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In the world of science, scientists often work with very
small numbers, like the diameter of
a cell, or very large numbers,
like the number of miles from the earth to the sun. In order
to make these numbers easier to work with they have developed a
system called
scientific notation. In this lesson, we will learn how to
translate numbers from scientific notation into standard form.
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A number written in
scientific notation
has 2 (two) factors.
**The first
factor is a number greater than, or equal to 1,and
also less than 10.
**The second factor is a power of 10.
If
the number we are expressing in scientific notation is greater than
1, then the power of 10 will be expressed with a
positive
exponent.
For example 105. But, if the number we
are expressing is between 0 and 1 we use a
negative
exponent for the power of 10.
For example: 10-6. |
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Before we go any further let's look at an example. Let's
imagine that the distance from planet Matho to planet Numero is
85,000,000,000 miles (that's 85 billion
miles!). Using scientific
notation our first term will be 8.5
( remember the first term must be between 1 and 10!),
and the second term will be 1010.
8.5 X 1010 .
Some of you may be asking where did the exponent
10 come from? Let me explain.
If you count the number of places between the end of the number and
where we have placed the decimal point (between the 8 and the 5) you
will discover that we have moved the decimal a total of 10 places!
So the
exponent is determined by how many places the decimal point has
moved from the original number to the number expressed in
scientific notation.
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Let's look at
another example.
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This time we will express a
very small number with
scientific notation.
If the diameter of a red blood cell is .00075 centimeters, how would
you express that in scientific
notation?
Again, remember the first factor must be a number between 1 and 10,
so it must be 7.5. The second factor is a power of 10, and we
determine the exponent by counting how many places the decimal point must
move from where it begins in the original number, to where it ends
up between the 7 and the 5.
We also will be using a
negative exponent because we are
working with a number
that is less than 1.
.00075 = 7.5 X 10-4
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Before we go to the practice page let's look at one more example of
the use of scientific notation
for a very large, and a very small number.
The distance from Earth to
the Sun is 93,000,000 miles.
In scientific notation that would be: 9.3 X 107
A micro-ampere is .000001 of
an ampere.
In
scientific notation that would be: 1 X 10-6
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