SCIENTIFIC NOTATION

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SCIENTIFIC NOTATION

• A QUICK WAY TO WRITE
• REALLY, REALLY BIG
• OR
• REALLY, REALLY SMALL NUMBERS.

2
Mathematicians are Lazy!!!

• They decided that by using powers of 10, they can
  create short versions of long numbers.

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Scientific Notation

• A number is expressed in scientific notation when
  it is in the form
• a x 10n
• where a is from 1 to 9
• and n is an integer
• 23 X 105 is not in proper scientific notation.
  Why?

4
Soooo

• 137,000,000 can be rewritten as
• 1.37 X 108

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Now You Try
Using scientific notation, rewrite the following
numbers. 347,000. 3.47 X 105 902,000,000. 9.02 X
108 61,400. 6.14 X 104
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Try These

• 4,000
• 4 X 103
• 2.48 X 103
• 2,480
• 6.123 X 106
• 6,123,000
• 306,000,000
• 3.06 X 108

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Your Turn

• Using Scientific Notation,
• rewrite the following numbers.
• 0.000882
• 8.82 X 10-4
• 0.00000059
• 5.9 X 10-7
• 0.00004
• 4 X 10-5

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More Examples

• 1) 0.0004
• 4 X 10-4
• 2) 1.248 X 10-6
• .000001248
• 3) 6.123 X 10-5
• .00006123
• 4) 0.00000306
• 3.06 X 10-6
• 5) 0.000892
• 8.92 X 10-4

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Using your calculator

• Express 4.58 x 106 in decimal notation.
• 4,580,000
• On the graphing calculator, scientific notation
  is done with the button.
• 4.58 x 106 is typed 4.58 6

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Use a calculator to evaluate 4.5 x
10-5 1.6 x 10-2

• Type 4.5 -5 1.6 -2
• You must include parentheses if you dont use
  those buttons!!
• (4.5 x 10 -5) (1.6 x 10 -2)
• 0.0028125
• Write in scientific notation.
• 2.8125 x 10-3

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Use a calculator to evaluate 7.2 x
10-9 1.2 x 102On the calculator, the answer
is

• 6.E -11
• The answer in scientific notation is
• 6 x 10 -11
• The answer in decimal notation is
• 0.00000000006

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Use a calculator to evaluate (0.0042)(330,000).O
n the calculator, the answer is

• 1386
• The answer in decimal notation is
• 1386.
• The answer in scientific notation is
• 1.386 x 103

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Use a calculator to evaluate (3,600,000,000)(23).
On the calculator, the answer is

• 8.28 E 10
• The answer in scientific notation is
• 8.28 x 10 10
• The answer in decimal notation is
• 82,800,000,000

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Write in PROPER scientific notation.(Notice the
number is not between 1 and 10)234.6 x 109

• 2.346 x 1011
• 0.0642 x 104
• on calculator 642
• 6.42 x 10 2