Ordering large numbers: least to greatest

0:00- [Instructor] So we have two groups of numbers here. One I wrote in this yellow color and one in this purple color. And what I want you to do is pause this video and for each of these groups, the yellow group and the purple group, I want you to order them from least to greatest.

0:13So pause the video and have a shot of that. Okay, now let's work on this together. So the way that I would order numbers, whether I'm going from least to greatest or greatest to least, is I would look at the same place value. Now I'd start at the most significant, the largest place value that I have in either, in any of the numbers, and I would see which one has the largest digit there.

0:35So if I go, all of these are in the hundred thousands. They all have a hundred thousand place here, and we see that they're all seven. They're all 700,000s. So they're not looking too different there. Then we could go to the ten-thousandths place. So this one has nine 10-thousands, nine 10-thousands, nine 10-thousands.

0:54So they're both looking pretty, all three of them, I should say, are looking pretty similar there. All right, now let's go to the thousands place. I have a zero, a zero, and now I have a one. So this one over here, the 791,000, this is actually going to be the largest of all of these three numbers.

1:14So I'm gonna order from least to greatest. So I know that this one's going to be in third place. So 791,000, this is the greatest. It's going to be greater than whatever we put before it. Now it's a competition between these two for whichever one is least. So let's go to the next place value.

1:33The next place value. We go to the hundreds place. They both have four hundreds, so they are looking similar so far. Then we go to the tens place. This has zero tens. This has five tens. So this one over here is larger five tens. This says zero tens. So actually, I could have just, it's already written in order from least to greatest.

1:54I could have just done that, but let me just write it this way again. 790,450 and 790,408 is less than, you could think of it as the small end of the sign, points of the smaller number is less than 790,450, which is less than 791,000. Now let's do these numbers here.

2:19Okay, so it might be tempting to look at the first digit and say, "Oh, I have a nine there, and then I have a three and a three. Nine is bigger than three. This must be the largest number." But then you have to be careful. You have to look at place value. If we pay careful attention, this nine is in a much less significant place.

2:37One way to think about it is this is 900,000s. While here, these threes, these are in the 100 millions. So these are much, much more significant. So we already know that this 900,000, it doesn't even get into the millions, much less the tens of millions or the hundreds of millions.

2:58This is going be the smallest of the numbers. So let me just write it over here. So it's 986,700. This is going to be smaller than the other two. But now let's figure out a competition between these two for which one is greater so we can go to the next place value.

3:15We can go to the 10 millions. They're the same. We could go to the millions. They're still the same. We can go to the hundred thousands. They're still the same. If one way to think about it, if you wanted to rewrite this first number, you could have written it as 0, 0, 0, then a 9 if you wanted to compare it directly.

3:35Obviously, most people don't write numbers like that, but we're now in the a hundred thousands place, which was right over there. That said zero for every other place before that. But they're still looking similar. All right, let's go to the ten thousandths place.

3:48Still looking similar, but then we go to the thousandths place and the number on the right is the larger of them. So we can say, actually these were already written from least to greatest. So this is going to be, this number is less than this number, 376, 392,109, which is less than this number, 376,394,400, and we're done.