|
 Sometimes
scientists have to work with very large and very small numbers. In
this lesson we will learn how to convert very large numbers to
scientific notation.
 For
example the number of cells in a human body is a huge 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 is 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 large number into scientific
notation.
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4,870,000,000 is a big
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 4 and 8, we get
4.870000000
(Do you see that 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 4 and the 8. |
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To find the
second factor (a power of 10) we will use a little trick. All
we have to do is count the number of digits after the decimal point
all the way to the end of the number.
4.8 7 0
0 0 0 0 0 0
There are 9 digits after
the decimal point.
That means that our second factor
is 10 to the ninth power or
109 |
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Now we put the 2 factors together
4.87 x 109 |
Let's look at another example of a very
big number.
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20,534,000
The first factor must be greater than 1 but less than 10.
2.0534000
(When we write our factor answer we will drop the zeros after the
"4") Now we count the digits
after the decimal point. 2.0
5 3 4 0 0 0
There are 7 digits
after the decimal.
So our second factor is 10 to the seventh power or 107
2.053 x 107 |
One last example.
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33,051,100,000
First factor: 3.30511(We
drop the zeros)
Second Factor: 1010
Final Answer: 3.30511 x 1010 |
Let's Practice!
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