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.
• Numbers expressed in scientific notation can be
  used in a calculation with far greater ease.

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Scientific notation two parts

• A number between 1 and 10 possibly followed by a
  decimal point and more numbers
• 1,2,3,4,5,6,7,8,or 9
• A power of 10
• N x 10z

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How to convert into Scientific Notation

• Rewrite all the digits as a number with only one
  digit in front of the decimal point and the rest
  of the digits after it.
• Count the number of places you moved the decimal
  point
• If you had to move the decimal point to the left,
  the exponent of the power of ten is positive.
• If you had to move the decimal point to the
  right, the exponent of the power of ten is
  negative.

http//www.stkate.edu/ysng/CLASSES/Independent/Me
ti/scientificnotation.html
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Examples

• Given 289,800,000
• Use 2.898 (moved 8 places)
• Answer 2.898 x 108
• Given 0.000567
• Use 5.67 (moved 4 places)
• Answer 5.67 x 10-4

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Practice Problems - Converting to Scientific
Notation
3.78 x 105

• 378000
• 0.00934
• 0.00000083
• 1.9284
• 34.903
• 783920

9.34 x 10-3
8.3 x 10-7
1.9284 x 10 0
3.4903 x 101
7.83920 x 105
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To change scientific notation to standard form

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

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Examples

• Given 5.093 x 106
• Answer 5,093,000
• (moved 6 places to the right)
• Given 1.976 x 10-4
• Answer 0.0001976
• (moved 4 places to the left)

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Practice Problems - Converting back to Standard
Form
149300

• 1.493 x 105
• 2.908 x 10-4
• 3.90284 x 102
• 1.333 x 10-1
• 6.0000009 x 107
• 2.345 x 104

0.0002908
390.284
0.1333
60000009
23450