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Let's look at scientific notation.
Scientific notation is a way to express or
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rewrite a large number or a small number
in a concise way. For example, let's write
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569,000 in scientific notation. Now, to
write a number in scientific notation
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means the following. It means we can
rewrite it in the form a ten^n where a
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an absolute value is between one and ten
and n is an integer. So, the first thing
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we need to do here with our number is to
move the decimal point until we get a
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number whose absolute value is between one
and ten.
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And you might be thinking, there is no
decimal point here. But isn't 569,000 =
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569,000.00? So, there is a decimal point.
So, if we move this decimal point one,
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two, three, four, five places to the left,
we get 5.69 which is equal to our a here.
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It's the number we're looking for here
whose absolute value is between one and
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ten.
Now, what about n? We need to find an
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integer n such that 5.69 ten^n =
569,000. Well, since we moved the decimal
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point five units to the left, to go from
here to here, going in the other
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direction, we'd have to multiply by ten^5,
or n = five.
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That is, 5.69 ten^5 = 569,000.
Therefore, our answer is 5.69 ten^5.
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And let's check this. What is 5.69
ten^5?
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This is equal to 5.69 ten ten ten
ten ten, five times. Or, 5.69 100,000,
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which is 569,000. So, to go from a big
number to scientific notation, n is
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positive. What about the other way? In
other words, what about going from a small
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number to scientific notation? Again,
we'll need to find our a and our n where a
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is a number, an absolute value between one
and ten, and n is an integer. So, let's
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look at our number here, -0.000000691. In
order to find our a, we need to move this
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decimal point one, two, three, four, five,
six, seven places to the right. Therefore,
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a = -6.91. But, what about our n? We need
to find an integer n such that -6.91
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ten^n = -0.000000691.
Well, since we moved our decimal point
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seven units to the right to get to a, then
to go in the other direction, we'll need
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to multiply by ten^-7.
So, n here will be -seven.
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That is -6.91 ten^-7 = -0.00000069 one.
So, our answer then is this -6.91
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ten^-7.
And again, let's check or verify that this
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is true. -6.91 ten^-7 is the same as
-6.91 one / ten^7, which is equal to
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-6.91 one / 10,000,000, seven zeroes, or
-6.91 / 10,000,000 which is -0.000000691.
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So, to go from a small number to
scientific notation, n will be negative.
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And this is how we write numbers in
scientific notation. Thank you, and we'll
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see you next time.