# Scientific Notation

**Scientific Notation** is a way to express very small and very large numbers using exponents, and is useful for brevity and for comparing orders of magnitude between numbers.

To convert a number to scientific notation, it is rewritten to be greater than zero but less than ten multiplied by $10$ raised to some exponent.

Simple Examples:

- $99,000$ expressed in scientific notation is $9.9 \cdot 10^4$.
- $0.00099$ expressed in scientific notation is $9.9 \cdot 10^{-4}$

SI number prefixes are commonly used in lieu of scientific or engineering notation. For example, rather than writing "$1.23 \cdot 10^3g$" (grams), we can write "$1.23kg$" (kilograms).

## Common large numbers expressed in scientific notation

**Avogadro's number**is $6.02214076 \cdot 10^{23}$.- The charge of an Electron is $0.6021766208 \cdot 10^{-19}$ coulombs.
- A
**googol**is, a one followed by 100 zeros, is $1 \cdot 10^{100}$ - The
**speed of light**is $2.99792458 \cdot 10^8$ meters per second.

## Video: Introduction to scientific notation

## Deeper Knowledge on Scientific Notation

### Engineering Notation

Expressions of very large and very small numbers for engineers

## Broader Topics Related to Scientific Notation

### Science

The most rigorous system of epistemology

### International System of Units (SI)

Formal terms and definitions of the metric system

### Math

Fun with numbers