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

Key concepts: Write expressions in Standard Form Write expressions in Scientific Notation Multiply scientific notation expressions Divide scientific notation expressions

Definitions Scientific Notation used to write very large or very small numbers expressed in the form: an integer a number between 1.0 and 9.9 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 3,780,000,000,000 = Example 1 12 jumps to the right Example 2 0.00000064 = 7 jumps to the left

Classwork 1) 46,000,000 = 7 jumps to the right 2) 620,000,000,000 = 11 jumps to the right 3) 0.000538 = 4 jumps left 4) 0.000004 = 6 jumps left

Rules From Scientific Notation to Standard Form 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 3.6 = 360,000 Example 1 8.43 Example 2 = 0.000000843

Classwork 5) 2.64 = 2,640,000,000 3.41 = 0.00000341 6) 7) 4 = 400,000,000 8) 7 = 0.000007

Rules Multiply the numbers that have no exponents. Multiplying Scientific Notation expressions 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 an integer a number between 1.0 and 9.9

Example 1 Example 2 (5.63)(3.4) 19.142 107+8 (2.1)(1.5) +1 bigger 3.15 108+6 smaller 1 jump right Not in Scientific Notation

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

Rules Divide the numbers that have no exponents. Dividing Scientific Notation expressions 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 an integer a number between 1.0 and 9.9

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

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