Strategies for multiplying multiples of 10, 100 and 1000
Sal uses strategies, such as an understanding of place value, to multiply numbers like 800x400.
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A Googolplex is considered to be the biggest number in the world. It is written as 10googol. The number 10googol can also be expressed in the exponential format that will equal 1010^100.(6 votes)
- [Instructor] What we're gonna do in this video is think about multiplying, or strategies for multiplying numbers that are expressed in terms of hundreds, or thousands, or tens. And so we see an example right over here. We have 800 times 400. Now like always, I encourage you to pause this video and see if you could work this out on your own. Now let's work this through together, and I'm going to work it out in a way that at least my head likes to tackle it. Once you get enough practice, you might even be able to do these types of multiplication problems without even needing to use paper. So the key realization here is to say, well look, this is eight 100s. So that's the same thing as eight times 100. And this over here is four 100s. So this is four times 100. And so it's eight times 100, times four times 100. And if you're multiplying a bunch of numbers like this, you can switch the order in which you're doing the multiplication. So you can view this as eight times four. Eight times four, times 100 times 100. Times 100 times 100. Times 100. Now why is this easier? Well what is eight times four going to be? Well eight times four, if we know our times tables, is 32. And so it's going to be 32 times, what's 100 times 100 going to be? Now there's multiple ways that you can think about this, and I want you to really think it through, but we'll soon see that there's a fairly fast way of making sure we got it right. But one way to think about it is, well let me do it over here. 10 times 100 is equal to 1,000. And so 100 times 100 is going to be 10 times that, or it's going to be equal to 10,000. So this stuff right over here is equal to 10,000. Now you might notice something interesting here. I have two zeroes, and then another two zeroes. So I have a total of four zeroes. And then I have four zeroes here. Because every time you multiply by 10 you're gonna add another zero. So if you're multiplying by 100 you're gonna add two zeroes. If you're multiplying by 1,000, you're gonna add three zeroes, and you see that here. So you have 32 times 10,000, which is going to be what? Well let's see. 32 times 1,000 would be 32,000. But this is 32 times 10,000. So it's going to be 320,000. Now you might already notice an interesting pattern here. 32 times one followed by four zeroes is 32 followed by four zeroes. This is 32 10,000s, which is 320,000. Now another was you could've thought about it is eight times four gives us our 32. And then we have two zeroes there, two zeroes there for a total of four zeroes, and we have our four zeroes right over there. Now I don't want you to just memorize that. It works because this is eight 100s times four 100s. Eight times four gives us the 32. And then the 100 times the 100s, that's where these four zeroes come from. Let's do another example. So let's do, let me delete this. And let us do, let me get my pen back. So let's do 30 times 70, or let's do 30 times 700. Pause the video and see if you can figure this out. So we can do it like we did before, 30 is three times 10. 700, so times 700, which is seven times 100. And so if you say three times seven, is going to be 21 times 10 times 100, is going to be 1,000. So what's 21 times 1,000? Well that's going to be 21,000. Now just like we saw before, once you get a hang of it, and I always want you to understand where it's coming from, three times seven is the 21, and then you're gonna multiply that times 10 and then 100. So you have one, two, three zeroes. One, two, three zeroes. Let's do one more of these. So let's say we wanted to multiply 2,000 times 8,000. Pause the video and see if you can figure out what this is. Maybe in your head. Try to do this one in your head. Or on paper, don't feel bad if you need to use paper. That's always prudent. Well you might get the hang of it now. You might be able to do this quite quickly. You might be able to say hey, two times eight, well that's going to be equal to 16. And then I have three plus three zeroes, so that's gonna be six zeroes. One, two, three, four, five, six, which gives me 16 million. You would absolutely be correct. Now I want to reinforce what you're doing when you're just counting zeroes like that. What you're doing, you're just saying hey, this is the same thing as two times 1,000, times eight times 1,000. Eight times 1,000. And then you're just changing the order of multiplication. You're saying hey, let me multiply the two and the eight. You multiply the two times the eight, and you get 16. And then you multiply the times 1,000 times 1,000. So times 1,000 times 1,000. And 1,000 1,000s, that's one million. This is one million right over here. And notice you see it there too. 1,000 times 1,000, you have three zeroes, three zeroes, you get six zeroes. 1,000 1,000s is a million. 16 times a million is 16 million. So hopefully that helps and makes you a little more comfortable multiplying these numbers that are multiples of ten, hundred, thousands, even millions.