1. 3-5 Scientific Notation Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

2. Warm Up Multiply. 1. 724  10 2 2. 837  10 3. 632.9  100 4. 18,256  10 5. 10  10  10 72,400 8,370 63,290 Course 1 3-5 Scientific Notation 182,560 1,000

3. Problem of the Day A rope ladder is hanging from the back of a yacht. At 10:00 A.M., the water reaches the third step on the ladder. If every 2 hours the water rises the height of two steps, at what step would the water level be at 5:00 P.M.? Explain. the third, because the boat will rise with the water Course 1 3-5 Scientific Notation

4. Learn to write large numbers in scientific notation. Course 1 3-5 Scientific Notation

5. Vocabulary scientific notation Insert Lesson Title Here Course 1 3-5 Scientific Notation

6. Course 1 3-5 Scientific Notation Scientific notation is a shorthand method for writing large numbers like 3,456,000.

7. Course 1 3-5 Scientific Notation To write the number 3,456,000 in scientific notation, do the following: 3,456,000 Move the decimal point left to form a number that is greater than 1 and less than 10. 3,456,000 Multiply that number by a power of ten. 3.456  10 6 The power of 10 is 6, because the decimal point is moved 6 places left.

8. Course 1 3-5 Scientific Notation The number of zeros in the power of ten, or the exponents in the power of ten, tells you how many places to move the decimal point Remember!

9. Course 1 3-5 Scientific Notation A number written in scientific notation has two parts that are multiplied. 3.456  10 6 The first part is a number that is greater than 1 and less than 10. The second part is a power of 10.

10. Course 1 3-5 Scientific Notation Additional Example 1A & 1B: Writing Numbers in Scientific Notation Write each number in scientific notation. A. 6,000,000 B. 411,000 6,000,000 Move the decimal point 6 places left. The power of 10 is 6. 6,000,000 = 6  10 6 411,000 Move the decimal point 5 places left. The power of 10 is 5. 411,000 = 4.11  10 5

11. Course 1 3-5 Scientific Notation Additional Example 1C: Writing Numbers in Scientific Notation Write the number in scientific notation. C. 79,000,000 79,000,000 Move the decimal point 7 places left. The power of 10 is 7. 79,000,000 = 7.9  10 7

12. Course 1 3-5 Scientific Notation Try This: Example 1A & 1B Write each number in scientific notation. A. 8,000,000 B. 587,000 8,000,000 Move the decimal point 6 places left. The power of 10 is 6. 8,000,000 = 8  10 6 587,000 Move the decimal point 5 places left. The power of 10 is 5. 587,000 = 5.87  10 5

13. Course 1 3-5 Scientific Notation Try This: Example 1C Write the number in scientific notation. C. 13,000,000 13,000,000 Move the decimal point 7 places left. The power of 10 is 7. 13,000,000 = 1.3  10 7

14. Course 1 3-5 Scientific Notation You can write a large number written in scientific notation in standard form. Look at the power of 10 and move the decimal point that number of places to the right.

15. Course 1 3-5 Scientific Notation Additional Example 2A & 2B: Writing Numbers in Standard From Write each number in standard form. A. 6.2174  10 3 B. 9.5  10 8 The power of 10 is 3. 6.2174  10 3 = 6,217.4 6.2174 The power of 10 is 8. 9.50000000 Move the decimal point 3 places right. Move the decimal point 8 places right. Use zeros as placeholders. 9.5  10 8 = 950,000,000

16. Course 1 3-5 Scientific Notation Additional Example 2C: Writing Numbers in Standard From Write the number in standard form. C. 4.83  10 5 The power of 10 is 5. 4.83  10 5 = 483,000 4.83000 Move the decimal point 5 places right. Use zeros as placeholders.

17. Course 1 3-5 Scientific Notation Try This: Example 2A & 2B Write each number in standard form. A. 8.1974  10 3 B. 2.3  10 6 The power of 10 is 3. 8.1974  10 3 = 8,197.4 8.1974 The power of 10 is 6. 2.300000 Move the decimal point 3 places right. Move the decimal point 6 places right. Use zeros as placeholders. 2.3  10 6 = 2,300,000

18. Course 1 3-5 Scientific Notation Try This: Example 2C Write the number in standard form. C. 9.77  10 5 The power of 10 is 5. 9.77  10 5 = 977,000 9.77000 Move the decimal point 5 places right. Use zeros as placeholders.

19. Lesson Quiz Write each number in scientific notation. 1. 6,300 2. 70,400,000 Write each number in standard form. 3. 7.241  10 4 4. 8.2137  10 7 5. A Wall Street report indicated that a fast-moving stock had sold 3,295,000 shares. Write this number in scientific notation. Insert Lesson Title Here 72,410 82,137,000 Course 1 3-5 Scientific Notation 6.3  10 3 7.04  10 7 3.295  10 6