Transcript Scientific Notation

MAT111
Working with
Scientific Notation
or
Was Scientific Notation Invented
by
Mad Scientists?
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Doctor Frankenstein
• A scientist, Dr. Frankenstein, applied
5.0 x 104 volts for 6.66 x 10-2 seconds to
the terminals on the neck of his monster
• Question: How many orders of
McDonald’s™ supersized fries could he
have fried up using that power instead?
• Answer: Who cares? He was mad.
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Scientific Notation
Another short review…
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Scientific Notation
• Definition
Scientific notation is a format in which a
number is expressed as a number between
1 and 10 multiplied by a power of 10
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Scientific Notation
Converting to Scientific Notation
1. Move the decimal point to come after the
first nonzero digit
1234  1.234 x 10?
2. The power of 10 will be the number of
places the decimal point moves
•
•
The power is positive if the decimal point moves
to the left
1234  1.234 x 103
The power is negative if the decimal point moves
to the right
.01234  1.234 x 10-2
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More Examples
3042  3.042 x 103 (decimal moves 3 places to the left)
0.00012  1.2 x 10-4 (decimal move 4 places right)
226 x 102  (2.26 x 102) x 102 = 2.26 x 104
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More Scientific Notation Tricks
Converting from Scientific Notation
1. The power of 10 tells how many places to
move the decimal point:
•
•
Move it to the right if the power of 10 is positive
Move it to the left if the power of 10 is negative
2. If moving the decimal point creates any
“open places,” fill them with zeros
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Examples
1.23 x 102  123
3.6 x 106  3,600,000
5.7 x 10-3  0.0057
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Scientific Notation
Multiplying or Dividing Scientific Notation
• Separately,
– Operate on the powers of 10
– Operate on the other parts of the number
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Examples
(6 x 102) x (4 x 105) = (6 x 4) x (102 x 105)
= 24 x 107
= 2.4 x 108
(4.2 x 10-2)
4.2
10-2
————— = —— x —— = 0.5 x 10-2 - (-5)
(8.4 x 10-5)
8.4
10-5
= 0.5 x 103
= 5 x 102
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Scientific Notation
Addition or Subtraction with Scientific
Notation
In general, must write numbers in ordinary
notation before adding or subtracting
Except when both numbers have the same power
of 10, then we may factor out the power of 10 first
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Examples
(7 x 1010) + (4 x 1010) = (7 + 4) x 1010
= 11 x 1010
= 1.1 x 1011
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The End!
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