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Mastering Scientific Notation in Math: Warm-Up, Problems, Quizzes, Lessons

Explore scientific notation through warm-up exercises, daily problems, textbook examples, group quizzes, and interactive lessons. Enhance your math skills in real-world scenarios using quick daily journal entries for maximum learning.

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Mastering Scientific Notation in Math: Warm-Up, Problems, Quizzes, Lessons

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  1. WarmUp Problem of the Day Lesson Presentation Lesson Quizzes

  2. Math Journal (5 Min) • 3-2-1 - Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write 3 statements that they already know about the lesson being presented, 2 questions that they have before the lesson is presented, and 1 connection that they feel can be made between what they already know and what they think they will be taught in the new lesson before they have been taught the lesson, and at the end of class, write 3 statements that they now know about the lesson being presented, answer the 2 questions that they had written previously, and 1 connection that they now know can be made between what they knew before the lesson and what they now know after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 statement or connection that pertained to the lesson.

  3. Homework Review (5 Min)

  4. Warm Up Write each number in scientific notation. 1.3x104 1. 13000 2.091x106 2. 2,091,000 1.08009x10-3 3. 0.001080090

  5. Problem of the Day The population of the Earth reached 6,690,000,000 in 2008. How can you represent this population in scientific notation? 6.69x109

  6. Textbook Examples (I Do) (5 Min)

  7. LearnOperate with scientific notation in real- world situations.

  8. Masses of objects in space are so great that astronomers often need to use scientific notation to describe them. The approximate masses of planets in the solar system are given in the table.

  9. Helpful Hint You can use the properties of exponents to multiply and divide numbers expressed in scientific notation.

  10. Additional Example 1: Division With Scientific Notation Pluto was demoted from planet to dwarf planet in 2006, in part because of its small size. The mass of Pluto is about 1.3  1022 kg. About how many times smaller is Pluto’s mass than Earth’s mass? Write a unit ratio, or divide, to find how many times. 5.97 1024 1.3 1022 Write the ratio of Earth’s mass to Pluto’s mass. Divide the coefficients and divide the powers. Subtract exponents. 5.971024 1.3 1022 Write the result in scientific notation. 4.6 102 About 4.6 102, or about 460, times smaller.

  11. Check It Out: Example 1 About how many times greater is the mass of Saturn than the mass of Earth? Write your answer in scientific notation. Write a unit ratio, or divide, to find how many times. 5.69 1026 5.97 1024 Write the ratio of Saturn’s mass to Earth’s mass. Divide the coefficients and divide the powers. Subtract exponents. 5.691026 5.97 1024 0.9531 102 9.531 101 Write the result in scientific notation. Saturn’s mass is about 9.531 101 times the mass of Earth.

  12. Additional Example 2: Multiplication with Scientific Notation The mass of Venus is about 66 times the mass of the moon. What is the mass of the moon? Write your answer in scientific notation. 4.87 1024 kg mass of moon 66 Solve for the mass of the moon.. 4.87 1024 kg 66 mass of moon 0.0738 1024 kg 7.4 1022 kg The mass of the moon is about 7.4 102 2 kg.

  13. Check It Out: Example 2 The average mass of a grain of sand on a beach is about 1.5  10–5 g. There are about 6.1  1012 grains of sand in a beach volleyball court. What is the mass of the grains of sand in the beach volleyball court? Mass of grains of sands in court =(1.5 x 10-5 g)(6.1 x 1012 ) = 9.15 x 107 g

  14. Remember! A number written in scientific notation has one factor greater than or equal to 1 and less than 10 and the other factor a power of 10.

  15. Additional Example 3: Addition and Subtraction with Scientific Notation The water in Mono Lake, CA, was used for residents of LA. As a result, the lake’s volume, in acre-feet, dropped from 4.3  107 to 2.1  107 from 1941 to 1982. After becoming protected, the lake increased in volume by 5.0  106 acre-feet in the next 20 years. What was its volume in 2002? 2.1 x 107 21 106 +5.0 x 106+5.0 106 26.1106 2.6 107 Rewrite so that the powers are the same; then add. Write the result in scientific notation. The volume was about 2.6  107 acre-feet.

  16. Check It Out: Example 3 How much greater is the mass of Neptune than the mass of Earth? Write your answer in scientific notation. Write your answer in scientific notation. 1.02 1026 kg 102 1024 kg -5.97 1024 kg 96.03 1024 kg 9.603 1025 kg -5.97 1024 kg Neptune’s is about 9.603 1025 kg greater in mass than Earth.

  17. Class work Problems (We Do) (10 Min) • Pg. 107-108 (1-3)

  18. Small Group CW(Yall Do) (10 Min) • Pg. 107-108 (4-28 EOE)

  19. Homework (You Do) (10 Min) • Pg. 107-108 (5, 7, 19, 21, 23 odd)

  20. Math Journal (5 Min) • 3-2-1 - Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write 3 statements that they already know about the lesson being presented, 2 questions that they have before the lesson is presented, and 1 connection that they feel can be made between what they already know and what they think they will be taught in the new lesson before they have been taught the lesson, and at the end of class, write 3 statements that they now know about the lesson being presented, answer the 2 questions that they had written previously, and 1 connection that they now know can be made between what they knew before the lesson and what they now know after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 statement or connection that pertained to the lesson.

  21. Lesson Quizzes Standard LessonQuiz Lesson Quiz forStudent Response Systems

  22. Write your answer in scientific notation. 1. The GDP of China in 2009 was about $8.7 x 1012. The GDP of Togo in 2009 was about $5.5 x 109. How many times greater was China’s GDP than Togo’s GDP in 2009? 1.58 x 103 times greater 2. A web site averages 4.5 x 104 hits per day. How many hits will it get in 3.6 x 102 days? 1.62 x 107 hits

  23. 3. Two companies merged to form a new company. One company was worth $3.5 x 107. The other was worth $7.8 x 108. What is the combined value of the new company? $8.15 x 108

  24. 1. Perform the indicated operation. Write your answer in scientific notation. (8.3 x 1022) (4.3 x 1018) A. 1.93 B. 0.193  104 C. 1.93 104 D. 1.93 1040 2. Perform the indicated operation. Write your answer in scientific notation. (8.3 x 1022) (4.3 x 1018) A. 1.26  104 B. 3.569  1040 C. 3.569 104 D. 3.569 1041 Lesson Quiz for Student Response Systems

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