Scientific Notation

1. Scientific Notation • Scientific notation is used when working with, very large or very small numbers. • Easy for expressing the number and calculation • Numbers in scientific notation are made up of three parts: the coefficient, the base and the exponent.

2. Scientific Notation • Example: • 567 000 • The scientific number is 5.67 x 105 5.67 x 105 coefficient                base   exponent

3. Rules of Scientific Notation • 1≤ coefficient< 10 • base = 10 • Exponent must show the number of decimal places that the decimal needs to be moved to change back to the number of standard notation. • When change back to the number of standard notation: • If the exponent is positive, move the decimal to the right. • If the exponent is negative, move the decimal to the left.

4. Exercise of Scientific Notation- Positive Exponent • Change 5.09 x 107 to standard notation. • 107= 10 x 10 x 10 x 10 x 10 x 10 x 10 • 5.09 x 107 = 5.09 x 10,000,000= 5,090,000,000 • answer = 5,090,000,000

5. Exercise of Scientific Notation- Negative Exponent • Change 5.3 x 10-4 to standard notation. • The exponent tells us to move the decimal four places to the left. • 5.3 x 10-4 = 0.00053

6. Change Standard Notation to Scientific Notation • Change 43 920 000 000 to scientific notation • Remember, the decimal is at the end of the final zero. 43 920 000 000. • 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 4.392 • The decimal will move 10 places to the left, making the exponent equal to 10. • Answer equals 4.392 x 1010

7. Change Standard Notation to Scientific Notation • 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