Lesson 7-2 Warm-Up

“Scientific Notation” (7-2) What is “scientific notation”? How do you write a number in scientific notation? What is “standard 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 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) Standard Notation: the usual way to write a number using commas, etc. Examples: __._____ x 10 ___  decimal jumps it would take to make the number   first rest of nonzero the nonzero digit digits Standard Notation Scientific Notation 3,600,000,000,000 = = 3.6 x 1012 (3.6 trillion)    0.0000000000436 = = 4.36 x 10-11

Is each number written in scientific notation? If not, explain. 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.

Write each number in scientific notation. LESSON 7-2 Additional Examples Write each number in scientific notation. a. 234,000,000 Move the decimal point 8 places to the left and use 8 as an exponent. 234,000,000 = Drop the zeros after the 4. 2.34  108 b. 0.000063 Move the decimal point 5 places to the right and use –5 as an exponent. 0.000063 = 6.3  10–5 Drop the zeros before the 6.

Write each number in standard notation. Scientific Notation LESSON 7-2 Additional Examples Write each number in standard notation. a. elephant’s mass: 8.8  104 kg 8.8  104 = A positive exponent indicates a number greater than 10. Move the decimal point 4 places to the right. 8.8000. = 88,000 kg b. ant’s mass: 7.3  10–5 kg   7.3  10–5 = A negative exponent indicates a number between 0 and 1. Move the decimal point 5 places to the left. 0.00007.3 = 0.000073 kg

List the planets in order of their distance from the Scientific Notation LESSON 7-2 Additional Examples List the planets in order of their distance from the sun from least to greatest. Jupiter Earth Neptune Mercury 4.84  108 mi 9.3  107 mi 2.8  109 mi 3.8  107 mi Planet Distance from the Sun Order the powers of 10; Arrange the decimals with the same power of 10 in order by place value.

Mercury Earth Jupiter Neptune Scientific Notation LESSON 7-2 Additional Examples (continued) 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 is Mercury, Earth, Jupiter, and Neptune.

Write each number in 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 6.03  104 6103 63.1  103 6.3  102 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

Simplify. Write each answer using scientific notation. LESSON 7-2 Additional Examples Simplify. Write each answer using scientific notation. Use the Associative Property of Multiplication. (6 • 8)  10–4 = a. 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 = b. 0.3(1.3  103) = 0.39  103 Simplify inside the parentheses. = 3.9  102 Write the product in scientific notation.

1. Write each number in scientific notation. a. 0.00627 b. 3,486,000 LESSON 7-2 Lesson Quiz 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