3-4 Scientific Notation Warm Up Problem of the Day Lesson Presentation Lesson Quizzes 3-4 Scientific Notation Warm Up Multiply. 1. 724 102 2. 837 10 72,400 8,370 3. 632.9 100 63,290 3-4 Scientific Notation 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 the water rises the height of 2 steps every 2 hours, at what step would the water level be at 5:00 P.M.? Explain. the third, because the boat will rise with the water 3-4 Scientific Notation Learn to write large numbers in scientific notation. 3-4 Scientific Notation Vocabulary scientific notation 3-4 Scientific Notation Additional Example 1A: Multiplying by Powers of Ten Find each product. 5,892 1,000 5,892.000 There are 3 zeros in 1,000. To multiply, move the decimal 3 places right. = 5,892,000 Write 3 placeholder zeros. 3-4 Scientific Notation Additional Example 1B: Multiplying by Powers of Ten Find each product. 47.75 10,000 47.7500 There are 4 zeros in 10,000. To multiply, move the decimal 4 places right. = 477,500 Write 4 placeholder zeros. 3-4 Scientific Notation Check It Out: Example 1A Find each product. 901 1,000 901.000 There are 3 zeros in 1,000. To multiply, move the decimal 3 places right. = 901,000 Write 3 placeholder zeros. 3-4 Scientific Notation Check It Out: Example 1B Find each product. 15.425 10,000 15.4250 There are 4 zeros in 10,000. To multiply, move the decimal 4 places right. = 154,250 Write 4 placeholder zeros. 3-4 Scientific Notation Scientific notation is a shorthand method that can be used to write large numbers. A number written in scientific notation has two numbers that are multiplied. 4.123 105 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. 3-4 Scientific Notation Additional Example 2: Writing Numbers in Standard Notation Write 6,000,000 in scientific notation. 6,000,000 6,000,000 Move the decimal point 6 places left. The power of 10 is 6. 6,000,000 = 6 106 3-4 Scientific Notation Check It Out: Example 2 Write 4,325,000 in scientific notation. 4,325,000 Move the decimal point 6 places left. The power of 10 is 6. 4,325,000 = 4.325 106 3-4 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. 3-4 Scientific Notation Additional Example 3: Writing Numbers in Standard From Write 6.2174 103 in standard form. 6.2174 103 6.2174 The power of 10 is 3. Move the decimal point 3 places right. 6.2174 103 = 6,217.4 3-4 Scientific Notation Check It Out: Example 3 Write 3.21975 103 in standard form. 3.21975 103 3.21975 The power of 10 is 3. Move the decimal point 3 places right. 3.21975 103 = 3,219.75 3-4 Scientific Notation Additional Example 4 Write the distance to the sun, 93,000,000 miles, in scientific notation. Move the decimal point left to 93,000,000 form a number that is greater than or equal to 1 and less than 10. Multiply that number by a power 93,000,000 of ten. 9.3 107 The power of 10 is 7, because the decimal point is moved 7 places left. The distance to the sun is 9.3 107. 3-4 Scientific Notation Check It Out: Example 4 Write the distance 132,500 in scientific notation. Move the decimal point left to 132,500 form a number that is greater than or equal to 1 and less than 10. Multiply that number by a power of ten. 132,500 1.325 105 The power of 10 is 5, because the decimal point is moved 5 places left. The distance is 1.325 105. 3-4 Scientific Notation Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 3-4 Scientific Notation Lesson Quiz Write each number in scientific notation. 1. 6,300 6.3 103 2. 70,400,000 7.04 107 Write each number in standard form. 3. 7.241 104 72,410 4. 8.2137 107 82,137,000 5. A Wall Street report indicated that a fast-moving stock had sold 3,295,000 shares. Write this number in scientific notation. 3.295 106 3-4 Scientific Notation Lesson Quiz for Student Response Systems 1. Which of the following represents 9,400 in scientific notation? A. 9.4 102 B. 9.4 103 C. 94 102 D. 94 103 3-4 Scientific Notation Lesson Quiz for Student Response Systems 2. Which of the following represents 5,328,000 in scientific notation? A. 5328 103 B. 532.8 103 C. 53.28 105 D. 5.328 106 3-4 Scientific Notation Lesson Quiz for Student Response Systems 3. Which of the following represents 1.1132 105 in scientific notation? A. 11,132,000 B. 1,113,200 C. 111,320 D. 11,132 3-4 Scientific Notation Lesson Quiz for Student Response Systems 4. Which of the following represents 7.9132 106 in scientific notation? A. 79,132 B. 791,320 C. 7,913,200 D. 79,132,000 3-4 Scientific Notation Lesson Quiz for Student Response Systems 5. Jupiter is at a distance of 778,600,000 km from the sun. Identify this number in scientific notation. A. 7.786 108 B. 7.786 107 C. 7.786 106 D. 7.786 105