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Pass out calculators. Warm Up Questions: 1.What is the solution to the system of equations shown below? Y = 2x – 2 8x + 2y = - 16 2.What value of n makes this equation true? 7 + 3(6 – 4n) = 2n A. -0.56 B. 0.4C. 2.5D. 12.5 DO NOW

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Objective: To numbers in scientific notation and to compare two numbers written in scientific notation.

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How many turkey’s were raised in the U.S. IN 2005??

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256,000,000

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How much does the earth way???

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6,588,000,00000 0,000,000,000,0 00,000,000 TONS

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How many atoms does a quarter contain??

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97, 700, 000, 000,000,000,00 0,000,000,000 … atoms.

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What is the average size of an atom?

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The average size of an atom is about 0.00000003 centimeters across.

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Numbers written in scientific notation are written as two factors. One factor is a number greater than or equal to 1 and less than 10. The other factor is a power of 10.

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To write scientific notation for numbers greater than or equal to 1 and less than 10, use a 0 exponent. 5.63 = 5.63 x 10°. Writing Math

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EXAMPLE 1 Write numbers in standard form a. 2.0075 10 6 Exponent is 6. Move decimal point 6 places to the right. b. 1.685 10 -4 Exponent is – 4. Move decimal point 4 places to the left. = 2,007,500 =0.0001685

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135,000 1.35 100,000 * Move the decimal from where you want it to where it actually is. 1.35 10 5 1.35 10 5 10 = 100,000 5 Write the number in standard notation. A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left. Helpful Hint

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1.9 100,000 0.000019 Divide by the reciprocal. Think: Move the decimal left 5 places. 1.9 10 –5 1.9 10 –5 –5 1 10 = 100,000 Write the number in standard notation. 1.9 1 100,000

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EXAMPLE 2 Write numbers in scientific notation 4.259 10 7 a. 42,590,000 = b.0.0000574=5.74 10 -5 Move decimal point 7 places to the left. Exponent is 7. Move decimal point 5 places to the right. Exponent is – 5.

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Example 2A: Translating Standard Notation to Scientific Notation Write 250790 in scientific notation.

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Check It Out: Example 2B Think: The decimal needs to move left to change 8.11 to 0.000811, so the exponent will be negative. 0.000811 Think: The decimal needs to move 4 places to get a number between 1 and 10. 8.11 8.11 10 Set up scientific notation. Check 8.11 10 = 8.11 0.0001 = 0.000811 –4 Write 0.000811 in scientific notation. So 0.000811 written in scientific notation is 8.11 10 –4.

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GUIDED PRACTICE for Examples 1 and 2 Write the number 539,000 in scientific notation. Then write the number 4.5 10 – 4 in standard form. 1. 539,000 5.39 10 5 = 4.5 10 – 4 =0.00045

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Compute with numbers in scientific notation EXAMPLE 4 Evaluate the expression. Write your answer in scientific notation. a. (8.5 10 2 )(1.7 10 6 ) (8.5 1.7) (10 2 10 6 )= 14.45 10 8 = (1.445 10 1 ) = 10 8 1.445 (10 1 ) = 10 8 Commutative property and associative property Product of powers property Write 14.45 in scientific notation. Associative property 1.445 10 9 = Product of powers property

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Compute with numbers in scientific notation EXAMPLE 4 b. (1.5 10 3 ) – 2 (10 3 ) – 2 = 1.5 2 (10 6 ) – = 2.25 Power of a product property Power of a power property 10 −3 c. 1.2 10 4 1.6 = 10 3 – 1.2 1.6 10 4 Product rule for fractions (10 7 ) = 0.75 (7.5 10 1 ) – = 10 7 7.5 (10 1 – = 10 7 ) (10 6 ) = 7.5 Quotient of powers property Write 0.75 in scientific notation. Associative property Product of powers property

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GUIDED PRACTICE for Examples 3 and 4 Evaluate the expression. Write your answer in scientific notation. 3. (1.3 10 5 ) – 2 (10 10 ) – = 1.69 10 2 4. 4.5 10 5 – 1.5 10 7 = 3 5. (1.1 10 7 ) (4.2 10 2 ) 4.62 10 9 =

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Scientific Notation: A brand new one-dollar bill is 4.3x10 -3 inches thick. What would be the thickness of a stack of 200 brand new one-dollar bills?

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Scientific Notation: One mole of an element is defined as a sample containing 6.0 x 10 23 atoms of that element. Based on the information, how many atoms are there in 1.5 x 10 -4 mole of an element?

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Scientific Notation: On February 2, 2013, the U.S. Treasury estimated the national debt at $1.2278 x 10 13. The U.S. Census Bureau’s estimate for that population was about 3.086 x 10 8. Using these estimates calculate the per person share of the national debt.

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Scientific Notation: A red blood cell is 8 x 10 -6 meters long. A skin cell is 3 x 10 -5 meters long. How many times longer is the skin blood cell than the red blood cell.

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Scientific Notation: The start Vega is approximately 2.38 x 10 14 kilometers from earth. The start Antares is approximately 4.94 x 10 15 kilometers from earth. How much further from earth is the start Antares than the star Vega?

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Scientific Notation: A ship’s weight is 1.2 x 10 4 tons when it is empty. The ship’s cargo, fuel, and crew weigh a total of 4.6 x 10 3 tons. What is the total weight of the ship with the cargo, fuel, and crew onboard?

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