Scientific Notation

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Scientific Notation
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What is scientific notation?

• Scientific notation is a way of expressing really
  big numbers or really small numbers.
• It is most often used in scientific
  calculations where the analysis must be very
  precise.

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Why use scientific notation?

• For very large and very small numbers, these
  numbers can be converted into scientific notation
  to express them in a more concise form.
• Numbers expressed in scientific notation can be
  used in a computation with far greater ease.

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Scientific notation consists of two parts

• A number between 1 and 10
• A power of 10
• N x 10x

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Changing standard form to scientific notation.
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To change standard form to scientific notation

• Place the decimal point so that there is one
  non-zero digit to the left of the decimal point.
• Count the number of decimal places the decimal
  point has moved from the original number. This
  will be the exponent on the 10.

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Continued

• If the original number was less than 1, then the
  exponent is negative. If the original number was
  greater than 1, then the exponent is positive.

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Example 1

• Given 289,800,000
• Use 2.898 (moved 8 places)
• Answer 2.898 x 108

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Example 2

• Given 0.000567
• Use 5.67 (moved 4 places)
• Answer 5.67 x 10-4

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Practice Problems

• Answer each questions by converting the given
  standard form
• to the correct scientific notation.
• 1) 378000
• 2) 0.00934
• 3) 0.000000983
• 4) 1.9284
• 5) 34.903
• 6)783920
• 7) 1039
• 8) 0.167
• 9) 90.3827
• 10) 12.34

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Changing scientific notation to standard form.
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To change scientific notation to standard form

• Simply move the decimal point to the right for
  positive exponent 10.
• Move the decimal point to the left for negative
  exponent 10.
• (Use zeros to fill in places.)

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Example 3

• Given 5.093 x 106
• Answer 5,093,000 (moved 6 places to the right)

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Example 4

• Given 1.976 x 10-4
• Answer 0.0001976 (moved 4 places to the left)

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Practice Problems Part II

• Answer each questions by converting the given
• scientific notation to the correct standard form.
• 1) 1.493 x 105
• 2) 2.908 x 10-4
• 3) 3.90284 x 102
• 4) 1.333 x 10-1
• 5) 6.0000009 x 107
• 6) 2.345 x 104
• 7) 4.56343 x 100
• 8) 7.904 x 10-3
• 9) 3.5093 x 10-6
• 10) 2.309 x 10-2