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2-2 Powers of Ten and Scientific Notation Warm Up Problem of the Day Lesson Presentation Course 2 2-2 Powers of Ten and Scientific Notation Warm Up Find each value. 1. 92 81 2. 122 144 3. 152 225 4. 102 100 5. 103 1,000 6. 104 10,000 Course 2 2-2 Powers of Ten and Scientific Notation Problem of the Day Each day, Lowell runs one more lap than he did the day before. After seven days he has run 77 laps. How many laps did he run on the first day? 8 Course 2 2-2 Powers of Ten and Scientific Notation Learn to express large numbers in scientific notation. Course 2 of Ten and Scientific 2-2 Powers Insert Lesson Title Here Notation Vocabulary standard form scientific notation Course 2 2-2 Powers of Ten and Scientific Notation The distance from Venus to the Sun is over 100,000,000 kilometers. You can write this number as a power of ten by using a base of ten and an exponent. 10 · 10 · 10 · 10 · 10 · 10 · 10 · 10 = 108 Power of ten Course 2 2-2 Powers of Ten and Scientific Notation The table shows several powers of ten. Power of 10 Course 2 Meaning Value 101 10 10 102 10 · 10 100 103 10 · 10 · 10 1,000 104 10 · 10 · 10 · 10 10,000 2-2 Powers of Ten and Scientific Notation Additional Example 1: Multiplying by Powers of Ten Multiply 14 · 103. 14 · 103 = 14 · (10 · 10 · 10) = 14 · 1,000 = 14,000 Course 2 Use 10 as a factor 3 times. Multiply. Powers Lesson of Ten and Scientific 2-2 Insert Title Here Notation Try This: Example 1 Multiply 12 · 102. 12 · 102 = 12 · (10 · 10) = 12 · 100 = 1,200 Course 2 Use 10 as a factor 2 times. Multiply. 2-2 Powers of Ten and Scientific Notation You can also find the product of a number and a power of ten simply by moving the decimal point of the number. For powers of ten with positive exponents, move the decimal point to the right. Course 2 2-2 Powers of Ten and Scientific Notation Additional Example 2: Multiplying by Powers of Ten Mentally Find each product. A. 212 · 104 4 places 212 · 104 = 212.0000 = 2,120,000 B. 31.6 · 103 31.6 · 103 = 31.600 = 31,600 Course 2 Move the decimal point 4 places. (You will need to add 4 zeros.) 3 places Move the decimal point 3 places. (You will need to add 2 zeros.) Powers Lesson of Ten and Scientific 2-2 Insert Title Here Notation Try This: Example 2 Find each product. A. 22.5 · 102 2 places 22.5 · 102 = 22.50 = 2,250 B. 39.5 · 103 39.5 · 103 = 39.500 = 39,500 Course 2 Move the decimal point 2 places. (You will need to add 1 zero.) 3 places Move the decimal point 3 places. (You will need to add 2 zeros.) 2-2 Powers of Ten and Scientific Notation Numbers are usually written in standard form. For example, 17,900,000 is in standard form. Scientific notation is a kind of shorthand that can be used to write large numbers. Numbers expressed in scientific notation are written as the product of two factors. In scientific notation, 17,900,000 is written as A number greater than or equal to 1 but less than 10 Course 2 A power of 10 2-2 Powers of Ten and Scientific Notation Writing Math In scientific notation, it is customary to use a multiplication cross () instead of a dot. Course 2 2-2 Powers of Ten and Scientific Notation Additional Example 3A: Writing Numbers in Scientific Notation Write the number in scientific notation. A. 4,340,000 6 places Move the decimal point to 4,340,000 = 4,340,000 get a number that is greater than or equal to 1 and less than 10. The exponent is equal to = 4.34 106 the number of places the decimal point is moved. Course 2 2-2 Powers of Ten and Scientific Notation Additional Example 3B: Writing Numbers in Scientific Notation Write the number in scientific notation. B. 327,000,000 8 places Move the decimal point to 327,000,000 = 327,000,000 get a number that is greater than or equal to 1 and less than 10. = 3.27 Course 2 108 The exponent is equal to the number of places the decimal point is moved. Powers Lesson of Ten and Scientific 2-2 Insert Title Here Notation Try This: Example 3A Write the number in scientific notation. A. 8,421,000 8,421,000 = 8,421,000 = 8.421 106 Course 2 6 places Move the decimal point to get a number that is greater than or equal to 1 and less than 10. The exponent is equal to the number of places the decimal point is moved. Powers Lesson of Ten and Scientific 2-2 Insert Title Here Notation Try This: Example 3B Write the number in scientific notation. 5 places B. 327,000 327,000 = 327,000 = 3.27 Course 2 105 Move the decimal point to get a number that is greater than or equal to 1 and less than 10. The exponent is equal to the number of places the decimal point is moved. 2-2 Powers of Ten and Scientific Notation Additional Example 4: Writing Numbers in Standard Form The population of China in the year 2000 was estimated to be about 1.262 109. Write this number in standard form. Since the 9 1.262 10 = 1.262000000 exponent is 9, move the decimal point 9 places to the right. = 1,262,000,000 The population of China was about 1,262,000,000 people. Course 2 Powers Lesson of Ten and Scientific 2-2 Insert Title Here Notation Try This: Example 4 The distance from the Earth to the Sun is calculated to be 1.5 108 kilometers. Write this distance in standard form. 1.5 108 = 1.50000000 Since the exponent is 8, move the decimal point 8 places to the right. = 150,000,000 The distance from the Earth to the Sun is about 150,000,000 kilometers. Course 2 of Ten and Scientific 2-2 Powers Insert Lesson Title Here Notation Lesson Quiz: Part 1 Multiply. 1. 25 102 2,500 2. 18 104 180,000 Find each product. 3. 110 102 11,000 4. 3.742 103 3,742 Course 2 of Ten and Scientific 2-2 Powers Insert Lesson Title Here Notation Lesson Quiz: Part 2 Write each number in scientific notation.. 5. 7,400,000 7.4 106 6. 45,000 4.5 104 7. Earth is about 9.292 107 miles from the Sun. Write this number in standard form. 92,920,000 Course 2