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

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is get a little bit of[br]practice subtracting

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in scientific notation.

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

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4.1 x 10 to the -2 power

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and from that I want to subtract,

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

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Like always, I encourage[br]you to pause this video

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and see if you can solve this on your own

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and then we could work[br]through it together.

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

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So the easiest thing[br]that I can think of doing

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is try to convert one of these numbers

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so that it has the same,[br]it's being multiplied

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by the same power of ten as the other one.

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What I could think about doing,

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

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

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So we have 4.1 times 10 to the -2.

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Well if we want 10 to the[br]-2 to go to 10 to the -3

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

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That would literally change[br]the value of the number.

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In order to not change it, we want

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to multiply by 10 as well.

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So we're multiplying by[br]10 and dividing by 10.

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I could have written it like this.

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I could have written 10/10 times,

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let me write this a little bit neater.

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I could have written 10/10 x this

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

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and then 10 to the -2 divided by 10

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is going to be 10 to the -3.

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

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is 41 times 10 to the -3.

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And that makes sense.

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41 thousandths is the same[br]thing as 4.1 hundredths

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and all we did is we[br]multiplied this times 10

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and we divided this times 10.

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So let's rewrite this.

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

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

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So now we have two things.

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

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Well this is going to be the same thing as

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41 - 2.6.

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

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That was purple.

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- 2.6, 10 to the -3.

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10, whoops, 10 to the -3.

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There's 10 to the -3[br]there, 10 to the -3 there.

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

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a 10 to the -3.

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Now what's 41 - 2.6?

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

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38.4 and then you're going to have

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times 10 to the -3 power.

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x 10 to the -3 power.

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Now, this is what the product,

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or this is what the difference[br]of these two numbers is

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but this is no longer[br]in scientific notation.

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In order to be scientific notation

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this number right over[br]here has to be between 1,

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has to be greater than or equal to 1

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and less than 10.

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So what we could do is we[br]could divide this number

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right over here by 10.

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We can divide this by 10[br]and then we can multiply,

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

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

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We could divide this by 10[br]and then multiply by 10.

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So if you divide by 10 and multiply by 10

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you're not changing the value.

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So 38.4 divided by 10 is 3.84

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and then all of this business,

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10 to the -3, 10 to the -3[br]x 10 is 10 to the -2 power.

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