Multiplying whole numbers by 10 | Math | 4th grade | Khan Academy

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 2 * 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 2 * 10.

2 * 10 means we have 2 tens, or we have a 10 plus another 10, which is equal to 10 + another 10 is equal to 20. Again, maybe we didn't need this middle part; maybe we already knew 2 * 10 was 20. But it'll be helpful to think about what 2 * 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 5 * 10. 5 * 10 is going to be 5 tens, or 1 10 plus another 10 plus a third 10 plus a fourth 10 plus a fifth 10. So we have five tens. We have 1, 2, 3, 4, 5 tens, and we can solve that; we can add those together: 10, 20, 30, 40, 50. So our solution here is 50; 5 * 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 * 10. Maybe we don't know the answer to 13 * 10, but we do know that 13 * 10 is 13 tens, and we can count. 13 tens would be a 10 plus another 10 plus another, there's three, four, five, six tens, seven, eight, nine, ten. We're almost there: 11 tens, 12 tens, and finally a 13th 10.

Let's count to make sure: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. Great! So we have 13 tens. So let's count this; 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: 2 * 10 is 20, 5 * 10 is 50, 13 * 10 is 130. In every case, we took the number that we started with, and we kept that; that was part of our answer. Then we added one new thing, which was a zero at the end. Anytime we multiply a whole number by 10, we're going to 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 * 10? Well, 49 * 10, you may guess, is going to be a 49 with what at the end? A zero, or 490 because this would be 49 tens. If we counted 49 tens, we would get to 490.

Let's go even tougher than that. What if we had something like 723 * 10? Well, our solution, and maybe you've guessed it, is going to be 723 with a zero on the end, or 7,230 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 what multiplying by 10 does to these numbers in terms of their place values. So, here we have a place value chart. Let's start back with one of the simpler ones we did, like 2. 2 is 2 ones, but when we multiply that 2 * 10, the two moved up a place value, and then we had to fill in this empty place value with a zero. So, 2 * 10 was 20.

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. Well, we multiplied 723 * 10. We multiplied this one by 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, uh, 27. If we multiply 27 * 10, well, the two is going to move one place value over, so it will now be in the hundreds, and the seven is going to move over a place value so it will be in the tens. Then we'll have to fill in that empty place value with a zero.

So we can say that 27 * 10 is equal to 270. So whether we think about it as adding a zero to the end or moving a place value to the left, multiplying by 10 creates a really neat pattern that we can use to help us to solve these problems.