1. 4-4 Scientific Notation Warm Up Order each set of numbers from least to greatest. 1. 10, 10, 10, 10 2. 8, 8, 8, 8 3. 2, 2, 2, 2 4. 5.2, 5.2, 5.2, 5.2 04 –1 –2 10, 10, 10, 10 40 –1–2 302 8, 8, 8, 8 320 –2 13 –4 –6 –2 29 –1 5.2, 5.2, 5.2, 5.2 92 –1–2 2, 2, 2, 2 31 –4–6

2. 4-4 Scientific Notation Learn to express large and small numbers in scientific notation and to compare two numbers written in scientific notation.

3. 4-4 Scientific Notation Numbers written in scientific notation are written as two factors. One factor is a number greater than or equal to 1 and less than 10. The other factor is a power of 10.

4. 4-4 Scientific Notation 135,000 Think: Move the decimal right 5 places. 1.35  10 5 1.35  10 5 10 = 100,000 5 Example 1A: Translating Scientific Notation to Standard Notation Write the number in standard notation. A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left. Helpful Hint

5. 4-4 Scientific Notation 0.0027 Think: Move the decimal left 3 places. 2.7  10 –3 Write the number in standard notation. Example 1B: Translating Scientific Notation to Standard Notation Continued

6. 4-4 Scientific Notation 2.01  10 4 20,100 Think: Move the decimal right 4 places. 2.01  10 4 Example 1C: Translating Scientific Notation to Standard Notation Continued Write the number in standard notation.

7. 4-4 Scientific Notation 2,870,000,000 Think: Move the decimal right 9 places. 2.87  10 9 2.87  10 9 Write the number in standard notation. Example 2A

8. 4-4 Scientific Notation 0.000019 Think: Move the decimal left 5 places. 1.9  10 –5 1.9  10 –5 Write the number in standard notation. Example 2B

9. 4-4 Scientific Notation 5.09  10 8 Write the number in standard notation. Example 2C 509,000,000 Think: Move the decimal right 8 places.

10. 4-4 Scientific Notation

11. 4-4 Scientific Notation To write scientific notation for numbers greater than or equal to 1 and less than 10, use a 0 exponent. 5.63 = 5.63 x 10°. Writing Math

12. 4-4 Scientific Notation Example 3: Translating Standard Notation to Scientific Notation Think: The decimal needs to move left to change 7.09 to 0.00709, so the exponent will be negative. 0.00709 Think: The decimal needs to move 3 places to get a number between 1 and 10. 7.09 7.09  10 Set up scientific notation. Check 7.09  10 –3 = 7.09  0.001 = 0.00709 Write 0.00709 in scientific notation. So 0.00709 written in scientific notation is 7.09  10 –3.

13. 4-4 Scientific Notation Example 4 Think: The decimal needs to move left to change 8.11 to 0.000811, so the exponent will be negative. 0.000811 Think: The decimal needs to move 4 places to get a number between 1 and 10. 8.11 8.11  10 Set up scientific notation. Check 8.11  10 = 8.11  0.0001 = 0.000811 –4 Write 0.000811 in scientific notation. So 0.000811 written in scientific notation is 8.11  10 –4.

14. 4-4 Scientific Notation Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

15. 4-4 Scientific Notation Lesson Quiz: Part I Write each number in standard notation. 1. 1.72  10 4 2. 6.9  10 –3 4. 57,000,000 17,200 0.0069 3. 0.0053 5.3  10 –3 5.7  10 7 Write each number in scientific notation. 5. Order the numbers from least to greatest. T 2  10 –4, 9  10 –5, 7  10 –5 7  10 –5, 9  10 –5, 2  10 –4

16. 4-4 Scientific Notation Lesson Quiz: Part II 6. A human body contains about 5.6  10 6 microliters of blood. Write this number in standard notation. 5,600,000

17. 4-4 Scientific Notation 1. Write the number in standard notation. 3.2  10 3 A. 32 B. 320 C. 3200 D. 32000 Lesson Quiz for Student Response Systems

18. 4-4 Scientific Notation 2. Write the number in standard notation. 0.9  10 –3 A. 0.9 B. 0.09 C. 0.009 D. 0.0009 Lesson Quiz for Student Response Systems

19. 4-4 Scientific Notation 3. Write the number in scientific notation. 0.0978 A. 0.978  10 –1 B. 9.78  10 –1 C. 9.78  10 –2 D. 9.78  10 –3 Lesson Quiz for Student Response Systems

20. 4-4 Scientific Notation 4. Write the number in scientific notation. 13,432 A. 1.3432  10 4 B. 13.432  10 –4 C. 1.3432  10 –4 D. 13.432  10 4 Lesson Quiz for Student Response Systems