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.

  1. Any number can be represented as two numbers multiplied together.
    1. 66 = 6 x 11
    2. 225 = 15 x 15
    3. 4 = 2 x 2
    4. 0.08 = 4 x .02
  2. Always making one of those numbers a multiple of the number 10, simplifies doing arithmetic.
    1. 220 = 22 x 10
    2. 66 = 6.6 x 10
    3. 4 = 4 x 1
    4. 0.8 = 8 x .1
  3. Multiples of 10 (or any number) can be described using exponents (the little number is the exponent).
    1. 10 = 101
    2. 100 = 102 = 10 x 10
    3. 0.1 = 10-1 = 1/10
    4. 0.01 = 10-2 = 1/10 x 1/10

Rules for writing a number in scientific notation

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

Examples

  1. 66 = 6.6 x 10
  2. 225 = 2.25 x 102
  3. 4 = 4 x 10-1
  4. .08 = 8 x 10-2
  5. 602,214,000,000,000,000,000,000 = 6.02214 x 1023Avogadro's number

Hints and Help:

  1. Remember that you haven't changed the value of the number, we have just changed how we describe it!
  2. If you started with a large number, you should end up with a large number!
  3. 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.
  4. If you have to move the decimal to the right, the exponent is negative.
  5. If you have to move the decimal to the left, the exponent is positive.