1. Scientific Notation Section 7-2

2. Goals Goal To write numbers in scientific notation and standard form. To compare and order numbers using scientific notation. Rubric Level 1 – Know the goals. Level 2 – Fully understand the goals. Level 3 – Use the goals to solve simple problems. Level 4 – Use the goals to solve more advanced problems. Level 5 – Adapts and applies the goals to different and more complex problems.

3. Vocabulary Scientific Notation

4. The table shows relationships between several powers of 10. Each time you divide by 10, the exponent in the power decreases by 1 and the decimal point in the value moves one place to the left. Each time you multiply by 10, the exponent in the power increases by 1 and the decimal point in the value moves one place to the right. Powers of 10

5. You can find the product of a number and a power of 10 by moving the decimal point of the number. –If the exponent is positive, move the decimal point to the right. –If the exponent is negative, move the decimal point to the left. You may need to write zeros to the right or left of the number in order to move the decimal point.

6. A. 14  10 4 Multiply. 14.0 0 0 0 Since the exponent is a positive 4, move the decimal point 4 places to the right. 140,000 B. 3.6  10  5 0 0 0 0 3.6 Since the exponent is a negative 5, move the decimal point 5 places to the left. 0.000036 Example: Multiplying by Powers of 10

7. A. 2.5  10 5 Multiply. 2.5 0 0 0 0 Since the exponent is a positive 5, move the decimal point 5 places to the right. 250,000 B. 10.2  10  3 0 10.2 Since the exponent is a negative 3, move the decimal point 3 places to the left. 0.0102 Your Turn:

8. Definition Scientific Notation - is a way to express numbers that are very large or very small. –Powers of 10 are used when writing numbers in scientific notation. –Numbers written in scientific notation are expressed as 2 factors. One factor is a number greater than or equal to 1. The other factor is a power of 10. –Example: 1.43 ⨯ 10 12 5.8 ⨯ 10 -9

9. The first part is a number that is greater than or equal to 1 and less than 10. The second part is a power of 10. Scientific Notation

10. Why Use Scientific Notation? For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form. Numbers expressed in scientific notation can be used in a computation with far greater ease.

11. Example: Recognizing Scientific Notation Is the number written in scientific notation? Explain. 1.53 ⨯ 10 4 2.3.42 ⨯ 10 -7 3.0.35 ⨯ 10 2 4.9.6 ⨯ 100 No, 53 is not less than 10 Yes No, 0.35 is not greater than or equal to 1 No, 100 is not in power of 10 form

12. Your Turn: Is the number written in scientific notation? Explain. 1.8.15 ⨯ 10 -6 2.12.9 ⨯ 10 8 3.1.003 ⨯ 10 7 4.0.0045 ⨯ 10 -32 Yes No, 12.9 is greater than 10 Yes No, 0.0045 is not greater than or equal to 1

13. Procedure: Writing Numbers in Scientific Notation 1.Place the decimal point so that there is one non- zero digit to the left of the decimal point. 2.Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. 3.If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

14. Think: The number is less than 1, so the exponent will be negative. A. 0.00709 Think: The decimal needs to move 3 places to get a number between 1 and 10. 7.09  10  3 Write the number in scientific notation. So 0.00709 written in scientific notation is 7.09  10 –3. Example: Writing Numbers in Scientific Notation

15. Think: The number is greater than 1, so the exponent will be positive. B. 23,000,000,000 Think: The decimal needs to move 10 places to get a number between 1 and 10. 2.3  10 10 Write the number in scientific notation. So 23,000,000,000 written in scientific notation is 2.3  10 10. Example: Writing Numbers in Scientific Notation

16. Think: The number is less than 1, so the exponent will be negative. A. 0.000811 Think: The decimal needs to move 4 places to get a number between 1 and 10. 8.11  10 4 4 Write the number in scientific notation. So 0.000811 written in scientific notation is 8.11  10 –4. Your Turn:

17. Think: The number is greater than 1, so the exponent will be positive. B. 480,000,000 Think: The decimal needs to move 8 places to get a number between 1 and 10. 4.8  10 8 Write the number in scientific notation. So 480,000,000 written in scientific notation is 4.8  10 8. Your Turn:

18. Standard form refers to the usual way that numbers are written—not in scientific notation. Reading Math

19. Procedure: Writing Numbers in Standard Form 1.Simply move the decimal point to the right for positive exponent 10. 2.Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.)

20. 1.35000 135,000 Think: Move the decimal right 5 places. A. 1.35  10 5 1.35  10 5 Write the number in standard form. Example: Writing a Number in Standard Form

21. 0002.7 Think: Move the decimal left 3 places. 2.7  10 –3 B. 2.7  10 –3 Write the number in standard form. 0.0027 Example: Writing a Number in Standard Form

22. 2.870000000 Think: Move the decimal right 9 places. A. 2.87  10 9 2.87  10 9 Write the number in standard form. 2,870,000,000 Your Turn:

23. 000001.9 Think: Move the decimal left 5 places. 1.9  10 –5 B. 1.9  10 –5 Write the number in standard form. 0.000019 Your Turn:

24. A certain cell has a diameter of approximately 4.11  10 -5 meters. A second cell has a diameter of 1.5  10 -5 meters. Which cell has a greater diameter? 4.11  10 -5 1.5  10 -5 Compare the exponents. Compare the values between 1 and 10. The first cell has a greater diameter. 4.11 > 1.5 Notice that 4.11  10 -5 > 1.5  10 -5. Example: Comparing Numbers in Scientific Notation

25. A star has a diameter of approximately 5.11  10 3 kilometers. A second star has a diameter of 5  10 4 kilometers. Which star has a greater diameter? 5.11  10 3 5  10 4 Compare the exponents. The second star has a greater diameter. Notice that 3 < 4. So 5.11  10 3 < 5  10 4 Your Turn:

26. Order the list of numbers from least to greatest. Step 1 List the numbers in order by powers of 10. Step 2 Order the numbers that have the same power of 10 Example: Ordering Numbers in Scientific Notation

27. Order the list of numbers from least to greatest. Step 1 List the numbers in order by powers of 10. Step 2 Order the numbers that have the same power of 10 2  10 -12, 4  10 -3, 5.2  10 -3, 3  10 14, 4.5  10 14, 4.5  10 30 Your Turn:

28. Joke Time Did you hear about the red ship and the blue ship that collided? Both crews were marooned! What did one shark say to the other while eating a clownfish? This tastes funny! What did the cobbler say when a cat wandered into his shop? Shoe!

29. Assignment 7-2 Exercises Pg. 450 - 452: #12 – 48 even