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Scientific
Notation Tutorial
Part 1
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Science deals with both very
large and very small numbers. For example, the diameter of the Earth is
about 13,000,000 meters. The radius of a hydrogen atom is 0.00000000012
meters. Consequently,scientists use a "shorthand" way (scientific
or exponential notation) to write very large or very small numbers. Scientific
notation expresses numbers as powers of ten. For
example:
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1 = 100
10 = 101
100 = 102
1000 = 103
10,000 = 104
100,000 = 105
1,000,000 = 106
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0.1 = 1/10 = 10-1
0.01 = 1/100 = 10-2
0.001 = 1/1000 = 10-3
0.0001 = 1/10,000 = 10-4
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In general, any number X can be written as
the product of another number N and a power of ten. It's important to
remember that 1 < N <10. In other words, N MUST be at least
1 but less than 10.
The general format for a number written in
scientific notation will be:
N x 10power
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Examples:
20 = 2 x 10 = 2 x 101
3500 = 3.5 x 1000 = 3.5 x 103
0.0055 = 5.5 x 0.001 = 5.5 x 10-3
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Converting a Number into Proper Scientific
Notation
Find all of the significant figures in the
number. Re-write those digits as a number with 1 digit in front of the
decimal point and the rest of the digits after the decimal point (i.e.
as a number greater than or equal to 1 but less than 10)
Look at the new number you have written.
Count the number of places you must move the decimal point in order to
get back to where the decimal point was originally located.
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If you have to move the decimal point
to the right to get the original
number, then write the exponent as a positive
number.
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If you have to move the decimal point
to the left to get the original
number, then write the exponent as a negative
number.
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Examples:
Write 22,650,000 in proper
scientific notation:
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Write all significant figures as a number
> 1 but <10:
22,650,000 = 2.265 x 10?
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To get back to the original number the
decimal place must be moved 7 places to the right so the exponent
will be positive 7.
22,650,000 = 2.265 x 107.
Write 0.0004050 in proper
scientific notation:
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Write all significant figures as a number
> 1 but < 10:
0.0004050 = 4.050 x 10?
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To get back to the original number, the
decimal place must be moved 4 places to the left so the exponent will
be negative 4.
0.0004050 = 4.050 x 10-4
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Practice Problems
Express the following numbers
using proper scientific notation.
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13,000,000
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7500.3
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209,000
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0.00970
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0.0000605
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0.00300
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