## 1.3 Outline

- Exponential notation (see below)
- base
- exponent
- power or exponential
- extended order of operations

- Scientific notation (see below)
- Calculators
- arithmetic logic
- algebraic logic
- RPN logic
- floating-point form

- Estimation
- Laws of exponents (see below)
- addition law
- multiplication law
- subtractive law
- distributive law

- Comprehending large numbers
- million
- billion
- trillion

## 1.3 Essential Ideas

**Exponents and Laws of Logarithms **Exponents play a central role in mathematical notation. Especially pay attention to the definition notation: For any number

*b*and any counting number

*n:*

Closely related to exponential notation, there are five laws of exponents:

Let *a* and *b* be any nonzero real numbers, and let *m* and *n* be any integers. Then,

**Scientific Notation**

The scientific notation for a nonzero number is that number written as a power of 10 times another number *x*, such that *x* is between 1 and 10, including 1.