Notes 6 – 4 Day 2 Scientific Notation Date ________ Algebra 1 Objective: At the end of this lesson, students will be able to multiply and divide numbers in scientific notation. change a number in scientific notation to decimal notation. In 6 – 4 Day 1, we learned how to change a decimal number into scientific notation. Today we are going to go the other direction – change a number in scientific notation to decimal notation. Remember: A BIG number (like 700,000,000,000,000) will have a POSITIVE exponent. A SMALL number (like 0.0000000000007) will have a NEGATIVE exponent. Since 3.4 x 104 has a positive exponent, it will be a BIG number. To change it to decimal notation, we would have to move the decimal to the ___________________ How many places do we move the decimal? ____________________ Since 1.8 x 10-2 has a negative exponent, it will be a SMALL number. To change it to decimal notation, we would have to move the decimal to the ___________________ How many places do we move the decimal? ____________________ Example 1 – Express each number in decimal notation. a. 2.0 x 10-3 b. 6.05 x 10 c. 4.6656 x 10-2 d. 3.3 x 103 Now we are going to put EVERYTHING together – multiplying monomials, dividing monomials and scientific notation. Let’s use problems we already know how to do to help us with something that looks new! Example 2 – Simplify. a. (5a2)(4a3) c. 9b 6 3b 2 b. (5 x 102)(4 x 103) d. 9 x 10 6 3 x 10 2 For Example 3, we’re just combining Examples 1 & 2!! Example 3 – Evaluate. Express each result in decimal notation. 1.17 x 10 7 a. 5 x 10 2 c. 1.68 x 10 4 8.4 x 10 4 b. (8.3 x 102)(9.1 x 10-7) d. (3.8 x 10-6)(1.9 x 106) Example 4 – Express each result from Example 3 in scientific notation. a. b. c. d.