Section 3B Putting Numbers in Perspective Pages 154-171

3-B Scientific Notation Absolutely critical for very large and very small numbers Ex1/155 The federal debt is $9,100,000,000,000. The diameter of a hydrogen nucleus is 0.0000000000000001 meter. Your calculators automatically use it!

3-B Scientific Notation 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: 9,100,000,000,000 = 9.1  1012 = 9.1 E 12 (calculator) 0.0000000000000001 = 1.0  1016 = 1 E -16 (calculator)

Scientific Notation 109 = 1 billion = 1,000,000,000 106 = 1 million = 1,000,000 109 = 1 billion = 1,000,000,000 1012 = 1 trillion = 1,000,000,000,000 The U.S. federal debt is about $9.1 trillion ($9.1×1012)

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

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

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

Using your Calculator Look for an “EE” key 1.7842  103 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 = 0.00091 1000 = 1.0 x 103 1.0 EE 3 not (10) EE 3

More Practice 25/164 Convert from scientific to ordinary 27/164 Convert from ordinary to scientific. 33/164 Total annual energy consumption in the US is about 100,000,000,000,000,000,000 joules. 35/164 The hard drive on my computer has a capacity of 12.0 gigabytes (recall ‘giga’ = billion). 37/164 The diameter of a typical bacterium is about 0.000001 meter.

Multiply or Dividing with scientific notation: 3-B Examples: 6200 x 300000 (6.2  103)× (3  105) = (6.2×3)×(103×105) = 18.6×10(3+5) = 1.86 ×10 x 108 = 1.86 x 109 420 4.2  102 = 4.2 × 102 .000084 8.4  10-5 8.4 10-5 = .5×102-(-5) = .5×107 = 5.×10(-1) x 107 = 5.0 x 106 More Practice 29/168

Why Scientific Notation: Approximations 3-B Why Scientific Notation: Approximations Example: 14927  2213 ≈ 15000 × 2000 = (1.5×104)× (2 × 103) = 3×107 = 30,000,000 (30 million) check: 14927  2213 = 33,033,451 More Practice: Ex2/155 8 million residents produce 1.8 lb or .0009 tons of trash each day. Estimate the total amount of trash produced each day. [225 tons?]

Why Scientific Notation: Calculator Issues 3-B Why Scientific Notation: Calculator Issues Total annual energy consumption in the US is about 100,000,000,000,000,000,000 joules. Convert to kilowatt-hours. = .278 x 1014 = 2.78 x 10(-1) x 1014 = 2.78 x 1013

Homework: Pages 168 # 26 28, 34, 36, 38, 40