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Section 3B Putting Numbers in Perspective Pages 152-164

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Scientific Notation Absolutely critical for very large and very small numbers The federal debt is $8,700,000,000,000. The diameter of a hydrogen nucleus is 0.0000000000000001 meter. Your calculators automatically use it! 3-B

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Scientific Notation number between 1 and 10 Scientific Notation is a format in which a number is expressed as a number between 1 and 10 multiplied by a power of 10. Examples: 6,700,000,000 6,700,000,000 = 6.7 × 10 9 = 6.7 E 9 (calculator) 0.000000000000002 0.000000000000002 = 2.0 × 10 15 = 2 E -15 (calculator) 3-B

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Scientific Notation 10 6 = 1 million 10 9 = 1 billion 10 12 = 1 trillion The U.S. federal debt is about $8.7 trillion (8.7×10 12 ) 3-B

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Ordinary vs Scientific Notation An exercise in powers of 10 and moving the decimal KEY: × 10 (positive p) moves decimal p places to right. × 10 (negative p) moves decimal p places to left. 3-B

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To convert from scientific notation: to ordinary notation: Move the decimal point as many spaces as you have powers of 10 -- Move to the right if the power is positive and move to the if the power is. Move to the right if the power is positive and move to the left if the power is negative. Fill in any open spaces with zeros. 3-B

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Conversion from scientific to ordinary Examples: 1.7842 × 10 3 = 1784.2 2.111 × 10 7 = 21,110,000 9.1 × 10 -4 =.00091 3-B

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To convert from ordinary to scientific notation: Move (and count) the decimal point until it lies the non-zero digit. Move (and count) the decimal point until it lies after the first non-zero digit. The power of 10 = number of moves. The power is if the decimal moved to the and negative if the decimal moved to the right. The power is positive if the decimal moved to the left and negative if the decimal moved to the right. 3-B

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Conversion from ordinary to scientific Example: 1330 = 1.330 × 10 3.00000345 = 3.45 × 10 -6 527 10 3 = 5.27 × 10 2 × 10 3 = 5.27 × 10 5 3-B

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Using your Calculator “EE” Look for an “EE” key 1.7842 10 3 1.7842 EE 3 = 1784.2 2.111 10 7 2.111 EE 7 = 21110000 9.1 10 -4 9.1EE-4= 9.1 E-4 3-B

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Multiply or Dividing with scientific notation: Examples: (6.2 × 10 3 ) × (3 × 10 5 ) = (6.2 × 3) × (10 3 × 10 5 ) = 18.6×10 (3+5) = 1.86 ×10×10 8 = 1.86×10 9 = 1.86 ×10×10 8 = 1.86×10 9 4.2 10 2 = 4.2 × 10 2 8.4 10 -5 8.4 10 -5 =.5× 10 2-(-5) =.5×10 7 = 5.×10 (-1) × 10 7 = 5.0× 10 6 3-B

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More Practice: (3× 10 4 )×(8 × 10 5 ) = = 24×10 9 = 2.4×10×10 9 = 2.4×10 10 (6.3× 10 2 )×(1.5 × 10) = = 9.45×10 3

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More Practice: (9× 10 3 )×(5 × 10 -7 ) = = 45×10 -4 = 4.5×10×10 -4 = 4.5×10 -3 (4.4× 10 99 )∕(2 × 10 11 ) = = 2.2×10 88

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Approximations with scientific notation: Example: 14927 2213 ≈ 15000 × 2000 = (1.5×10 4 )× (2 × 10 3 ) = 3×10 7 = 30,000,000 (30 million) check: 14927 2213 = 33,033,451 3-B

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More Practice: 9642 / 31 ≈ 9,000 / 30 = (9×10 3 ) / (3 × 10) = 3×10 2 = 300 check: 9642 / 31 = 311.0322... 3-B

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More Practice: 7.253 × 291 ≈ 7 × 300 = 7 × (3×10 2 ) = 21×10 2 = 21×10 2 = 2100 check: 7.253 / 291 = 2110.623 3-B

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Homework for Wednesday: Pages 164-165 # 10, 16, 18, 20a-c, 24, 26 3-B

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