Scientific Notation

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Scientific Notation

• Lesson 9-lab

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What is scientific notation?

• It is a method that scientists use to express
  very large and very small numbers.
• We use exponents with a base of 10 to express
  place value.

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Remember
100 102
1,000
103
10,000
104
107
10,000,000
1011
100,000,000,000
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Strategy for Large Numbers

• Place a decimal point after the first digit.
• The nonzero part of the expression will be called
  the coefficient. The coefficient will always be
  between 1 and 10.
• Count the number of spaces it takes to get to the
  end of the number.
• That number of spaces will be the exponent for
  the base of 10.

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Example Write 93,000,000 in scientific notation.
9.3 is the coefficient.
.
9 3 0 0 0 0 0 0
It takes 7 spaces to get to the end.
9.3 x 107
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Strategy for Small Numbers

• Place the decimal point after the first nonzero
  digit.
• The nonzero part will be the coefficient.
• Count the spaces between your new decimal point
  and the original one.
• The number of spaces you moved back will be your
  negative exponent.

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Example Write 0.0000023 in scientific notation.
.
0. 0 0 0 0 0 2 3
2.3 is the coefficient.
There are 6 spaces between the new decimal point
and the old one.
The negative exponent shows us that we are going
left on the number line.
2.3 x 10-6
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Homework Time!