Scientific Notation

Scientific Notation ALGEBRA 1 LESSON 8-2 (For help, go to Lesson 8-1.) Simplify each expression. 1. 6 • 1042. 7 • 10–23. 8.2 • 105 4. 3 • 10–35. 3.4 • 1016. 5.24 • 102 7. Simplify 3  102 + 6  101 + 7  100 + 8  10–1. 8-2

Scientific Notation ALGEBRA 1 LESSON 8-2 Solutions 1. 6 • 104 = 6 • 10,000 = 60,000 2. 7 • 10–2 = 7 • 0.01 = 0.07 3. 8.2 • 105 = 8.2 • 100,000 = 820,000 4. 3 • 10–3 = 3 • 0.001 = 0.003 5. 3.4 • 101 = 3.4 • 10 = 34 6. 5.24 • 102 = 5.24 • 100 = 524 7. 3  102 + 6  101 + 7  100 + 8  10–1 = (3  102) + (6  101) + (7  100) + (8  10–1) = (3  100) + (6  10) + (7  1) + (8  0.1) = 300 + 60 + 7 + 0.8 = 367.8 8-2

Scientific Notation ALGEBRA 1 LESSON 8-2 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. 8-2

Move the decimal point 8 places to the left and use 8 as an exponent. 2.34  108 234,000,000 = Drop the zeros after the 4. Move the decimal point 5 places to the right and use –5 as an exponent. 6.3  10–5 0.000063 = Drop the zeros before the 6. Scientific Notation ALGEBRA 1 LESSON 8-2 Write each number in scientific notation. a. 234,000,000 b. 0.000063 8-2

A positive exponent indicates a number greater than 10. Move the decimal point 4 places to the right. 8.8  104 = 8.8000. A negative exponent indicates a number between 0 and 1. Move the decimal point 5 places to the left. 7.3  10–5 = 0.00007.3 Scientific Notation ALGEBRA 1 LESSON 8-2 Write each number in standard notation. a. elephant’s mass: 8.8  104 kg = 88,000 b. ant’s mass: 7.3  10–5 kg = 0.000073 8-2

Distance from the Sun Planet 4.84  108 mi Jupiter 9.3  107 mi Earth 4.5  109 mi Neptune 3.8  107 mi Mercury Scientific Notation ALGEBRA 1 LESSON 8-2 List the planets in order from least to greatest distance from the sun. Order the powers of 10. Arrange the decimals with the same power of 10 in order. 8-2

Distance from the Sun Planet 4.84  108 mi Jupiter 9.3  107 mi Earth 4.5  109 mi Neptune 3.8  107 mi Mercury Scientific Notation ALGEBRA 1 LESSON 8-2 (continued) 3.8  107 9.3  107 4.84  108 4.5  109 Mercury Earth Jupiter Neptune From least to greatest distance from the sun, the order of the planets isMercury, Earth, Jupiter, and Neptune. 8-2

Write each number in scientific notation. 0.0063 105 6.03  104 6103 63.1  103 6.3  102 6.03  104 6.103  103 6.31  104 Scientific Notation ALGEBRA 1 LESSON 8-2 Order 0.0063  105, 6.03  104, 6103, and 63.1  103 from least to greatest. 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 8-2

Use the Associative Property of Multiplication. (6 • 8)  10–4 = = 48 10–4 Simplify inside the parentheses. = 4.8  10–3 Write the product in scientific notation. Use the Associative Property of Multiplication. (0.3 • 1.3)  103 = = 0.39 103 Simplify inside the parentheses. = 3.9  102 Write the product in scientific notation. Scientific Notation ALGEBRA 1 LESSON 8-2 Simplify. Write each answer using scientific notation. 6(8 10–4) a. 0.3(1.3 103) b. 8-2

Scientific Notation ALGEBRA 1 LESSON 8-2 1. Write each number in scientific notation. a. 0.00627 b. 3,486,000 2. Write each number in standard form. a. 9.4  104 b. 2.3  10–6 3. Order the following numbers from least to greatest. 0.98  10–1, 1.6  103, 2.4  10–1, 11  100 4. Simplify. Write the answer in scientific notation. 7(6.1  10–2) 6.27  10–3 3.486  106 94,000 0.0000023 0.98  10–1, 2.4  10–1, 11  100, 1.6  103 4.27  10–1 8-2

Scientific Notation