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 Sometimes
scientists have to work with very large and very small numbers. In
this lesson we will learn how to convert very small numbers to
Scientific Notation.
 For
example the diameter of an atom is a tiny number. To make
working with these types of numbers easier, a system for changing them
into a more convenient form was created.
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The system is called
Scientific Notation. |
The method for converting a number into
scientific notation works like this. The original number is broken into
2 factors. (numbers connected by multiplication)
The
first factor must be a number
greater than 1 but less than 10. The
second factor is a power
of 10.
Let's look at an example.
In this example we will convert a very small number into scientific
notation.
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.00000345 is a small
number...right? |
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So let's find the
first factor...
Remember it has to be between 1 and 10. If we place a
decimal point between 3 and 4, we get
000003.45
(Do you see that if you ignore the zeros it is now greater than 1 but less
than 10?) If we put the
decimal anywhere else we would create a number which is greater than
10 or less than 1. As you can see, it can only be placed between
the 3 and the 4. |
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To find the
second factor (a power of 10) we need to pay attention to the
zeros. All
we have to do is count the number of digits (including the zeros) in
front of the decimal point. There is one other very important
rule. When changing very small numbers into scientific
notation we use a negative
exponent for the power of 10.
000003.45
There are 6 digits in front of
the decimal point.
That means that our second factor
is 10 to the negative
sixth power or
10-6 |
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Now we put the 2 factors together
3.45 x 10-6 |
Let's look at another example of a very
small number.
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.00000007108
The first factor must be greater than 1 but less than 10.
00000007.108
(When we write our factor answer we will drop the zeros in front of
the "7") Now we count the digits
in front of the decimal point.
00000007.108
There are 8 digits in
front of the decimal.
Our second factor is10 to the
negative eighth power or 10-8
(remember we use a negative exponent
for small numbers!)
7.108 x 10-8 |
One last example.
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.00000000095
First factor: 9.5(We
drop the zeros)
Second Factor: 10-10
Final Answer: 9.5 x 10-10 |
Let's Practice!
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