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Section 3B Putting Numbers in Perspective

Section 3B Putting Numbers in Perspective. Pages 152-164. 3-B. 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!.

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Section 3B Putting Numbers in Perspective

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  1. Section 3BPutting Numbers in Perspective Pages 152-164

  2. 3-B 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. 3-B Scientific Notation Scientific Notation is a format in which a number is expressed as anumber between 1 and 10multiplied by a power of 10. Examples: 6,700,000,000 = 6.7 ×109 = 6.7 E 9 (calculator) 0.000000000000002 =2.0 × 1015 =2 E -15 (calculator)

  4. 3-B Scientific Notation 106 = 1 million 109 = 1 billion 1012 = 1 trillion • The U.S. federal debt is about $8.7 trillion (8.7×1012)

  5. 3-B 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(negativep) moves decimal p places to left.

  6. 3-B 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 positiveand move to theleftif the power is negative. • Fill in any open spaces with zeros.

  7. 3-B Conversion from scientific to ordinary Examples: 1.7842 × 103 = 1784.2 2.111 × 107 = 21,110,000 9.1 × 10-4 = .00091

  8. 3-B To convert from ordinary to scientific notation: • Move (and count) the decimal point until it lies after the firstnon-zero digit. • The power of 10 = number of moves. • The power is positive if the decimal moved to the leftand negative if the decimal moved to the right.

  9. 3-B Conversion from ordinary to scientific Example: 1330 = 1.330 × 103 .00000345 = 3.45 × 10-6 527  103 = 5.27 × 102 × 103 = 5.27 × 105

  10. 3-B Using your Calculator Look for an “EE” key 1.7842  103 1.7842 EE 3 = 1784.2 2.111  107 2.111 EE 7 =21110000 9.1  10-4 9.1 EE -4 = 9.1 E-4

  11. 3-B Multiply or Dividing with scientific notation: Examples: (6.2×103)×(3×105) = (6.2×3)×(103×105) = 18.6×10(3+5) = 1.86×10×108 = 1.86×109 4.2  102= 4.2× 102 8.4  10-5 8.410-5 = .5× 102-(-5) = .5×107 = 5.×10(-1) × 107 = 5.0× 106

  12. More Practice: (3×104)×(8 ×105) = = 24×109 = 2.4×10×109 = 2.4×1010 (6.3×102)×(1.5 ×10) = = 9.45×103

  13. More Practice: (9×103)×(5 ×10-7) = = 45×10-4 = 4.5×10×10-4 = 4.5×10-3 (4.4×1099)∕(2 ×1011) = = 2.2×1088

  14. 3-B Approximations with scientific notation: Example: 14927  2213 ≈ 15000 × 2000 = (1.5×104)× (2 × 103) = 3×107 = 30,000,000 (30 million) check: 14927  2213 = 33,033,451

  15. 3-B More Practice: 9642 / 31 ≈ 9,000 / 30 = (9×103) / (3 × 10) = 3×102 = 300 check: 9642 / 31 = 311.0322...

  16. 3-B More Practice: 7.253 × 291 ≈ 7 × 300 = 7× (3×102) = 21×102 = 2100 check: 7.253 / 291 = 2110.623

  17. 3-B Homework for Wednesday: Pages 164-165 # 10, 16, 18, 20a-c, 24, 26

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