Mathematical Notation
Scientific Notation
The speed of light is approximately 300,000,000 meters
per second. Working with a large number such as
this can quickly become awkward and cumbersome. To simplify matters,
we often use scientific
notation to represent very large and very small numbers.
Using scientific notation,300,000,000 m/sec
can also be written as
3 x 100,000,000
or in the shorter form,
3 x 10^{8},
where 8, the exponent,
is the number of zeros.
As you see, the larger or the smaller the number the more
beneficial the use of the scientific notation.
Positive exponents
Large numbers can be written in scientific notation by
moving the decimal point to the left. For example, Avogadro's
number is approximately 602,200,000,000,000,000,000,000 (where the decimal point implicitly resides to the right of the last zero).
Using scientific notation this impressive number is simplified
to: 6.022 x 10^{23 }
The decimal point is moved left to just
after the first number. That first number must be at least 1, but less
than 10. In the example above, the decimal point has been moved 23 places to the left. That number is now the positive exponent of the
base 10.
Negative exponents
Numbers less than 1 can be expressed in scientific notation
by moving the decimal point to the right. For example, how
would we express 0.0006022?
We still have to follow the convention of scientific notation
that the first number must be a least 1, but less than 10. In this
instance, the decimal point needs to move to the right by 4 places to the
first nonzero number. For every place we move the decimal to the right
we decrease the power of ten by one, starting from zero. That number can be written as 6.022
x 10^{4 }.
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In the next section we will introduce setbuilder and interval notations.
SetBuilder and Interval Notations
The Biology Project > Biomath> Notation > Scientific Notation
The Biology Project
Department
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The University
of Arizona
January 2006
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