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**2-2**Powers of Ten and Scientific Notation Course 2 Warm Up Problem of the Day Lesson Presentation**2-2**Powers of Ten and Scientific Notation Course 2 Warm Up Find each value. 1.92 3. 152 5. 103 81 2. 122 144 225 4. 102 100 1,000 10,000 6. 104**2-2**Powers of Ten and Scientific Notation Course 2 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**2-2**Powers of Ten and Scientific Notation Course 2 Learn to express large numbers in scientific notation.**2-2**Powers of Ten and Scientific Notation Course 2 Insert Lesson Title Here Vocabulary standard form scientific notation**2-2**Powers of Ten and Scientific Notation Course 2 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**2-2**Powers of Ten and Scientific Notation Course 2 The table shows several powers of ten. Power of 10 Meaning Value 101 10 10 102 10 · 10 100 10 · 10 · 10 1,000 103 104 10 · 10 · 10 · 10 10,000**2-2**Powers of Ten and Scientific Notation Course 2 Additional Example 1: Multiplying by Powers of Ten Multiply 14 · 103. Use 10 as a factor 3 times. 14 · 103 = 14 · (10 · 10 · 10) Multiply. = 14 · 1,000 = 14,000**2-2**Powers of Ten and Scientific Notation Course 2 Insert Lesson Title Here Try This: Example 1 Multiply 12 · 102. Use 10 as a factor 2 times. 12 · 102 = 12 · (10 · 10) Multiply. = 12 · 100 = 1,200**2-2**Powers of Ten and Scientific Notation Course 2 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.**2-2**Powers of Ten and Scientific Notation Course 2 Additional Example 2: Multiplying by Powers of Ten Mentally Find each product. A. 212 · 104 4 places Move the decimal point 4 places. 212 · 104 = 212.0000 (You will need to add 4 zeros.) = 2,120,000 B. 31.6 · 103 3 places 31.6 · 103 = 31.600 Move the decimal point 3 places. = 31,600 (You will need to add 2 zeros.)**2-2**Powers of Ten and Scientific Notation Course 2 Insert Lesson Title Here Try This: Example 2 Find each product. A. 22.5 · 102 2 places Move the decimal point 2 places. 22.5 · 102 = 22.50 (You will need to add 1 zero.) = 2,250 B. 39.5 · 103 3 places 39.5 · 103 = 39.500 Move the decimal point 3 places. = 39,500 (You will need to add 2 zeros.)**2-2**Powers of Ten and Scientific Notation Course 2 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 7 1.79 x 10 A power of 10 A number greater than or equal to 1 but less than 10**2-2**Powers of Ten and Scientific Notation Course 2 Writing Math In scientific notation, it is customary to use a multiplication cross () instead of a dot.**2-2**Powers of Ten and Scientific Notation 6 places Course 2 Additional Example 3A: Writing Numbers in Scientific Notation Write the number in scientific notation. A. 4,340,000 Move the decimal point to get a number that is greater than or equal to 1 and less than 10. 4,340,000 = 4,340,000 The exponent is equal to the number of places the decimal point is moved. = 4.34 106**2-2**Powers of Ten and Scientific Notation 8 places Course 2 Additional Example 3B: Writing Numbers in Scientific Notation Write the number in scientific notation. B. 327,000,000 Move the decimal point to get a number that is greater than or equal to 1 and less than 10. 327,000,000 = 327,000,000 The exponent is equal to the number of places the decimal point is moved. = 3.27 108**2-2**Powers of Ten and Scientific Notation 6 places Course 2 Insert Lesson Title Here Try This: Example 3A Write the number in scientific notation. A. 8,421,000 Move the decimal point to get a number that is greater than or equal to 1 and less than 10. 8,421,000 = 8,421,000 The exponent is equal to the number of places the decimal point is moved. = 8.421 106**2-2**Powers of Ten and Scientific Notation 5 places Course 2 Insert Lesson Title Here Try This: Example 3B Write the number in scientific notation. B. 327,000 Move the decimal point to get a number that is greater than or equal to 1 and less than 10. 327,000 = 327,000 The exponent is equal to the number of places the decimal point is moved. = 3.27 105**2-2**Powers of Ten and Scientific Notation Course 2 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 exponent is 9, move the decimal point 9 places to the right. 1.262 109 = 1.262000000 = 1,262,000,000 The population of China was about 1,262,000,000 people.**2-2**Powers of Ten and Scientific Notation Course 2 Insert Lesson Title Here 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. Since the exponent is 8, move the decimal point 8 places to the right. 1.5 108 = 1.50000000 = 150,000,000 The distance from the Earth to the Sun is about 150,000,000 kilometers.**2-2**Powers of Ten and Scientific Notation Course 2 Insert Lesson Title Here Lesson Quiz: Part 1 Multiply. 2,500 1. 25 102 2. 18 104 180,000 Find each product. 3. 110 102 11,000 4. 3.742 103 3,742**2-2**Powers of Ten and Scientific Notation Course 2 Insert Lesson Title Here Lesson Quiz: Part 2 Write each number in scientific notation.. 5. 7,400,000 6. 45,000 7. Earth is about 9.292 107 miles from the Sun. Write this number in standard form. 7.4 106 4.5 104 92,920,000