Transcript Scientific Notation

Scientific Notation
Scientific Notation
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A number is in scientific notation when
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There is a number (I’ll call “n”) that is bigger than
or equal to one, but less than ten.
This number “n” is multiplied by a power of ten.
A power of ten is 10 to the something power.
So it will look something like this:
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-3
N x 10
Examples
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Which are in
scientific notation?
3.5 x 103
62.6 x 10-2
0.86 x 108
3.82 x 100-6
4.6 x 100
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Yes
No
No
No
Yes
Writing Numbers in Scientific
Notation
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Move the decimal so that the new number is
greater than or equal to one, but less than
ten (so that there is one nonzero number to
the left of the decimal).
Count the number of places you moved the
decimal (This will be the exponent of 10)
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If the number started out bigger than one, the
exponent will be positive.
If the number started out less than one, the
exponent will be negative.
Examples
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Write in scientific
notation
13,030,000
0.000 092
0.003 5
4,825,000,000
675 million
283 hundred
thousandths
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1.303 x 107
9.2 x 10-5
3.5 x 10-3
4.825 x 109
6.75 x 108
2.83 x 10-3
To change to a standard
number:
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Look at the exponent on the 10.
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If it is positive, MOVE the decimal that
many places to the right.
If it is negative, MOVE the decimal that
many places to the left.
Examples
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Write as a standard
number:
3.84 x 106
6.2 x 10-5
5 x 10-3
1.2345 x 1010
7.91 x 100
5 x (7 x 106)
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3,840,000
0.000 062
0.005
12,345,000,000
7.91
35,000,000
Powers of 10
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When the exponent is positive, it is
telling you how many zeroes you will
have.
When the exponent is negative, it is
telling you how many places you will
have in the number.
Examples
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106
10-3
107
10-5
0.00001
10,000
100,000,000,000
0.01
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1,000,000
0.001
10,000,000
0.00001
10-5
104
1011
10-2