Scientific Notation

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Scientific Notation

• Class Notes 11/06/08

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WHY do we use scientific notation?

• Used to show very large or very small numbers
• Example the mass of the Earth is
  5,974,200,000,000,000,000,000,000 kg. It is
  easier to write it in this form 5.9742 1024
  kilograms
• Sci. Not. uses the powers of 10 to show the size
  of things.

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How to write in Scientific Notation

• The general format looks like
• N x 10x
• 4.3 x 102

Exponent shows the number of places the decimal
must be moved
Coefficient Must be greater than or equal to one
and less than 10
BASE Must always be 10
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Changing Scientific Notation to Standard Notation

• Exponents can be NEGATIVE or POSITIVE
• If exp is positive move decimal (in coefficient)
  to the right
• If exp is negative move decimal (in coefficient)
  to the left

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REMEMBER .

• If the exponent is positive the coefficient gets
  bigger
• If the exponent is negative the coefficient gets
  smaller

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EXAMPLES

• Change to standard notation
• 3.45 x 103 mL

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• Change to standard notation
• 8.4 x 108 kg

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• Change to standard notation
• 3.45 x 10-3 L

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• Change to standard notation
• 9.2 x 10-2 ºC

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Standard Notation

• Standard Notation is how you normally write a
  number.
• Example 62,987 kg

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Changing from Standard Notation to Scientific
Notation

• 1. Find the decimal in the measurement
• 2. Move the decimal so that there is only
• ONE number (1-9) to the left of the decimal
• 3. Count how many places you had to move
• the decimal (this becomes the exponent)
• 4. Determine if the exponent is or -

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Changing from Standard Notation to Scientific
Notation

• How to determine if the exponent is or -
• 5. If you start with a number GREATER than 1,
  your exponent will be POSITIVE, and
• 6. if you start with a number LESS than 1, your
  exponent will be NEGATIVE.

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Practice Problems

• Change to Scientific Notation
• 98,000 cm

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• Change to Scientific Notation
• 34,789 cm

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• Change to Scientific Notation
• 0.00067 cm

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• Change to Scientific Notation
• 0.00457 cm

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• Change to the correct format
• 995.06 X 104

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Change to the correct format 0.009506 X 104
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Change to the correct format 0.009506 X 10-4
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Change to the correct format 995.06 X 10-4