4-4 Scientific Notation

Transcription

1 Warm Up Problem of the Day Lesson Presentation

2 Warm Up Order each set of numbers from least to greatest , 10, 10, , 10 1, 10 0, , 8, 8, 8 8 2, 8 0, 8 2, , 2, 2, 2 2 6, 2 4, 2 1, , 5.2, 5.2, , 5.2 1, 5.2 2, 5.2 9

3 Problem of the Day Explain which problems you can or cannot solve. 1) 2 4 x 2 6 2) 43 x 812 3) n 9 x m 1 4) t 7 x t 13 Can solve 1 and 4 because the bases are the same Cannot solve 2 and 3 because the bases are not the same

4 Learn to express large and small numbers in scientific notation and to compare two numbers written in scientific notation.

5 Vocabulary scientific notation: is a shorthand way of writing large or small numbers by using a power of 10 has to be a number between 1 and 10 Example: 1.7 or 9.4

6 Examples of number written in standard notation, that are easier to work with if written in scientific notation. An ordinary quarter contains about 97,700,000,000,000,000,000,000 atoms. The average size of an atom is about centimeters across. The length of these numbers in standard notation makes them awkward to work with.

7 To express any number in scientific notation: In standard notation the number of atoms in a quarter is 97,700,000,000,000,000,000,000 In scientific notation the number of atoms in a quarter is

8 Hint when expressing any number in scientific notation: A positive exponent means move the decimal to the right A negative exponent means move the decimal to the left.

9 Translating Scientific Notation to Standard Notation Write the number in standard notation = 100, , ,000 Helpful Hint Think: Move the decimal right 5 places. A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left.

10 Translating Scientific Notation to Standard Notation Write the number in standard notation ,100 Think: Move the decimal right 4 places.

11 Translating Scientific Notation to Standard Notation Write the number in standard notation = 1000 Divide by the reciprocal. Think: Move the decimal left 3 places.

12 Write the number in standard notation ,870,000,000 Think: Move the decimal right 9 places.

13 Write the number in standard notation Think: Move the decimal left 5 places.

14 Write the number in standard notation ,000,000 Think: Move the decimal right 8 places.

15 Helpful Hint A number less than 1 will have a negative exponent when written in scientific notation.

16 Translating Standard Notation to Scientific Notation Write in scientific notation Think: The decimal needs to move 3 places to get a number between 1 and Set up scientific notation. Think: The decimal needs to move left to change 7.09 to , so the exponent will be negative. So written in scientific notation is Check = =

17 Write in scientific notation Think: The decimal needs to move 4 places to get a number between 1 and Set up scientific notation. Think: The decimal needs to move left to change 8.11 to , so the exponent will be negative. So written in scientific notation is Check = =

18 Life Science Application 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? 4.11 x x = > 1.5 Compare powers of 10. Compare the values between 1 and x 10-5 > 1.5 x 10-5 The first cell has a greater diameter.

19 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? 5 x x = < 5.11 Compare powers of 10. Compare the values between 1 and x 10-3 < 5.11 x 10-3 The second cell has a greater diameter.

20 Lesson Quiz: Part I Write each number in standard notation , Write each number in scientific notation ,000, Order the numbers from least to greatest. T , , , ,

21 Lesson Quiz: Part II 6. A human body contains about microliters of blood. Write this number in standard notation. 5,600,000

22 Textbook pgs. 177 # s 21, 23, 25, 27, 29, 37, 39, 40, 41, 43, 45, 46, 49, 57, 58