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