1. Scientific Notation

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1. Scientific Notation

• Every positive number X can be written as
• (1 lt N lt 10) x 10some positive or negative
  integer
• Where N represents the numerals of X with the
  decimal point after the first nonzero digit.

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2. Positive Exponents

• 101 10
• 102 10X10 100
• 103 10X10X10 1000
• 104 10X10X10X10 10,000

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3. Negative Exponents

• 10-1 1/10 0.1
• 10-2 1/100 0.01
• 10-3 1/1000 0.001
• 10-4 1/10000 0.0001

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4. Scientific Notation

• We use the idea of exponents to make it easier to
  work with large and small numbers.
• 10,000 1 X 104
• 250,000 2.5 X 105
• Count places to the left until there is one
  number to the left of the decimal point.
• 230,000 ?
• 35,000 ?

2.3 x 105
3.5 x 104
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5. Scientific Notation Continued

• 0.00006 6 X 10-5
• 0.00045 4.5 X 10-4
• Count places to the right until there is one
  number to the left of the decimal point
• 0.003 ?
• 0.0000025 ?

3 x 10-3
2.5 x 10-6
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Multiplying with Scientific Notation

• Add the Exponents
• 102 X 103 105
• 100 X 1000 100,000

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Multiplying with Scientific Notation

• (2.3 X 102)(3.3 X 103)
• 230 X 3300
• Multiply the Coefficients
• 2.3 X 3.3 7.59
• Add the Exponents
• 102 X 103 105
• 7.59 X 105
• 759,000

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Multiplying with Scientific Notation

• (4.6 X 104) X (5.5 X 103) ?
• (3.1 X 103) X (4.2 X 105) ?

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Dividing with Scientific Notation

• Subtract the Exponents
• 104/103 101
• 10000X 1000 10

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Dividing with Scientific Notation

• (3.3 X 104)/ (2.3 X 102)
• 33000 / 230 143.4783
• Divide the Coefficients
• 3.3/ 2.3 1.434783
• Subtract the Exponents
• 104 / 102 102
• 1.4347823 X 102
• 143.4783

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Dividing with Scientific Notation

• (4.6 X 104) / (5.5 X 103) ?
• (3.1 X 103) / (4.2 X 105) ?