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e x p l o r at i o n Georgia Performance Standards 4D Scientific Notation M8N1.j 1. Complete the table of values for the powers of ten. Exponent Power –6 10–6 –5 10–5 –4 10–4 –3 10–3 –2 0.01 10–2 2 10 10 –1 1 1 10 1 1 10–1 1 1 0.1 0 10 0 100 1 1 101 10 2 102 10 10 100 3 103 4 104 5 105 6 106 Think and Discuss 2. Discuss the pattern you see in the table of values for powers of ten. 3. Explain how you know that 109 0.000000001. Copyright © by Holt, Rinehart and Winston. All rights reserved. 110 Holt Mathematics Name Date LAB Technology Lab 4D Scientific Notation Class Some numbers are so big that even calculators use scientific notation to display them. A scientific calculator displays numbers in standard form up to a certain number of digits. Beyond that limit, the calculator displays numbers in scientific notation. A scientific calculator makes it easy to multiply numbers in scientific notation. Activity 1 Using a scientific or graphing calculator, you can determine the distance a ray of light travels in one day. The calculator will display the answer in scientific notation when it exceeds the display limit. Light travels at a constant speed of 186,000 miles per second. To find out how far a ray of light travels in 1 minute, multiply 186,000 by 60 (1 minute 60 seconds) to get 11,160,000. To find out how far the light travels in an hour, multiply 11,160,000 by 60 (1 hour 60 minutes) to get 669,600,000 miles. Next, multiply 669,600,000 by 24 (24 hours 1 day). The calculator automatically converts the final answer to scientific notation. This number can be used for further calculations. Copyright © by Holt, Rinehart and Winston. All rights reserved. 111 Holt Mathematics Name Date LAB Technology Lab 4D Scientific Notation, continued Class Activity 2 A scientific calculator allows you to easily multiply numbers written in scientific notation. Take the final answer from the previous activity (1.60704E10) and multiply that number by 8.96 103. Enter the first number in scientific notation with the following EE keystrokes: 1.60704 2nd , 10. Then press the multiplication button. EE Enter the second number with the following keystrokes: 8.96 Then press “Enter” to obtain the product. 2nd , 3. Think and Discuss 1. Which of the following products is displayed in scientific notation on your calculator? 9,217,400,938 • 385,474,609 771,247,792 • 7.6312345 Were both of them displayed in scientific notation? Why or why not? Try This Perform each operation using a scientific calculator. 1. (4.7 • 109) • (3.33 • 106) 2. (9.92415 • 103) • (8.3 • 107) 3. (4.3 • 102) (6.3 • 108) Copyright © by Holt, Rinehart and Winston. All rights reserved. 112 Holt Mathematics Name LESSON 4D Date Class Review for Mastery Scientific Notation Standard Notation Scientific Notation ( 430,000 0.0000057 )( ) 1st factor is between 1 and 10. 2nd factor is an integer power of 10. 4.3 108 5.7 106 positive integer for large number negative integer for small number To convert from scientific notation, look at the power of 10 to tell how many places and which way to move the decimal point. Complete to write each in standard notation. 1. 4.12 106 2. 3.4 105 Is the exponent positive or negative? Move the decimal point right or left? How many places? Write the number in standard notation. Write each number in standard notation. 3. 8 105 4. 7.1 104 5. 3.14 108 To convert to scientific notation, determine the factor between 1 and 10. Then determine the power of 10 by counting from the decimal point in the first factor to the decimal point in the given number. Complete to write each in scientific notation. 6. 32,000,000 7. 0.0000000712 What is the first factor? From its location in the first factor, which way must the decimal move to its location in the given number? How many places? Write the number in scientific notation. Write each number in scientific notation. 8. 41,000,000 Copyright © by Holt, Rinehart and Winston. All rights reserved. 9. 0.0000000643 113 10. 1,370,000,000 Holt Mathematics Name LESSON 4D Date Class Homework and Practice Scientific Notation Write each number in standard notation. 1. 6.12 102 2. 7.9 103 3. 4.87 104 4. 9.3 102 5. 8.06 103 6. 5.7 104 7. 3.17 105 8. 9.00613 102 9. 9.85 105 10. 6.004 107 11. 8.23 104 12. 1.48 106 Write each number in scientific notation. 13. 108,000,000 14. 0.5943 15. 42 16. 0.0000673 17. 0.0056 18. 6004 19. 0.00852 20. 24,631,500 21. 89450 22. 0.005702 23. 8,005,000,000 24. 0.00012805 25. The mass of the Earth is 5,980,000,000,000,000,000,000,000 kilograms. Write this number in scientific notation. 26. The mass of a dust particle is 7.53 1010. Write this number in standard notation. Copyright © by Holt, Rinehart and Winston. All rights reserved. 114 Holt Mathematics