1. Scientific Notation Scientific notation is simply a method for expressing, and working with, very large or very small numbers. Short hand method 5.2 x 10 8

2. Scientific Notation This is the scientific notation for the standard number, 567 000. Now look at the number again, with the three parts labeled. 5.67 x 10 5 coefficient base exponent

3. Scientific Notation In order for a number to be in correct scientific notation, the following conditions must be true: 1. The coefficient must be greater than or equal to 1 and less than 10. 2. The base must be 10. 3. The exponent must show the number of decimal places that the decimal needs to be moved to change the number to scientific notation. A negative exponent means that the decimal is moved to the right when changing from standard notation to scientific notation.

4. Scientific Notation Ex.1 Change 56 760 000 000 to scientific notation Remember, the decimal is at the end of the final zero. The decimal must be moved behind the five to ensure that the coefficient is less than 10, but greater than or equal to one. The coefficient will then read 5.676 The decimal will move 10 places to the left, making the exponent equal to 10. Answer equals 5.676 x 10 10

5. Scientific Notation Ex.2 Change 0.000000902 to scientific notation The decimal must be moved behind the 9 to ensure a proper coefficient. The coefficient will be 9.02 The decimal moves seven spaces to the right, making the exponent -7 Answer equals 9.02 x 10 -7

6. Practice Change the following numbers to scientific notation 1. 345 678 000 2..000 000 567 3. 342 4..000 749

7. Practice Change the following numbers back to standard numbers 1. 8.5 x 10 6 2. 3.9 x 10 -7 3. 6.75 x 10 9 4. 3.34 x 10 -4