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# Multiplying & dividing in scientific notation

Video transcript

We have 7 times 10 to
the fifth over 2 times 10 to the negative 2 times
2.5 times 10 to the ninth. So let's try to simplify
this a little bit. And I'll start off by trying to
simplify this denominator here. So the numerator's just
7 times 10 to the fifth. And the denominator,
I just have a bunch of numbers that are being
multiplied times each other. So I can do it in any order. So let me swap the order. So I'm going to do over
2 times 2.5 times 10 to the negative 2
times 10 to the ninth. And this is going to be equal
to-- so the numerator I haven't changed yet-- 7 times
10 to the fifth over-- and here in the
denominator, 2 times-- let me do this in
a new color now. 2 times 2.5 is 5. And then 10 to the negative
2 times 10 to the ninth, when you multiply
two numbers that are being raised to exponents
and have the exact same base-- so it's 10 to the negative 2
times 10 to the negative 9-- we can add the exponents. So this is going to be
10 to the 9 minus 2, or 10 to the seventh. So times 10 to the seventh. And now we can
view this as being equal to 7 over 5 times
10 to the fifth over 10 to the seventh. Let me do that in
that orange color to keep track of the colors. 10 to the seventh. Now, what is 7 divided by 5? 7 divided by 5 is equal to--
let's see, it's 1 and 2/5, or 1.4. So I'll just write it as 1.4. And then 10 to the fifth
divided by 10 to the seventh. So that's going to be
the same thing as-- and there's two
ways to view this. You could view this as
10 to the fifth times 10 to the negative 7. You add the exponents. You get 10 to the negative 2. Or you say, hey, look,
I'm dividing this by this. We have the same base. We can subtract exponents. So it's going to be
10 to the 5 minus 7, which is 10 to the negative 2. So this part right over here is
going to simplify to times 10 to the negative 2. Now, are we done? Have we written what we have
here in scientific notation? It looks like we have. This value right over here is
greater than or equal to 1, but it is less
than or equal to 9. It's a digit between 1
and 9, including 1 and 9. And it's being multiplied
by 10 to some power. So it looks like we're done. This simplified to 1.4
times 10 to the negative 2.