How 10 relates to place value
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- [Voiceover] Multiplying by 10 creates a really neat pattern with numbers, so let's try a few out and see if we can discover the pattern. Let's try to figure it out. We'll start with one that maybe we already know, let's start something like two times 10. And maybe we know the solution but let's think about more than just the solution, let's think about what it really means to multiply two times 10. Two times 10 means we have two 10s. Or, we have a 10, plus another 10. Which is equal 10 plus another 10, is equal to 20. And again, maybe we didn't need this middle part, maybe we already knew two times 10 is 20, but it'll be helpful to think about what two times 10 means because it will help us when we get to much trickier ones. Let's try one that's maybe just a little bit trickier, let's try five times 10. Five times 10 is going to be five 10s, or, one 10 plus another 10 plus a third 10 plus a fourth 10 plus a fifth 10, so we have five 10s, we have one, two, three, four, five 10s. And we can solve that, we can add those together, 10, 20, 30, 40, 50. So our solution here, is 50. Five 10s is 50, or five times 10 is 50. Let's go to one more, maybe one that we don't know the answer to off the top of our head, let's try something like 13 times 10. Maybe we don't know the answer to 13 times 10 but we do know that 13 times 10 is 13 10s. And we can count 13 tens. We have a 10, plus another 10, plus another, there's three, four, five, six 10s, seven, eight, nine, 10, we're almost there, 11 10s, 12 10s, and finally a thirteenth 10. Let's count to make sure. One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, great. So we have 13 10s, so let's count those, let's see how much that is. We have 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130. So our solution is 130. I think we can pause here and look at the ones we've done so far and see if we can figure out this pattern. Two times 10 is 20, five times 10, 50, 13 times 10, 130. In every case we took the number that we started with, and we kept that, that was part of our answer, and then we added one new thing, which was a zero at the end. Any time we multiply a whole number by 10 we're gonna keep the original number and simply add a zero to the end. So let's try some without all this middle stuff. What if we had something like, a little bit tougher, maybe like 49 times 10. Well 49 times 10, you may guess is, is gonna be a 49 with what at the end, a zero. Or 490, because this would be 49 10s, and if we counted 49 10s we would get to 490. Let's go even tougher than that. What if we had something like 723 times 10? Well our solution, and maybe you've guessed it, is going to be 723 with a zero on the end, or, 7000 200 and 30 is the way we would actually read that answer. But looking at it, it quite simply is the original number, 723, with a zero on the end. Let's take this one step further and let's think about it in terms of place value. Let's think about what multiplying by 10 did to these numbers in terms of their place values. So here we have a place value chart, and let's start back with one of the simpler ones we did, like two. Two is two ones. And when we multiply that two times 10, the two moved up a place value. And then we had to fill in this empty place value with a zero. So two times 10 was 20, and what happened in terms of place value, was the two moved up one place value, it went from ones to tens, it moved to the left one place value. Let's look at another one, maybe one of the tougher ones, something like 723. When we multiply 723 times 10, we multiplied this one times 10, the seven moved one place value to the left to the thousands, the two moved up to the hundreds, and the three moved up to the tens. And then again, we simply added a zero in the empty place value in the end. So multiplying by 10, one way to describe the pattern, is that it adds a zero to the end of a whole number. But another way to describe the pattern, is that it moves every place value, every number, one place value to the left. So if we tried one looking at it this way, let's say we tried something like, 20, let's do 27. If we multiply 27 times 10, well the two's gonna move one place value over, so it will now be in the hundreds, and the seven's gonna move over a place value, so it will be in the tens, and then we'll have to fill in that empty place value with a zero. So we can say that 27 times 10 is equal to 270. So whether we think about it as adding the zero to the end or moving the place value to the left, multiplying by 10 creates a really neat pattern, that we can use to help us to solve these problems.