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Lesson Menu 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

Over Lesson 9–4 5-Minute Check 1 Write 2 –3 using a positive exponent. A.(–3) 2 B.2 3 C. D.

Over Lesson 9–4 5-Minute Check 2 Write a –1 using a positive exponent. A.a B.–a C. D.

Over Lesson 9–4 5-Minute Check 3 Write (–5) –4 using a positive exponent. A. B. C.5 4 D.(–5) 4

Over Lesson 9–4 5-Minute Check 4 A.4 5 B.4 –5 C.(–4) –5 D.

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

Over Lesson 9–4 5-Minute Check 6 Evaluate z –3 if z = 5. A.125 B.–125 C. D.

Then/Now 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.

Vocabulary standard form scientific notation

Concept

Example 1 Express Numbers in Standard Form A. Express 3 × 10 5 in standard form. 3 × 10 5 = 3 × 100, = 100,000 =300,000Move the decimal point 5 places to the right. Answer: 300,000

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

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

Example 1 CYP A A.5,000 B.50,000 C.500,000 D.5,000,000 A. Express 5 × 10 4 in standard form.

Example 1 CYP B A.2,614,000 B.261,400 C D B. Express × 10 6 in standard form.

Example 1 CYP C A.80,300 B C D C. Express 8.03 × 10 –4 in standard form.

Example 2 A Express Numbers in Scientific Notation A. Express 800,000 in scientific notation. 800,000 = 8.0 × 100,000The decimal point moves 5 places. Answer: 8.0 × 10 5 =8.0 × 10 5 The exponent is positive.

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

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

Example 2 CYP A A.6.5 × 10 5 B.6.5 × 10 –4 C.6.5 × 10 4 D.65 × 10 3 A. Express 65,000 in scientific notation.

Example 2 CYP B A.9.5 × 10 6 B.9.5 × 10 7 C.95 × 10 6 D.95 × 10 7 B. Express 95,000,000 in scientific notation.

Example 2 CYP C A.42 × 10 –5 B.4.2 × 10 –4 C.4.2 × 10 4 D.4.2 × 10 –3 C. Express in scientific notation.

Example 3 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. PlanWrite 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.

Solve1 million = 1.0 × 10 6 thickness of = thickness of 1 dime × stack number in stack = (1.35 × 10 –3 m) × (1.0 × 10 6 ) = 1.35 × 10 –3 + 6 m = 1.35 × 10 3 m Example 3 Solve Problems Using Scientific Notation CheckCheck using mental math. (1.35 × 10 –3 )(1 × 10 6 )= (1.35 × 1.0)(10 –3 × 10 6 ) = 1.35 × 10 3 Answer: So, the height of the stack is 1.35 × 10 3 m.

Example 3 A.1.75 × 10 6 m B.1.75 × 10 9 m C.1.75 × m D.1.75 × m A quarter is 1.75 × 10 –3 meters thick. What would be the height of a stack of one billion quarters in scientific notation?

Example 4 Order Numbers in Scientific Notation SPACE The diameters of Neptune, Saturn, and Uranus are 4.9 × 10 4 km, 1.2 × 10 5 km, and 5.1 × 10 4 km, respectively. Order the planets from greatest to least diameter. Step 1Order the numbers according to their exponents. Saturn has the greatest exponent so it is the largest.

Example 4 Order Numbers in Scientific Notation 5.1>4.9 UranusNeptune 5.1 × 10 4 >4.9 × 10 4 Answer: So, the order is Saturn, Uranus, and Neptune. Step 2Order the numbers with the same exponent by comparing the factors.

Example 4 A.Mercury, Earth, Jupiter B.Mercury, Jupiter, Earth C.Earth, Jupiter, Mercury D.Earth, Mercury, Jupiter The diameters of Earth, Jupiter, and Mercury are 1.55 × 10 8 km, 7.79 × 10 8 km, and 5.80 × 10 7 km, respectively. Order the diameters from smallest to largest diameter.

End of the Lesson