Identifying value in digits

So I'm going to write down a number, and I'm going to think about how much do each of these digits of the number—what value do they represent? And actually, let me pick on this 2 here. What does that 2 represent? Does it just represent two, or does it represent something different than just two? Pause the video and think about that.

All right, now let's think about it together. And actually, I'm going to start with the seven here. The seven is in the ones place, so this seven represents seven ones, which is, of course, still just seven. So nothing too surprising there.

Then we could go to the tens place. So this one doesn't just represent one; it represents one. Or another way to think about it, it represents 10. And then this 2, it is in the hundreds place, so it doesn't just represent 2; it represents 2 hundreds. We could write it that way, or it represents the value 200. So the number here is 217. The 2 represents 200s or 200.

Now let me give you a slightly different question. I'm going to write down three numbers. So we have this number, and I'm intentionally not saying it out loud. That number, I have this number, and I have this number. And what I want you to do is pause the video and tell me in which of these three numbers does the 7 represent 70? Pause the video and think about that.

All right, now let's work through this together. So let's start with this top number. In this number, the seven is in the ones place, so that seven really just represents seven ones, which is still just seven. So this seven does not represent 70.

Now this next number, the 2 is in the ones place, and we see that the 7 is in the tens place. So this actually represents 7 tens. Well, 7 tens is the same thing as 70. So it's actually in this second situation where the 7 does represent 70. This number is 572; the 7 represents 70.

And let's just check this last number here. Well, here the 7 is not in the ones place, not in the tens place; it is in the hundreds place. So this represents 7 hundreds or 700, and that makes sense. This number here is 705.