Scientific Notation

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Scientific Notation
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Scientific NotationAt the conclusion of our time
together, you should be able to

1. Define scientific notation
2. Convert numbers into scientific notation
3. Convert scientific notation to a standard number

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What is Scientific Notation?

• Scientific notation is a way of expressing really
  big numbers or really small numbers.
• For very large and very small numbers, scientific
  notation is more concise.

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Scientific Notation Consists Of Two Parts

• M A number between 1 and 10
• n A power of 10
• M x 10n

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Scientific Notation

• M x 10n
• M is the coefficient 1ltMlt10
• 10 is the base
• n is the exponent or power of 10

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Other Examples

• 5.45E6
• 5.45 x 106

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Chemical Compound Quiz

• What do sand and water have in common from a
  chemical point of view?
• Oxygen

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• Numbers Less Than 1 Will Have A Negative
  Exponent.
• A millionth of a second is
• 0.000 001 sec 1 x 10-6 s
• 1.0E-6 s 1.0 x 10-6 s

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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.
• 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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Examples

• Given 289 800 000 m
• Use 2.898 m (moved 8 places)
• Answer 2.898 x 108 m
• Easier Way M term smaller, so make n
  term larger - 100 to 108
• Given 0.000 567 m
• Use 5.67 m (moved 4 places)
• Answer 5.67 x 10-4 m
• Easier Way M term larger, so make n term
  smaller - 100 to 10-4

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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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Example

• Given 5.093 x 106 m
• Answer 5 093 000 m (moved 6 places to
  the right)
• Easier Way 106 to 100 n smaller, so make
  M term larger!
• Given 1.976 x 10-4 m
• Answer 0.000 197 6 m (moved 4 places to the
  left)
• Easier Way 10-4 to 100 n larger, so make
  M term smaller!

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Scientific NotationLets see if you can

1. Define scientific notation
2. Convert numbers into scientific notation
3. Convert scientific notation to a standard number

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Learning Check

• Express these numbers in Scientific Notation
• 405 000 cm
• 0.003 872 cm
• 3 000 000 000 cm
• 2 cm
• 0.000 000 478 cm

4.05 x 105 cm 3.872 x 10-3 cm 3 x 109 cm 2 x 100
cm 4.78 x 10-7 cm
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Scientific Notation
Calculations
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Scientific NotationAt the conclusion of our time
together, you should be able to

1. Multiply and divide numbers that are in
   scientific notation
2. Add and subtract numbers that are in scientific
   notation

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Example 16

• (3 x 102 m)(8 x 10-4 m)
• Answer multiply M terms
• 24
• Add n terms
• -2
• 24 x 10-2 m2
• Adjust to correct scientific notation
• 2.4 x 10-1 m2
• Adjust to correct number of sig figs
• 2 x 10-1 m2

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Example 17

• (5.000 x 105 m)/(3500 m)
• Answer divide M terms
• 0.001 428
• Subtract n terms
• 5
• 0.001 428 x 105
• Adjust to correct scientific notation
• 1.428 x 102
• Adjust to correct number of sig figs
• 1.4 x 102

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Example 18

• (5.0 x 104 m)(8.230 x 106 m) /(1.99 x 1018
  m)
• Answer multiply and divide M terms
• 20.678 m
• Add and subtract n terms
• -8
• 20.678 x 10-8 m
• Adjust to correct scientific notation
• 2.0678 x 10-7 m
• Adjust to correct number of sig figs
• 2.1 x 10-7 m

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Example 13

• (5.0 x 10-3 m)-(5.0 x 10-8 m)
• Answer can only subtract like powers
• Adjust to larger power
• (5.0 x 10-3 m)-(0.000050 x 10-3 m)
• 4.999950 x 10-3 m
• Adjust to correct number of decimal places
• 5.0 x 10-3 m
• Adjust to correct scientific notation
• 5.0 x 10-3 m

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Example 14

• (5.0 x 10-3 m) 0.774 m
• Answer can only add like powers
• Adjust to larger power
• (0.0050 x 100 m) 0.774 m
• 0.7790 m
• Adjust to correct number of decimal places
• 0.779 m
• Adjust to correct scientific notation
• 7.79 x 10-1 m

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Example 15

• (5.0 x 10-3 m) (5.0 x 10-4 m) - 0.009 38 m
• Answer can only add like powers
• Adjust to larger power
• (0.0050 x 100 m) (0.000 50 m) 0.009 38 m
• -0.003 88 m
• Adjust to correct number of decimal places
• -0.003 9 m
• Adjust to correct scientific notation
• -3.9 x 10-3 m

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Scientific NotationLets see if you can

1. Multiply and divide numbers that are in
   scientific notation
2. Add and subtract numbers that are in scientific
   notation