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Welcome to the presentation on multiplying decimals.

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Let's get started.

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So I think you'll find out that multiplying decimals is not a

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lot more difficult than just multiplying regular numbers.

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And I'll show you in a problem.

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Let me pick some random numbers.

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Let's say I had 7,518.

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Actually, let's make that's 75.18.

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Clearly you can tell I'm doing this on the fly.

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75.18 times 0.97.

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So first you look at this problem you're like,

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oh boy, that's tough.

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These decimals-- I don't even know how to approach it.

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Well this is what you do.

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You ignore the decimals when you start the problem and you

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pretend like it's just a regular multiplication problem.

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And if you ignore the decimals like I said, at

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the beginning, 7,518 on top and 97 on the bottom.

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And if that doesn't make sense let me just show you.

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I'm just going to ignore the decimals and do this like a

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normal multiplication problem.

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So normal multiplication.

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I'd start at the 1's place right here.

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I'd say 7 times 8.

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Well, 7 times 8 is 56.

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Carry the 5.

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7 times 1 is 7.

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Plus the 5 is 12.

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2 down here.

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Carry the 1.

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7 times 5 is 35.

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Plus the 1 is 36.

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Put the 6 here.

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Carry the 3.

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And then 7 times 7 is 49.

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Plus 2 is 52.

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So just put 52 here.

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So just like normal multiplication we just took the

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1's place right here, the 7, so it's actually not the 1's, but

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we're ignoring the decimals so if there were no decimals this

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would be the 1's place.

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And we're multiplying it by the top number.

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7 times 7,518 is equal to 52,626.

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And like regular multiplication, we

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do the 10's place.

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And this isn't really the 10's place, but if you ignore

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the decimals it would be.

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And let's cross all this stuff out since we're not using it.

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9 times 8 is 72.

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Carry the 7.

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9 times 1 is 9.

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Plus 7 is 16.

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Carry the 1.

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9 times 5 is 45.

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This is good practice for me too, I haven't done

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my multiplication tables in a long time.

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9 times 5 is 45.

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Plus 1 is 46.

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Carry the 4.

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9 times 7 is 63.

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Plus 4 is 67.

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Now we add.

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So you're probably thinking, boy, what do decimals have

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to do with this at all.

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I'm just doing a regular multiplication problem.

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And I'll show you.

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Actually the decimals only come in right at the very end.

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So what I do is now I just add like I do a regular level

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4 multiplication problem.

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So I say 6 plus 0 is 6.

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2 plus 2 is 4.

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6 plus 6 is 12.

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Carry the 1.

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1 plus 2 plus 6 is 9.

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5 plus 7 is 12.

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Carry the 1.

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1 plus 6 is 7.

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OK, so now here's where the decimals come into play.

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And your I think you're going to be shocked by how

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straightforward this is.

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What I do is I go back to the original problem and now I

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actually pay attention to the decimals.

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And I say, how many total numbers are behind

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the decimal point?

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Well, there's 1 number behind the decimal point, 2 numbers

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behind the decimal point, 3 numbers behind the decimal

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point, 4 numbers behind the decimal point.

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1, 2, 3, 4.

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So there are 4 numbers behind the decimal point in the

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problem I did, and I just count here.

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1, 2, 3, 4.

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The answer will also have 4 numbers behind the decimal

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point, and that's the answer.

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72.9246.

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Now let me ask you a question.

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If I had a 0 here, would that count as an extra number

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behind the decimal point?

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Well, it only would have been if you actually used the

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0 in the multiplication.

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Maybe that confuses you.

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What I would recommend if you have any trailing 0's

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with a decimal like this.

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you actually should just ignore those 0's and then do the

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problem just the way I did it.

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And when remember, that's only for trailing 0's.

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If this was the bottom number then that 0 would matter

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because it's not a trailing 0, it's actually part

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of the number.

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Let's do a couple more examples and I think that'll make sense.

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So let's say I had 5-- and I'm going to do a simpler

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example arithmetically.

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I think it'll help you with some principles.

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If I said 5.10 times 1.09.

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So there's two things we could do.

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We could just multiply it the way it is.

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Actually let's do it both ways and I'll show you you get the

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same answer whether or not you ignore that 0.

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So in the first case let's not ignore the 0.

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Let's use that 0, even though that trailing 0 in the

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decimal-- 5.10 is the same thing as 5.1.

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But let's use it.

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9 times 0 is 0.

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9 times 1 is 9.

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9 times 5 is 45.

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And in the 0's place you put a 0 and then 0

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times everything is 0.

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0 times 0, 0 times 1, 0 times 5.

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Put two 0's here.

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And then 1 times 0 is 0.

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1 times 1 is 1.

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And 1 times 5 is 5.

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And now we add it all.

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We get 0, 9, 5, 5, 5.

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And like we did before, we just count the decimals.

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1, 2, 3, 4.

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So 1, 2 3, 4.

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So the decimal will go here.

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So we got 5.5590 as the answer.

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Now what if we did like I was recommending, we

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actually ignored the 0?

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And I can actually rewrite it as 1.09 times 5.1.

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Because you know in multiplication order

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doesn't matter.

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a times b is the same thing as b times a.

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2 times 3 is the same thing as 3 times 2.

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So 1.09 times 5.1 is the same thing as 5.1 times 1.09.

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So let's just multiply this out.

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And notice, these are the same numbers.

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All I did is I took the 0 off.

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So first, I just ignore the decimals I say 1 times 9 is 9.

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1 times 0 is 0.

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1 times 1 is 1.

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Put a 0 here.

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5 times 9 is 45.

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Carry the 4.

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5 two 0 is 0.

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Plus 4 is 4.

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5 times 1 is 5.

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Now I add.

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9, 5, 5, 5.

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Now I'm at the point that I can actually pay attention

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to the decimal points.

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How many numbers are behind the decimals?

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Well, there's 1, 2, 3.

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So I go 1, 2, 3 and put the decimal point right here.

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Notice I got the same exact answer.

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The only difference is that this one had a trailing 0,

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which really doesn't make a number any different.

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I could add a hundred 0's here and the number's really

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not a different number.

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If you were a computer programmer or a statistician

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of some kind, this could be an important number.

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But ignore what I just said.

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And for your purposes, these trailing 0's mean nothing.

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Same way a leading 0 actually wouldn't mean nothing.

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No one ever does that.

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Well, let me see how much time I have.

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I have 2 more minutes.

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Let me do one more problem just to maybe hit the point home.

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You know, this is really no different than level

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4 multiplication.

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And at the end you just have to count the numbers

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behind the decimal point.

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So 5 times 5 is 25.

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Whoops.

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25.

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I'm already getting messy.

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Carry the 2.

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5 times 7 is 35.

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Plus 2 is 37.

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Bring down the 7, carry the 3.

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5 times 0 is 0.

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Plus 3.

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So it's 375, ignore that blob.

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I'm sorry for being so messy.

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And then you put a 0.

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1 times 5 is 5.

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1 times 7 is 7.

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Ignore that.

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Now we add.

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We say 5 plus 0 is 5.

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7 plus 5 is 12.

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1 plus 3 plus 7 is 11.

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So we got our answer, now we just have to

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count the decimals.

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So here we have 1, 2, 3, 4, 5 numbers behind

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the decimal point.

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But in our answer we only have 4 digits, so how can we get 5

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numbers behind the decimal point?

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Well, we start here.

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We say 1, 2, 3, 4 and we need one more number behind the

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decimal point, so we add a 0 here.

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And then we put the decimal point.

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See what I just did.

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We had to have 5 numbers behind the decimal point.

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And we only had 4 numbers in the answer.

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So I added a leading 0 and then put the decimal point.

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And now we have 5 numbers behind the decimal point.

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And I've shown you a very mechanical way of doing this.

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Hopefully in the future I can give you a seminar on actually

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why this method of counting the numbers behind the decimal

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points actually works.

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But I think you are ready to try some problems on

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multiplying decimals.

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Have fun.

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