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2-2 Powers of Ten and Scientific Notation 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 Lesson Title Here Notation Insert of Ten and Scientific Vocabulary Standard Form: a way to write numbers by using digits. Example: three hundred sixty five in standard notation is 365. Scientific Notation: a method of writing very large or very small numbers by using powers of 10. 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 Meaning Value 101 10 10 102 10 · 10 100 103 10 · 10 · 10 1,000 104 10 · 10 · 10 · 10 10,000 Course 2 2-2 Powers of Ten and Scientific Notation Example 1: Multiplying by Powers of Ten Multiply 14 · 103. 14 · 103 = 14 · (10 · 10 · 10) Use 10 as a factor 3 times. = 14 · 1,000 Multiply. = 14,000 Course 2 2-2 Insert Lesson Title Here Notation Powers of Ten and Scientific Try This: Example 1 Multiply 12 · 102. 12 · 102 = 12 · (10 · 10) Use 10 as a factor 2 times. = 12 · 100 Multiply. = 1,200 Course 2 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 Example 2: Multiplying by Powers of Ten Mentally Find each product. A. 212 · 104 4 places 212 · 104 = 212.0000 Move the decimal point 4 places. = 2,120,000 (You will need to add 4 zeros.) 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.) Course 2 2-2 Insert Lesson Title Here Notation Powers of Ten and Scientific Try This: Example 2 Find each product. A. 22.5 · 102 2 places 22.5 · 102 = 22.50 Move the decimal point 2 places. = 2,250 (You will need to add 1 zero.) 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.) Course 2 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 A power of 10 than or equal to 1 but less than 10 Course 2 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 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 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. The exponent is equal to = 3.27 108 the number of places the decimal point is moved. Course 2 2-2 Insert Lesson Title Here Notation Powers of Ten and Scientific Try This: Example 3A Write the number in scientific notation. A. 8,421,000 6 places Move the decimal point to 8,421,000 = 8,421,000 get a number that is greater than or equal to 1 and less than 10. The exponent is equal to = 8.421 106 the number of places the decimal point is moved. Course 2 2-2 Insert Lesson Title Here Notation Powers of Ten and Scientific Try This: Example 3B Write the number in scientific notation. B. 327,000 5 places Move the decimal point to 327,000 = 327,000 get a number that is greater than or equal to 1 and less than 10. The exponent is equal to = 3.27 105 the number of places the decimal point is moved. Course 2 2-2 Powers of Ten and Scientific Notation 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 1.262 109 = 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 2-2 Insert Lesson Title Here Notation Powers of Ten and Scientific 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 2-2 Powers Lesson Title Here Notation Insert of Ten and Scientific Assignment: pg. 66 14-39 Left Column Only Course 2

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