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2-2 Powers of Ten and Scientific Notation Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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Warm Up Find each value Course Powers of Ten and Scientific Notation ,000 10,000

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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 Powers of Ten and Scientific Notation

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Learn to express large numbers in scientific notation. Course Powers of Ten and Scientific Notation

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Vocabulary standard form scientific notation Insert Lesson Title Here Course Powers of Ten and Scientific Notation

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Course 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 = 10 8 Power of ten

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Course Powers of Ten and Scientific Notation The table shows several powers of ten. Power of 10MeaningValue · 10 · 10 · · 10 · · ,000 10,

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Multiply 14 · Additional Example 1: Multiplying by Powers of Ten Course Powers of Ten and Scientific Notation 14 · 10 3 = 14 · (10 · 10 · 10) = 14 · 1,000 = 14,000 Use 10 as a factor 3 times. Multiply.

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Try This: Example 1 Insert Lesson Title Here Course Powers of Ten and Scientific Notation Multiply 12 · · 10 2 = 12 · (10 · 10) = 12 · 100 = 1,200 Use 10 as a factor 2 times. Multiply.

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Course 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.

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Find each product. Additional Example 2: Multiplying by Powers of Ten Mentally Course Powers of Ten and Scientific Notation A. 212 · · 10 4 = = 2,120,000 4 places Move the decimal point 4 places. (You will need to add 4 zeros.) B · · 10 3 = places Move the decimal point 3 places. = 31,600 (You will need to add 2 zeros.)

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Try This: Example 2 Insert Lesson Title Here Course Powers of Ten and Scientific Notation Find each product. A · · 10 2 = = 2,250 2 places Move the decimal point 2 places. (You will need to add 1 zero.) B · · 10 3 = places Move the decimal point 3 places. = 39,500 (You will need to add 2 zeros.)

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Course 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 A power of 10

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Course Powers of Ten and Scientific Notation In scientific notation, it is customary to use a multiplication cross () instead of a dot. Writing Math

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Write the number in scientific notation. Additional Example 3A: Writing Numbers in Scientific Notation Course Powers of Ten and Scientific Notation A. 4,340,000 4,340,000 = 4,340,000 Move the decimal point to get a number that is greater than or equal to 1 and less than 10. = 4.34 10 6 The exponent is equal to the number of places the decimal point is moved. 6 places

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Additional Example 3B: Writing Numbers in Scientific Notation Course Powers of Ten and Scientific Notation Write the number in scientific notation. B. 327,000, ,000,000 = 327,000,000 Move the decimal point to get a number that is greater than or equal to 1 and less than 10. = 3.27 10 8 The exponent is equal to the number of places the decimal point is moved. 8 places

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Try This: Example 3A Insert Lesson Title Here Course Powers of Ten and Scientific Notation Write the number in scientific notation. A. 8,421,000 8,421,000 = 8,421,000 Move the decimal point to get a number that is greater than or equal to 1 and less than 10. = 10 6 The exponent is equal to the number of places the decimal point is moved. 6 places

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Try This: Example 3B Insert Lesson Title Here Course Powers of Ten and Scientific Notation Write the number in scientific notation. B. 327, ,000 = 327,000 Move the decimal point to get a number that is greater than or equal to 1 and less than 10. = 3.27 10 5 The exponent is equal to the number of places the decimal point is moved. 5 places

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The population of China in the year 2000 was estimated to be about Write this number in standard form. Additional Example 4: Writing Numbers in Standard Form Course Powers of Ten and Scientific Notation 10 9 = Since the 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.

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Try This: Example 4 The distance from the Earth to the Sun is calculated to be 1.5 10 8 kilometers. Write this distance in standard form. Insert Lesson Title Here Course Powers of Ten and Scientific Notation 1.5 10 8 = 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.

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Lesson Quiz: Part 1 Multiply. 180,000 2,500 Insert Lesson Title Here 11,000 3,742 Course Powers of Ten and Scientific Notation 10 3 Find each product.

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Lesson Quiz: Part 2 Write each number in scientific notation ,400, , Earth is about 10 7 miles from the Sun. Write this number in standard form. 4.5 10 6 Insert Lesson Title Here 92,920,000 Course Powers of Ten and Scientific Notation

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