# Scientific Notation

We will be working with rather small and large numbers in our science class. For example, Avogadro's number is 602,214,000,000,000,000,000,000 and a human hair is .0002 meters in diameter. Scientific notation uses three ideas to make working with large or small numbers easier.

- Any number can be represented as two numbers multiplied together.
- 66 = 6 x 11
- 225 = 15 x 15
- 4 = 2 x 2
- 0.08 = 4 x .02

- Always making one of those numbers a multiple of the number 10, simplifies doing arithmetic.
- 220 = 22 x 10
- 66 = 6.6 x 10
- 4 = 4 x 1
- 0.8 = 8 x .1

- Multiples of 10 (or any number) can be described using exponents (the little number is the exponent).
- 10 = 10
^{1} - 100 = 10
^{2}= 10 x 10 - 0.1 = 10
^{-1}= 1/10 - 0.01 = 10
^{-2}= 1/10 x 1/10

- 10 = 10

# Rules for writing a number in scientific notation

- The first number is
**always**between 1 and 9.9999... - Multiply the first number by 10 raised to an exponent.

# Examples

- 66 = 6.6 x 10
- 225 = 2.25 x 10
^{2} - 4 = 4 x 10
^{-1} - .08 = 8 x 10
^{-2} - 602,214,000,000,000,000,000,000 = 6.02214 x 10
^{23}Avogadro's number

# Hints and Help:

- Remember that you haven't changed the
**value**of the number, we have just changed how we**describe**it! - If you
**started**with a large number, you should**end**up with a large number! - When converting, count how many times you have to move the decimal place to get a number between 1 and 10. This will be the exponent on 10.
- If you have to move the decimal to the
**right**, the exponent is**negative**. - If you have to move the decimal to the
**left**, the exponent is**positive**.