Subtracting in scientific notation

- [Voiceover] What I
want to do in this video

is get a little bit of
practice subtracting

in scientific notation.

So let's say that I have
4.1 x 10 to the -2 power.

4.1 x 10 to the -2 power

and from that I want to subtract,

I want to subtract 2.6,
2.6 x 10 to the -3 power.

Like always, I encourage
you to pause this video

and see if you can solve this on your own

and then we could work
through it together.

All right, I'm assuming
you've had a go it.

So the easiest thing
that I can think of doing

is try to convert one of these numbers

so that it has the same,
it's being multiplied

by the same power of ten as the other one.

What I could think about doing,

well can we express
4.1 times 10 to the -2?

Can we express it as
something times 10 to the -3?

So we have 4.1 times 10 to the -2.

Well if we want 10 to the
-2 to go to 10 to the -3

we would divide by 10, but
we can't just divide by 10.

That would literally change
the value of the number.

In order to not change it, we want

to multiply by 10 as well.

So we're multiplying by
10 and dividing by 10.

I could have written it like this.

I could have written 10/10 times,

let me write this a little bit neater.

I could have written 10/10 x this

and then you take 10 x 4.1, you get 41,

and then 10 to the -2 divided by 10

is going to be 10 to the -3.

So this right over here,
this is equal to 10 x 4.1

is 41 times 10 to the -3.

And that makes sense.

41 thousandths is the same
thing as 4.1 hundredths

and all we did is we
multiplied this times 10

and we divided this times 10.

So let's rewrite this.

We can rewrite it now as 41 X 10 to the -3

minus 2.6, -2.6 x 10 to the -3.

So now we have two things.

We have 41 X 10 to the
-3 - 2.6 x 10 to the -3.

Well this is going to be the same thing as

41 - 2.6.

- 2.6, let me do it in that same color.

That was purple.

- 2.6, 10 to the -3.

10, whoops, 10 to the -3.

There's 10 to the -3
there, 10 to the -3 there.

One way to think about it,
I have just factored out

a 10 to the -3.

Now what's 41 - 2.6?

Well 41 - 2 is 39, and then
-.6 is going to be 38.4.

38.4 and then you're going to have

times 10 to the -3 power.

x 10 to the -3 power.

Now, this is what the product,

or this is what the difference
of these two numbers is

but this is no longer
in scientific notation.

In order to be scientific notation

this number right over
here has to be between 1,

has to be greater than or equal to 1

and less than 10.

So what we could do is we
could divide this number

right over here by 10.

We can divide this by 10
and then we can multiply,

then we can multi...so we could do this.

We could, kind of the opposite
of what we did up here.

We could divide this by 10
and then multiply by 10.

So if you divide by 10 and multiply by 10

you're not changing the value.

So 38.4 divided by 10 is 3.84

and then all of this business,

10 to the -3, 10 to the -3
x 10 is 10 to the -2 power.

So this is going to be
3.84 x 10 to the -2 power.