Learn about Multiplying decimals Video

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Learn about Multiplying decimals

Welcome to the presentation on multiplying decimals. Let's gets started. So I think you'll find out that multiplying decimal is not a lot more difficult than just multiplying regular numbers and I show you in the problem. So let say let me pick some random numbers. Let say I had 7518 actually let's make that 75.18. Clearly you can tell I'm doing this on apply. 75.18 x 0.97 so at first you look at this form like, “Oh boy, that’s tough this decimals I don’t really know how to approach it.” Well this is what you do, you ignore the decimals and you start the problem and you pretend like it just a regular multiplication problem. And if you ignore the decimals and you would be like I said at beginning 7518 on top and 97 on the button and if that doesn’t make sense let me just show you. I'm just going to ignore the decimals and do this like a normal multiplication problem. So normal multiplication I'd started at the one place right here and it say 7 x 8 is 56 carry the five, 7 x 1 is 7 plus the five is 12, 2 down here carry the one, 7 x 5 is 35 plus the one is 36, six here carry the three and then 7 x 7 is 49 + 2 is 52 so put 52 here. So just like normal multiplication we just took the once place right here at the seven that’s actually not the one but we’re ignoring the decimals so there were no decimal this should be the ones place and we’re multiplying it by the top number 7 x 7518 is equal to 52626. Its like regular multiplication we do the tens place, this isn’t really the tens place but if you ignore the decimals but let's cross all this top answer so that you see. 9 x 8 = 72, carry the 7, 9 x 1 is 9 + 7 is 16, carry the one, 9 x 5 is 45—this is a good practice for me too I haven’t—my multiplication tables in a long time. 9 x 5 is 45 + 1 is 46, carry the 4, 9 x 7 is 63 + 4 is 67. Now we add so you probably thinking, “Boy, what do the decimal have to do with this at all I'm just doing a regular multiplication. But I'm going to show you actually the decimals only come in right at the very end. So what I do is now I just add like I do a regular level for multiplication problem so I say 6 + 0 is 6, 2 + 2 is 4, 6 + 6 is 12, carry the one, 1 + 2 + 6 is 9, 5 + 7 is 12 carry the one, 1 + 6 is 7. So now here's where the decimals come to place and I think you're going to be shock by how straight forward this is. What I do is like go back to the original problem and now I actually pay attention to the decimals and I say, “How many total numbers are behind the decimal point?” Well, there's one number behind the decimal point, two numbers behind the decimal point, three numbers behind the decimal point, four numbers behind the decimal point. So there are four numbers behind the decimal point in the problem I did that I just count here. The answer will also have four numbers behind the decimal point and that’s the answer 72.9246. And let me ask you a question. If I had a zero here would that count as an extra number behind the decimal point? Well, it only would have been if you actually use the zero in the multiplication. Maybe that confuses you. What I would recommend if you have any trailing zeros with the decimal like this you actually should just ignore those zeros and then do the problem just the way I did it. And remember that’s only for trailing zeros. If this was the bottom number then that zero would matter because it’s not a trailing zero it actually adds, it’s actually part of the number. Let's do a couple of more examples and I think that will make sense. So let say I had five—I'm going to do a simpler example arithmetically but I think I'll help you with some principles. If I said 5.10 x 1.09, so there's two things we could do, we could just multiply it the way it is—actually let's do it both ways and I'll show you, you get the same answer whether or not you ignore that zero. So in the first case let's not ignore the zero let's pretend like that zero—let use that zero even though that trailing zero on the decimal 5.10 is the same thing as 5.1 but let's use it. 9 x 0 is 0, 9 x 1 is 9, 9 x 5 is 45 and then the zeros place you put a zero and then zero times everything is zero, right? Because 0 x 0, 0 x 1, 0 x 5, two zeros here and then 1 x 0 is 0, 1 x 1 is 1 and 1 x 5 is 5 and now we add it all, 0, 9, 5, 5, 5. And like we did before we just count the decimals, so the decimal would go here, right. So we got 5.5590 is the answer. Now what if we did like I was recommending we actually ignore the zero? So I say and I can actually rewrite it as 1.09 times 5.1 because you know in multiplication order doesn’t matter, 8 x b is the same thing as b x a, 2 x 3 is the same thing as 3 x 2 so 1.09 x 5.1 is the same thing as 5.1 x 1.09. So let's just multiply this out and notice these are the same numbers all I did is I took the zero off. So first I just ignore the decimal let say 1 x 9 is 9, 1 x 0 is 0, 1 x 1 is 1 put 0 here, 5 x 9 is 45 carry the 4, 5 x 0 is 0 + 4, 5 x 1 is 5. Now I add 9, 5, 5, 5 and I say look how many—now I'm at point that I can actually pay attention to the decimal point and let say how numbers are behind the decimals? Well there's three, so I go three the decimal point right here. Notice I got the same exact answer the only difference is at this one had a trailing zero which is really doesn’t make a number any different I can add a hundred zeros here and the numbers really not a different number this is just—well, if you're a computer programmer I guess this could become or statues station of some kind this could be an important number but ignore what I just said and for your purposes this trailing zeros mean nothing, right? Same way a leading zero actually could mean nothing no one ever does that. Let me do—well let me see how much time I have. I have two more minutes. Let me do one more problems just to maybe hit the point home but realize one of, you know, this is really no different than level up four multiplication and at the end you just count the numbers behind the decimal point. So 5 x 5 is 25 carry the two, 5 x 7 is 35 = 2 is 37 bring down the 7 carry the 3, 5 x 0 is 0 + 3 so its 375 ignore that bluff. I'm sorry for being so messy. And then you put a zero, 1 x 5 is 5, 1 x 7, is 7 ignore that, now we add let say 5 + 0 is 5, 7 + 5 is 12, 1 + 3 + 7 is 11 so we got our answer now we just have to count the decimals. So here we have five numbers behind the decimal points. But hey, in our answer we only have four digits so can we get five numbers behind the decimal point? Well, we start here we say four and we need one more number behind the decimal point so we add a zero here and then we put the decimal point. See what I just did? We had to had five numbers behind the decimal point. So, I mean I have four numbers in the answer so add in the leading zero and then put the decimal point and now we have five numbers behind the decimal point. And I’m shown you very mechanical way of doing this hopefully in the future I can give you a seminar and actually why this method of counting the numbers behind the decimal points actually work. But I think you are ready to try some problems multiplying decimals and have fun.

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Welcome to the presentation on multiplying decimals. Let's gets started. So I think you'll find out that multiplying decimal is not a lot more difficult than just multiplying regular numbers and I show you in the problem.

So let say let me pick some random numbers. Let say I had 7518 actually let's make that 75.18. Clearly you can tell I'm doing this on apply. 75.18 x 0.97 so at first you look at this form like, “Oh boy, that’s tough this decimals I don’t really know how to approach it.” Well this is what you do, you ignore the decimals and you start the problem and you pretend like it just a regular multiplication problem. And if you ignore the decimals and you would be like I said at beginning 7518 on top and 97 on the button and if that doesn’t make sense let me just show you. I'm just going to ignore the decimals and do this like a normal multiplication problem.

So normal multiplication I'd started at the one place right here and it say 7 x 8 is 56 carry the five, 7 x 1 is 7 plus the five is 12, 2 down here carry the one, 7 x 5 is 35 plus the one is 36, six here carry the three and then 7 x 7 is 49 + 2 is 52 so put 52 here. So just like normal multiplication we just took the once place right here at the seven that’s actually not the one but we’re ignoring the decimals so there were no decimal this should be the ones place and we’re multiplying it by the top number 7 x 7518 is equal to 52626. Its like regular multiplication we do the tens place, this isn’t really the tens place but if you ignore the decimals but let's cross all this top answer so that you see.

9 x 8 = 72, carry the 7, 9 x 1 is 9 + 7 is 16, carry the one, 9 x 5 is 45—this is a good practice for me too I haven’t—my multiplication tables in a long time. 9 x 5 is 45 + 1 is 46, carry the 4, 9 x 7 is 63 + 4 is 67. Now we add so you probably thinking, “Boy, what do the decimal have to do with this at all I'm just doing a regular multiplication. But I'm going to show you actually the decimals only come in right at the very end. So what I do is now I just add like I do a regular level for multiplication problem so I say 6 + 0 is 6, 2 + 2 is 4, 6 + 6 is 12, carry the one, 1 + 2 + 6 is 9, 5 + 7 is 12 carry the one, 1 + 6 is 7.

So now here's where the decimals come to place and I think you're going to be shock by how straight forward this is. What I do is like go back to the original problem and now I actually pay attention to the decimals and I say, “How many total numbers are behind the decimal point?” Well, there's one number behind the decimal point, two numbers behind the decimal point, three numbers behind the decimal point, four numbers behind the decimal point. So there are four numbers behind the decimal point in the problem I did that I just count here. The answer will also have four numbers behind the decimal point and that’s the answer 72.9246.

And let me ask you a question. If I had a zero here would that count as an extra number behind the decimal point? Well, it only would have been if you actually use the zero in the multiplication. Maybe that confuses you. What I would recommend if you have any trailing zeros with the decimal like this you actually should just ignore those zeros and then do the problem just the way I did it. And remember that’s only for trailing zeros. If this was the bottom number then that zero would matter because it’s not a trailing zero it actually adds, it’s actually part of the number.

Let's do a couple of more examples and I think that will make sense. So let say I had five—I'm going to do a simpler example arithmetically but I think I'll help you with some principles. If I said 5.10 x 1.09, so there's two things we could do, we could just multiply it the way it is—actually let's do it both ways and I'll show you, you get the same answer whether or not you ignore that zero. So in the first case let's not ignore the zero let's pretend like that zero—let use that zero even though that trailing zero on the decimal 5.10 is the same thing as 5.1 but let's use it.

9 x 0 is 0, 9 x 1 is 9, 9 x 5 is 45 and then the zeros place you put a zero and then zero times everything is zero, right? Because 0 x 0, 0 x 1, 0 x 5, two zeros here and then 1 x 0 is 0, 1 x 1 is 1 and 1 x 5 is 5 and now we add it all, 0, 9, 5, 5, 5. And like we did before we just count the decimals, so the decimal would go here, right. So we got 5.5590 is the answer.

Now what if we did like I was recommending we actually ignore the zero? So I say and I can actually rewrite it as 1.09 times 5.1 because you know in multiplication order doesn’t matter, 8 x b is the same thing as b x a, 2 x 3 is the same thing as 3 x 2 so 1.09 x 5.1 is the same thing as 5.1 x 1.09. So let's just multiply this out and notice these are the same numbers all I did is I took the zero off.

So first I just ignore the decimal let say 1 x 9 is 9, 1 x 0 is 0, 1 x 1 is 1 put 0 here, 5 x 9 is 45 carry the 4, 5 x 0 is 0 + 4, 5 x 1 is 5. Now I add 9, 5, 5, 5 and I say look how many—now I'm at point that I can actually pay attention to the decimal point and let say how numbers are behind the decimals? Well there's three, so I go three the decimal point right here. Notice I got the same exact answer the only difference is at this one had a trailing zero which is really doesn’t make a number any different I can add a hundred zeros here and the numbers really not a different number this is just—well, if you're a computer programmer I guess this could become or statues station of some kind this could be an important number but ignore what I just said and for your purposes this trailing zeros mean nothing, right? Same way a leading zero actually could mean nothing no one ever does that.

Let me do—well let me see how much time I have. I have two more minutes. Let me do one more problems just to maybe hit the point home but realize one of, you know, this is really no different than level up four multiplication and at the end you just count the numbers behind the decimal point. So 5 x 5 is 25 carry the two, 5 x 7 is 35 = 2 is 37 bring down the 7 carry the 3, 5 x 0 is 0 + 3 so its 375 ignore that bluff. I'm sorry for being so messy. And then you put a zero, 1 x 5 is 5, 1 x 7, is 7 ignore that, now we add let say 5 + 0 is 5, 7 + 5 is 12, 1 + 3 + 7 is 11 so we got our answer now we just have to count the decimals. So here we have five numbers behind the decimal points.

But hey, in our answer we only have four digits so can we get five numbers behind the decimal point? Well, we start here we say four and we need one more number behind the decimal point so we add a zero here and then we put the decimal point. See what I just did? We had to had five numbers behind the decimal point. So, I mean I have four numbers in the answer so add in the leading zero and then put the decimal point and now we have five numbers behind the decimal point.

And I’m shown you very mechanical way of doing this hopefully in the future I can give you a seminar and actually why this method of counting the numbers behind the decimal points actually work. But I think you are ready to try some problems multiplying decimals and have fun.

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