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7-2 Scientific Notation

7-2 Scientific Notation. Hubarth Algebra. Scientific Notation A number in scientific notation is written as the product of two factors in the form a x , where n is an integer and Example 3.4 x 5.43 x 2.1 x. When converting to scientific notation

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7-2 Scientific Notation

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  1. 7-2 Scientific Notation Hubarth Algebra

  2. Scientific Notation A number in scientific notation is written as the product of two factors in the form a x , where n is an integer and Example 3.4 x 5.43 x 2.1 x When converting to scientific notation moving the decimal to the left gives you a positive exponent. 35,000 = 3.5 x moving the decimal to the right gives you a negative exponent. .00296 = 2.96 x

  3. Ex 1 Recognizing Scientific Notation 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.

  4. 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. Ex 2 Writing a Number in Scientific Notation Write each number in scientific notation. a. 234,000,000 b. 0.000063

  5. 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. 0.00007.3 7.3  10–5 = Ex 3 Writing a Number in Standard Notation Write each number in standard notation. a. elephant’s mass: 8.8  104 kg = 88,000 kg b. ant’s mass: 7.3  10–5 kg   = 0.000073 kg

  6. Ex 4 Application Distance from the Sun Planet 4.84  108 mi Jupiter 9.3  107 mi Earth 2.8  109 mi Neptune 3.8  107 mi Mercury List the planets in order of their distance from the sun from least to greatest. 3.8  107 9.3  107 4.84  108 2.8  109 Mercury Earth Jupiter Neptune From least to greatest distance from the sun, the order of the planets isMercury, Earth, Jupiter, and Neptune.

  7. 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 Ex 5 Using Scientific Notation to Order Numbers 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. 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. Ex 6 Multiplying a Number in Scientific Notation Simplify. Write each answer using scientific notation. 6(8 10–4) a. 0.3(1.3 103) b.

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