1. Course 3 4-4 Scientific Notation Multiplication in Scientific Notation The number 123,000,000,000 in scientific notation is: 1.23 x 10 11 Rules for Multiplying in SN: 1.) Multiply the coefficients (decimal parts). 2.) Multiply the powers of 10. Keep the base of 10 & add the exponents. coefficient base (always 10 with exponent in SN)

2. Course 3 4-4 Scientific Notation Multiplication in Scientific Notation Example 1: (3.0 x 10 4 )(2.0 x 10 5 ) 3.0 x 2.0 = 6.0 10 4 x 10 5 = 10 9 So... 6.0 x 10 9

3. Course 3 4-4 Scientific Notation Multiplication in Scientific Notation * On Notes Sheet * Example 2: What happens if the coefficient is more than 10? (6.1 x 10 2 )(2.2 x 10 5 ) 6.1 x 2.2 = 13.42 10 2 x 10 5 = 10 7 So... 13.42 x 10 7 Remember: When the product is not written correctly in SN, you must move the decimal until the coefficient is between 1 and 10.

4. Course 3 4-4 Scientific Notation Multiplication in Scientific Notation Example 2 (cont.): What happens if the coefficient is more than 10? (6.1 x 10 2 )(2.2 x 10 5 ) So... 13.42 x 10 7 Becomes... 1.342 x 10 8 Remember: When the product is not written correctly in SN, you must move the decimal until the coefficient is between 1 and 10. **When decimal part gets smaller, exponent gets larger.

5. Course 3 4-4 Scientific Notation Multiplication in Scientific Notation Example 3: (2.2 x 10 4 )(7.1 x 10 5 ) 2.2 x 7.1 = 15.62 10 4 x 10 5 = 10 9 So... 1.562 x 10 10 Remember: When the product is not written correctly in SN, you must move the decimal until the coefficient is between 1 and 10. **When decimal part gets smaller, exponent gets larger.

6. Course 3 4-4 Scientific Notation Division in Scientific Notation The number 123,000,000,000 in scientific notation is: 1.23 x 10 11 Rules for Dividing in SN: 1.) Divide the coefficients (decimal parts). 2.) Divide the powers of 10. Keep the base of 10 & subtract the exponents. coefficient base (always 10 with exponent in SN)

7. Course 3 4-4 Scientific Notation Division in Scientific Notation * On Notes Sheet * Example 1: (8.2 x 10 3 ) ÷ (2.1 x 10 7 ) 8.2 ÷ 2.1 = 3.905 10 3 ÷ 10 7 = 10 -4 So... 3.905 x 10 -4

8. Course 3 4-4 Scientific Notation Division in Scientific Notation Example 2: What happens if the coefficient is not between 1 and 10? (1.8 x 10 7 ) ÷ (6.0 x 10 3 ) 1.8 ÷ 6 = 0.3 10 7 ÷ 10 3 = 10 4 So... 0.3 x 10 4 Remember: When the product is not written correctly in SN, you must move the decimal until the coefficient is between 1 and 10.

9. Course 3 4-4 Scientific Notation Division in Scientific Notation Example 2 (cont.): What happens if the coefficient is not between 1 and 10? (1.8 x 10 7 ) ÷ (6.0 x 10 3 ) So... 0.3 x 10 4 Becomes... 3.0 x 10 3 Remember: When the product is not written correctly in SN, you must move the decimal until the coefficient is between 1 and 10. **When decimal part gets bigger, exponent gets smaller.

10. Course 3 4-4 Scientific Notation Division in Scientific Notation Example 3: (4.2 x 10 2 ) ÷ (7.0 x 10 5 ) 4.2 ÷ 7.0 = 0.6 10 2 ÷ 10 5 = 10 -3 So... 0.6 x 10 -3 becomes... 6.0 x 10 -4 Remember: When the product is not written correctly in SN, you must move the decimal until the coefficient is between 1 and 10. **When decimal part gets bigger, exponent gets smaller.

11. Course 3 4-4 Scientific Notation A pencil is 18.7 cm long. If you were to lay 10,000 pencils end-to-end, how many millimeters long would they be? Write the answer in scientific notation. 187 mm  10,000 1 centimeter = 10 millimeters 18.7 centimeters = 187 millimeters Multiply by 10 to change from cm to mm. 1,870,000 mm Additional Example 3: Application Find the total length. Multiply.

12. Course 3 4-4 Scientific Notation Think: The decimal needs to move 6 places. In scientific notation the 10,000 pencils would be 1.87  10 6 mm long, laid end-to-end. Additional Example 3 Continued 1.87  10 Set up scientific notation. Think: The decimal needs to move right to change 1.87 to 1,870,000, so the exponent will be positive.

13. Course 3 4-4 Scientific Notation A certain cell has a diameter of approximately 4.11 x 10 -5 meters. A second cell has a diameter of 1.5 x 10 -5 meters. Which cell has a greater diameter? 10 -5 = 10 -5 4.11 x 10 -5 1.5 x 10 -5 Compare powers of 10. Additional Example 4: Life Science Application Compare the values between 1 and 10. The first cell has a greater diameter. 4.11 > 1.5 4.11 x 10 -5 > 1.5 x 10 -5

14. Course 3 4-4 Scientific Notation A certain cell has a diameter of approximately 5 x 10 -3 meters. A second cell has a diameter of 5.11 x 10 -3 meters. Which cell has a greater diameter? 10 -3 = 10 -3 5 x 10 -3 5.11 x 10 -3 Compare powers of 10. Check It Out: Example 4 Compare the values between 1 and 10. The second cell has a greater diameter. 5 < 5.11 5 x 10 -3 < 5.11 x 10 -3