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Multiplying 1-digit numbers by 10, 100, and 1000

Lindsay finds a pattern from multiplying 1-digit numbers by 10, 100, and 1000. 

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Video transcript

- [Voiceover] Let's talk about multiplying by 10, 100, and 1000. There's some cool number patterns that happen with each of these. So let's start here with something like four times 10, one that maybe we're comfortable with or already know. Four times 10 would be the same as four tens. Four tens. And four tens, one way we could represent that is a 10 plus a second 10 plus a third 10 plus a fourth 10. Or four tens. And now let's count that. 10 plus 10 is 20, plus 10 is 30, plus 10 is 40. So our solution is 40, or a four with a zero. And this is the pattern that we've seen before. When we multiply four times 10, we keep our whole number of four and we add a zero to the end for the times 10. So another example of that might be something like eight times 10. Well, eight times 10 is the same as eight tens. And this time let's just count them. If we count eight tens, it'll be 10, 20, 30, 40, 50, 60, 70, 80. So when I counted eight tens, the solution was 80, or an eight with a zero on the end. So times 10, when we multiply a whole number times 10, the pattern is that we end up adding a zero to the end of our whole number. So let's take now what we already know about tens and let's apply it to hundreds. Something like, let's say, two times 100. There's a couple ways we can think about this. One way is to say that this is the same as two hundreds. Two hundreds, which is 100 plus another 100. There's quite literally two hundreds, which is a total of 200, or two with two zeros on the end. Now we have two zeros on the end. Or another way to think about this is two, two times 100, instead of saying times 100, we could say times 10 times 10. Because 10 times 10 is the same as 100. And two times 10, we know as a two with a zero on the end, which is 20, and 20 times 10 then will be 20 with a zero on the end. Because we multiplied by 10 twice, we added two zeros. And multiplying by 100 is just that. It's exactly that. It's multiplying by 10 twice. So, if times 10 adds one zero, then times 100, or times 10 twice, adds two zeros to our answer. And we can go even further and think about thousands. Let's try something like nine times 1000. Well, we could think of this as nine thousands, and if we have nine thousands, then we have 1000, 2000, 3000, 4000, 5000, that was five, 6000, 7000, 8000, 9000. So when I counted to 1000 nine times, our solution was 9000. Or looking at the numbers, a nine, our original whole number, with three zeros after it. So nine times 1000 is 9000, or nine with three zeros. And we can go back to what we did before. Thinking about this in terms of tens we've worked out, when multiplying by 10 adds a zero, so let's think about 1000 in terms of tens. 1000 is equal to 10 times 10 times 10. 10 times 10 is 100, and 100 tens is 1000. So instead of 1000, we can write 10 times 10 times 10. These are equivalent. And so, when we multiply a number times 10, we add a zero. But here we're multiplying by three tens, so we add three zeros. So let's look at that all as one pattern. Let's take seven, the number seven, and let's multiply it by 10, by 100, and by 1000, and see what happens. Seven times 10 is going to be seven with one zero 'cause we have one ten. Seven times 100 will be seven with two zeros because, again, 100 is the same as 10 times 10. So this is seven times 10 twice so we have two zeros. And seven times 1000 will be 7000, or seven with three zeros because 1000 is equal to 10 times 10 times 10, or three tens. So we had one, two, three zeros. And so, we can see the pattern here. When we multiply by 10, which has one zero, we add one zero to the end of our whole number. When we multiply a whole number times 100, which has two zeros, we add two zeros for hundreds. And for thousands, when we multiply by 1000, we'll add three zeros to the end of a whole number.