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

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Section 3B Putting Numbers in Perspective Pages 152-164

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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