Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Lesson 7-2 Warm-Up ALGEBRA 1 “Scientific Notation” (7-2) What is “scientific notation”? Scientific Notation: a way to write very large numbers in short form using powers of 10 in the form a x 10n, where n is an integer and a is between 1 and 10 (1 ≤ a ≤ 10). Example: 7,500,000,000,000 (“7 trillion, 500 billion”) = 7.5 x 1012 How do you write a number in scientific notation? To write a number in scientific notation, move the decimal so it’s after the first nonzero (≠ 0) digit, write the rest of the nonzero numbers after the decimal, and multiply this by 10 to the power of the number of jumps it would take to make the original number (right jumps = positive exponent and left jumps = negative exponent) __._____ x 10 ___ decimal jumps it would take to make the number first rest of nonzero the nonzero digit digits What is “standard notation”? Standard Notation: the usual way to write a number using commas, etc. Examples: Standard Notation Scientific Notation 3,600,000,000,000 = = 3.6 x 1012 (3.6 trillion) 0.0000000000436 = = 4.36 x 10-11 ALGEBRA 1 Scientific Notation LESSON 7-2 Additional Examples Is each number written in scientific notation? If not, explain. a. 0.46 104 No; 0.46 is less than 1. b. 3.25 10–2 Yes c. 13.2 106 No; 13.2 is greater than 10. ALGEBRA 1 Scientific Notation LESSON 7-2 Additional Examples Write each number in scientific notation. a. 234,000,000 234,000,000 = 2.34 108 Move the decimal point 8 places to the left and use 8 as an exponent. Drop the zeros after the 4. b. 0.000063 0.000063 = 6.3 10–5 Move the decimal point 5 places to the right and use –5 as an exponent. Drop the zeros before the 6. ALGEBRA 1 Scientific Notation LESSON 7-2 Additional Examples Write each number in standard notation. a. elephant’s mass: 8.8 104 kg 8.8 104 = 8.8000. A positive exponent indicates a number greater than 10. Move the decimal point 4 places to the right. = 88,000 kg b. ant’s mass: 7.3 10–5 kg 7.3 10–5 = 0.00007.3 A negative exponent indicates a number between 0 and 1. Move the decimal point 5 places to the left. = 0.000073 kg ALGEBRA 1 Scientific Notation LESSON 7-2 Additional Examples List the planets in order of their distance from the sun from least to greatest. Planet Distance from the Sun Jupiter 4.84 108 mi Earth 9.3 107 mi Neptune 2.8 109 mi Mercury 3.8 107 mi 1. Order the powers of 10; 2. Arrange the decimals with the same power of 10 in order by place value. ALGEBRA 1 Scientific Notation LESSON 7-2 Additional Examples (continued) 3.8 107 Mercury 9.3 107 Earth 4.84 108 Jupiter 2.8 109 Neptune From least to greatest distance from the sun, the order of the planets is Mercury, Earth, Jupiter, and Neptune. ALGEBRA 1 Scientific Notation LESSON 7-2 Additional Examples Order 0.0063 105, 6.03 104, 6103, and 63.1 103 from least to greatest. Write each number in scientific notation. 0.0063 105 6.3 102 6.03 104 63.1 103 6103 6.03 104 6.103 103 6.31 104 Order the powers of 10. Arrange the decimals with the same power of 10 in order. 6.3 102 6.103 103 6.03 104 6.31 104 Write the original numbers in order. 0.0063 105 6103 6.03 104 63.1 103 ALGEBRA 1 Scientific Notation LESSON 7-2 Additional Examples Simplify. Write each answer using scientific notation. a. b. 6(8 10–4) = (6 • 8) 10–4 Use the Associative Property of Multiplication. = 48 10–4 Simplify inside the parentheses. = 4.8 10–3 Write the product in scientific notation. 0.3(1.3 103) = (0.3 • 1.3) 103 Use the Associative Property of Multiplication. = 0.39 103 Simplify inside the parentheses. = 3.9 102 Write the product in scientific notation. ALGEBRA 1 Scientific Notation LESSON 7-2 Lesson Quiz 1. Write each number in scientific notation. a. 0.00627 6.27 10–3 b. 3,486,000 3.486 106 2. Write each number in standard form. a. 9.4 104 94,000 b. 2.3 10–6 0.0000023 3. Order the following numbers from least to greatest. 0.98 10–1, 1.6 103, 2.4 10–1, 11 100 0.98 10–1, 2.4 10–1, 11 100, 1.6 103 4. Simplify. Write the answer in scientific notation. 7(6.1 10–2) 4.27 10–1 ALGEBRA 1