Mathematical Powers and Scientific Notation
This comprehensive page introduces fundamental concepts of mathematical powers, scientific notation, and metric prefixes. The content focuses on how to work with exponents and understand their relationship to scientific measurements.
Definition: A power (aⁿ) represents repeated multiplication of a number (a) by itself n times, where a is the base and n is the exponent.
Example: 10⁴ = 10 × 10 × 10 × 10 (multiplication of 10 four times)
Highlight: For any non-zero number a, a⁰ = 1 is a fundamental rule of exponents.
Vocabulary: Scientific notation expresses numbers as a product of a number between 1 and 10 multiplied by a power of 10.
The page includes a comprehensive table of metric prefixes and their corresponding powers of 10:
- Tera (10¹²)
- Giga (10⁹)
- Mega (10⁶)
- Kilo (10³)
- Hecto (10²)
- Deca (10¹)
- Deci (10⁻¹)
- Centi (10⁻²)
- Milli (10⁻³)
- Micro (10⁻⁶)
- Nano (10⁻⁹)
- Pico (10⁻¹²)
Example: When converting between metric prefixes, move the decimal point according to the difference in powers of 10. For instance, to convert from kilometers to meters, multiply by 10³.