Scientific Notation

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Scientific Notation
Let's talk about.....

• Standard Form Scientific Notation

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Numbers in Standard Form

• Numbers written in Standard Form look
• like the numbers we see every day.
• Ex. 0.00457 , 18,900.
• Notice the decimal in red.

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Making the ChangeStandard Form
Scientific Notation

• For whole numbers, move the decimal to the LEFT
  until you get a number that is
• Greater than or equal to 1, and
• Less than 10
• Ex. 18,900. 1.8900

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Making the ChangeStandard Form
Scientific Notation

• The new decimal is then multiplied by 10x, where
  x represents the number of times you moved the
  decimal to the LEFT.
• 18,900. 1.89
• x 4
• 1.89 x 104

There is no need to write the zeros!
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Making the ChangeStandard Form
Scientific Notation

• You have just written a number in ..
• Scientific Notation!
• 18,900 1.89 x 104

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Making the ChangeStandard Form
Scientific Notation

• For rational numbers in the form of a decimal,
  move the decimal to the RIGHT until you get a
  number that is
• Greater than or equal to 1, and
• Less than 10
• Ex. 0.00457 4.57

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Making the ChangeStandard Form
Scientific Notation

• The new decimal is then multiplied by 10-x, where
  x represents the number of times you moved the
  decimal to the RIGHT.
• 0.00457 4.57
• x 3
• 4.57 x 10-3

There is no need to write the zeros!
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Making the ChangeScientific Notation
Standard Form

• To take a number in Scientific Notation and write
  it in Standard Form, you work
• BACKWARDS!
• Remove the multiplication by 10x
• Move your decimal to the RIGHT or LEFT x number
  of places.

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Making the ChangeScientific Notation
Standard Form

• 1.89 x 104
• 1.89
• If your bowls ( ) are empty, fill them
  with zeros.
• 1.8900

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Making the ChangeScientific Notation
Standard Form

• 4.57 x 10-3
• 4.57
• If your bowls ( ) are empty, fill them
  with zeros.
• 004.57

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Making the ChangeScientific Notation
Standard Form

• Rewrite the number in standard form, removing the
  bowls.
• 1.8900 18,900.
• 004.57 0.00457

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Making the ChangeScientific Notation
Standard Form

• Congratulations! You have just taken a number
  written in scientific notation and changed it
  back into its standard form!
• 1.89 x 104 1.8900 18,900.
• 4.57 x 10-3 004.57 0.00457

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Making the Change Standard Form
Scientific Notation

• To learn more about changing back and forth
  between standard form and scientific notation,
  click on the link below.
• http//www.purplemath.com
• - Click on the Lesson Index link