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Five-Minute Check (over Lesson 9–4) Then/Now New Vocabulary Key Concept: Scientific Notation Example 1: Express Numbers in Standard Form Example 2: Express Numbers in Scientific Notation Example 3: Real-World Example: Solve Problems Using Scientific Notation Example 4: Real-World Example: Order Numbers in Scientific Notation Lesson Menu

Write 2–3 using a positive exponent. B. 23 C. D. 5-Minute Check 1

Write a–1 using a positive exponent. A. a B. –a C. D. 5-Minute Check 2

Write (–5)–4 using a positive exponent. B. C. 54 D. (–5)4 5-Minute Check 3

A. 45 B. 4–5 C. (–4)–5 D. 5-Minute Check 4

A. 49–0 B. 7–2 C. 4–9 D. 5-Minute Check 5

Evaluate z–3 if z = 5. A. 125 B. –125 C. D. 5-Minute Check 6

You have already compared and ordered integers. (Lesson 2–1) Express numbers in standard form and in scientific notation. Compare and order numbers written in scientific notation. Then/Now

standard form scientific notation Vocabulary

Concept

A. Express 3 × 105 in standard form. Express Numbers in Standard Form A. Express 3 × 105 in standard form. 3 × 105 = 3 × 100,000 105 = 100,000 = 300,000 Move the decimal point 5 places to the right. Answer: 300,000 Example 1

B. Express 4.395 × 104 in standard form. Express Numbers in Standard Form B. Express 4.395 × 104 in standard form. 4.395 × 104 = 4.395 × 10,000 104 = 10,000 = 43950 Move the decimal point 4 places to the right. Answer: 43,950 Example 1 B

C. Express 6.79 × 10–6 in standard form. Express Numbers in Standard Form C. Express 6.79 × 10–6 in standard form. 6.79 × 10–6 = 6.79 × 0.000001 10–6 = 0.000001 = 0.00000679 Move the decimal point 6 places to the left. Answer: 0.00000679 Example 1 C

A. Express 5 × 104 in standard form. B. 50,000 C. 500,000 D. 5,000,000 Example 1 CYP A

B. Express 2.614 × 106 in standard form. C. 0.000002614 D. 0.002614 Example 1 CYP B

C. Express 8.03 × 10–4 in standard form. B. 8.030 C. 0.000803 D. 0.0803 Example 1 CYP C

A. Express 800,000 in scientific notation. Express Numbers in Scientific Notation A. Express 800,000 in scientific notation. 800,000 = 8.0 × 100,000 The decimal point moves 5 places. = 8.0 × 105 The exponent is positive. Answer: 8.0 × 105 Example 2 A

B. Express 64,000 in scientific notation. Express Numbers in Scientific Notation B. Express 64,000 in scientific notation. 64,000 = 6.4 × 10,000 The decimal point moves 4 places. = 6.4 × 104 The exponent is positive. Answer: 6.4 × 104 Example 2

C. Express 0.0119 in scientific notation. Express Numbers in Scientific Notation C. Express 0.0119 in scientific notation. 0.0119 = 1.19 × 0.01 The decimal point moves 2 places. = 1.19 × 10–2 The exponent is negative. Answer: 1.19 × 10–2 Example 2 C

A. Express 65,000 in scientific notation. B. 6.5 × 10–4 C. 6.5 × 104 D. 65 × 103 Example 2 CYP A

B. Express 95,000,000 in scientific notation. D. 95 × 107 Example 2 CYP B

C. Express 0.00042 in scientific notation. B. 4.2 × 10–4 C. 4.2 × 104 D. 4.2 × 10–3 Example 2 CYP C

Solve Problems Using Scientific Notation DIMES A dime is 1.35 × 10–3 meters thick. What would the height of a stack of one million dimes be in scientific notation? Understand You know that a dime is 1.35 × 10–3 meters thick and that there are 1 million dimes in the stack. You need to know how thick the stack is. Plan Write 1 million in scientific notation. Multiply the thickness of a dime by the number of dimes in the stack to find the total thickness of the stack. Example 3

thickness of = thickness of 1 dime × stack number in stack Solve Problems Using Scientific Notation Solve 1 million = 1.0 × 106 thickness of = thickness of 1 dime × stack number in stack = (1.35 × 10–3 m) × (1.0 × 106) = 1.35 × 10–3 + 6 m = 1.35 × 103 m Answer: So, the height of the stack is 1.35 × 103 m. Check Check using mental math. (1.35 × 10–3)(1 × 106) = (1.35 × 1.0)(10–3 × 106) = 1.35 × 103  Example 3

A quarter is 1. 75 × 10–3 meters thick A quarter is 1.75 × 10–3 meters thick. What would be the height of a stack of one billion quarters in scientific notation? A. 1.75 × 106 m B. 1.75 × 109 m C. 1.75 × 1012 m D. 1.75 × 1015 m Example 3

Step 1 Order the numbers according to their exponents. Order Numbers in Scientific Notation SPACE The diameters of Neptune, Saturn, and Uranus are 4.9 × 104 km, 1.2 × 105 km, and 5.1 × 104 km, respectively. Order the planets from greatest to least diameter. Step 1 Order the numbers according to their exponents. Saturn has the greatest exponent so it is the largest. Example 4

Answer: So, the order is Saturn, Uranus, and Neptune. Order Numbers in Scientific Notation Step 2 Order the numbers with the same exponent by comparing the factors. 5.1 > 4.9 Uranus Neptune 5.1 × 104 > 4.9 × 104 Answer: So, the order is Saturn, Uranus, and Neptune. Example 4

A. Mercury, Earth, Jupiter B. Mercury, Jupiter, Earth The diameters of Earth, Jupiter, and Mercury are 1.55 × 108 km, 7.79 × 108 km, and 5.80 × 107 km, respectively. Order the diameters from smallest to largest diameter. A. Mercury, Earth, Jupiter B. Mercury, Jupiter, Earth C. Earth, Jupiter, Mercury D. Earth, Mercury, Jupiter Example 4

End of the Lesson