Downloaded 98 times
Powers of 10
- 1. 2-2 Powers ofTen and Scientific Notation Course 2 Warm Up Problem of the Day Lesson Presentation
- 2. 2-2 Powers ofTen and Scientific Notation Warm Up Find each value. 1. 92 3. 152 5. 103 81 144 225 Course 2 2. 122 4. 102 100 1,000 6. 104 10,000
- 3. 2-2 Powers ofTen 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
- 4. 2-2 Powers ofTen and Scientific Notation Learn to express large numbers in scientific notation. Course 2
- 5. 2-2 Powers ofTen and Scientific Notation Insert Lesson Title Here Vocabulary standard form scientific notation Course 2
- 6. 2-2 Powers ofTen 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
- 7. 2-2 Powers ofTen and Scientific Notation The table shows several powers of ten. Course 2 Power of 10 Meaning Value 101 10 10 10 · 10 10 · 10 · 10 10 · 10 · 10 · 10 100 1,000 10,000 102 103 104
- 8. 2-2 Powers ofTen and Scientific Notation Additional Example 1: Multiplying by Powers of Ten Multiply 14 · 103. Course 2 14 · 103 = 14 · (10 · 10 · 10) = 14 · 1,000 = 14,000 Use 10 as a factor 3 times. Multiply.
- 9. 2-2 Powers ofTen and Scientific Notation Insert Lesson Title Here Try This: Example 1 Multiply 12 · 102. Course 2 12 · 102 = 12 · (10 · 10) = 12 · 100 = 1,200 Use 10 as a factor 2 times. Multiply.
- 10. 2-2 Powers ofTen 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.
- 11. 2-2 Powers ofTen and Scientific Notation Additional Example 2: Multiplying by Powers of Ten Find each product. Mentally A. 212 · 104 Course 2 212 · 104 = 212.0000 = 2,120,000 4 places Move the decimal point 4 places. (You will need to add 4 zeros.) B. 31.6 · 103 31.6 · 103 = 31.600 3 places Move the decimal point 3 places. = 31,600 (You will need to add 2 zeros.)
- 12. 2-2 Powers ofTen and Scientific Notation Insert Lesson Title Here Try This: Example 2 Find each product. A. 22.5 · 102 Course 2 22.5 · 102 = 22.50 = 2,250 2 places Move the decimal point 2 places. (You will need to add 1 zero.) B. 39.5 · 103 39.5 · 103 = 39.500 3 places Move the decimal point 3 places. = 39,500 (You will need to add 2 zeros.)
- 13. 2-2 Powers ofTen 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
- 14. 2-2 Powers ofTen and Scientific Notation Writing Math In scientific notation, it is customary to use a multiplication cross (ď‚´) instead of a dot. Course 2
- 15. 2-2 Powers ofTen and Scientific Notation Additional Example 3A: Writing Numbers in Scientific Notation Write the number in scientific notation. A. 4,340,000 4,340,000 = 4,340,000 Course 2 6 places Move the decimal point to get a number that is greater than or equal to 1 and less than 10. = 4.34 ď‚´ 106 The exponent is equal to the number of places the decimal point is moved.
- 16. 2-2 Powers ofTen and Scientific Notation Additional Example 3B: Writing Numbers in Scientific Notation Write the number in scientific notation. B. 327,000,000 327,000,000 = 327,000,000 Course 2 8 places Move the decimal point to get a number that is greater than or equal to 1 and less than 10. = 3.27 ď‚´ 108 The exponent is equal to the number of places the decimal point is moved.
- 17. 2-2 Powers ofTen and Scientific Notation Insert Lesson Title Here Try This: Example 3A Write the number in scientific notation. A. 8,421,000 8,421,000 = 8,421,000 Course 2 6 places Move the decimal point to get a number that is greater than or equal to 1 and less than 10. = 8.421 ď‚´ 106 The exponent is equal to the number of places the decimal point is moved.
- 18. 2-2 Powers ofTen and Scientific Notation Insert Lesson Title Here Try This: Example 3B Write the number in scientific notation. B. 327,000 327,000 = 327,000 Course 2 5 places Move the decimal point to get a number that is greater than or equal to 1 and less than 10. = 3.27 ď‚´ 105 The exponent is equal to the number of places the decimal point is moved.
- 19. 2-2 Powers ofTen 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 ď‚´ 109. Write this number in standard form. 1.262 ď‚´ 109 = 1.262000000 Course 2 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.
- 20. 2-2 Powers ofTen and Scientific Notation Insert Lesson Title Here Try This: Example 4 The distance from the Earth to the Sun is calculated to be 1.5 ď‚´ 108 kilometers. Write this distance in standard form. 1.5 ď‚´ 108 = 1.50000000 Since the exponent is Course 2 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.
- 21. 2-2 Powers ofTen and Scientific Notation Insert Lesson Title Here Lesson Quiz: Part 1 Multiply. 2,500 180,000 Find each product. 11,000 3,742 1. 25 ď‚´ 102 2. 18 ď‚´ 104 3. 110 ď‚´ 102 4. 3.742 ď‚´ 103 Course 2
- 22. 2-2 Powers ofTen and Scientific Notation Insert Lesson Title Here Lesson Quiz: Part 2 Write each number in scientific notation.. 5. 7,400,000 6. 45,000 7.4 ď‚´ 106 4.5 ď‚´104 7. Earth is about 9.292 ď‚´ 107 miles from the Sun. Write this number in standard form. 92,920,000 Course 2