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Scientific Notation February 26, 2014 Pages 512-514

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4.259 10 7 1. 42,590,000 = 2.0.0000574=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. Write the number in scientific notation. 3. 539,000 5.39 10 5 = Move decimal point 5 places to the left. Exponent is 5.

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4. 2.0075 10 6 Exponent is 6. Move decimal point 6 places to the right. 5. 1.685 10 -4 Exponent is – 4. Move decimal point 4 places to the left. = 2,007,500 =0.0001685 Write the number in standard form. 4.5 10 – 4 =0.00045 Exponent is – 4. Move decimal point 4 places to the left. 6.

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SOLUTION STEP 1 Write each number in standard form. 7. Order 103,400,000, 7.8 10, and 80,760,000 from least to greatest. 8 7.8 x 10 8 = 780,000,000 STEP 2 Write in order from least to greatest. STEP 3 Write the original numbers in order from least to greatest. 80,760,000; 103,400,000; 7.8 10 8 80,760,000; 103,400,000; 780,000,000

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Evaluate the expression. Write your answer in scientific notation. 8. (8.5 10 2 )(1.7 10 6 ) (8.5 1.7) (10 2+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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9. (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 10. (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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SOLUTION STEP 1 Write each number in standard form. Order 2.7 × 10 5, 3.401 × 10 4, and 27,500 from least to greatest. 11. 2.75 × 10 5 = 275,000; 3.401 x 10 4 = 34,010 STEP 2 Write in order from least to greatest. 27,500; 34,010; 275,000 STEP 3 Write the original numbers in order from least to greatest. 27,500; 3.401 × 10 4, and 2.7 × 10 5

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Evaluate the expression. Write your answer in scientific notation. 12. (1.3 10 5 ) – 2 2 (10 5 ) – = 1.3 2 10 – = 1.69 Power of a product property Power of a power property 10 2 13. 4.5 10 5 – 1.5 = 10 2 – 4.5 1.5 10 5 Product rule for fractions 10 7 = 3 Quotient of powers property 14. (1.1 10 7 ) (1.7 10 2 ) 4.62 10 9 = Commutative property and associative property Product of powers property (1.1 1.7) (10 7 10 2 )=

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HOMEWORK Page 515, #4-38 even

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Order numbers in scientific notation EXAMPLE 3 SOLUTION STEP 1 Write each number in scientific notation, if necessary. 103,400,000 = 1.034 10 8 80,760,000.

Order numbers in scientific notation EXAMPLE 3 SOLUTION STEP 1 Write each number in scientific notation, if necessary. 103,400,000 = 1.034 10 8 80,760,000.

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