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 multiplicationof10fourtimes
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.