Ch 8 Exponents E Scientific Notation Objective To

Ch 8: Exponents E) Scientific Notation Objective: To simplify expressions involving scientific notation.

Key concepts: 1. Write expressions in Standard Form 2. Write expressions in Scientific Notation 3. Multiply scientific notation expressions 4. Divide scientific notation expressions

Definitions Scientific Notation used to write very large or very small numbers expressed in the form: a number between 1. 0 and 9. 9 an integer Standard Form An expression written without exponents

Rules From Standard Form to Scientific Notation 1) Determine where the decimal should be placed 2) Count how many places from the “new” decimal point to the “old” decimal point To the RIGHT = (+) positive exponent To the LEFT = (−) negative exponent Example 1 3, 780, 000, 000 = 12 jumps to the right Example 2 0. 00000064 = 7 jumps to the left

Classwork 1) 46, 000 = 7 jumps to the right 2) 620, 000, 000 = 11 jumps to the right 3) 0. 000538 = 4 jumps left 4) 0. 000004 = 6 jumps left

Rules From Scientific Notation to Standard Form 1) Move the current decimal point the number of places based on the exponent as follows: (+) positive exponent = to the RIGHT (−) negative exponent = to the LEFT Example 1 Example 2 3. 60000 = 360, 00000008. 43 = 0. 000000843

Classwork 5) 2. 640000000 = 2, 640, 000 6) 0000003. 41 = 0. 00000341 7) 40000 = 8) 0000007 = 400, 000 0. 000007

Rules Multiplying Scientific Notation expressions 1) Multiply the numbers that have no exponents. 2) Add the exponents to calculate the new exponent for 10. 3) Verify that the result is in scientific notation a number between 1. 0 and 9. 9 an integer

Example 1 Example 2 (5. 63)(3. 4) 19. 142 (2. 1)(1. 5) 3. 15 108+6 smaller 1 jump right 107+8 +1 bigger Not in Scientific Notation

Classwork 9) 10) smaller 1 jump right +1 bigger 11) smaller 1 jump right +1 bigger 12) smaller 1 jump right +1 bigger

Rules Dividing Scientific Notation expressions 1) Divide the numbers that have no exponents. 2) Subtract the exponents to calculate the new exponent for 10. 3) Verify that the result is in scientific notation a number between 1. 0 and 9. 9 an integer

Example 1 = = Example 2 = = bigger = 1 jump left − 1 smaller

Classwork 13) 14) = − 1 = bigger 1 jump left smaller =