Place value example: 42

Voiceover:What I want to do in this video is take this quantity represented by these greenish emerald-looking bars, where each bar represents one, and try to represent them using the digits that we know, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. And the way I'm going to do it is I'm going to group this into tens so I'm going to see how many tens I have and then essentially how many ones that I have left over, so let's try to group this into groups of ten. So 1, 2, 3, 4, 5, 6, 7, 8, 9, Let me actually, I messed that up, let see, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. So that's one group of ten right over there. Let me box that off so that i know that is ten. So, that's one group of ten, now let's see, let's see if I can get a few more groups of ten in there. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. That's my second group of ten right over there. Second group of ten and now let's see, it looks like I got several more groups of ten here. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. So that's a third group of ten, and it looks like I might be able to get one more, so that's my third group of ten and then we have, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. So that's my fourth group of ten. Fourth group of ten right over here. So I was able to fit in at least just this is 1, This is a ten right over here, This is another ten right over here. That's the third ten, and then that's the fourth ten. So we can say that's 10+10+10+10. Or all of this combined is equal to 4, 1, 2, 3, 4, tens but I'm not done with the number, I still have 1, 2, I have 2 ones left over. So this is a one, so that's a one right over there. And then this is another one, so that's another one. So I have 2 ones, so this right over here, That is 2 ones, remember for each of these little green bars we said represents a one. So this whole number is what? What's going to be the 4 tens, 1 ten, 2 ten, 3 tens, 4 tens. Plus the 2 ones, so let me write that down. So it is 4 tens plus 2 ones, but what is that? Well if we use the number systems that we're used to representing, we would say, "Well look, our number system gives us a way of representing that." Because the first place, this is the ones' place So let me gets some of this blue color, So this is the ones' place. There we use one of the digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, To see how many ones we have. And we have 2 ones. And then the next place over to the left, that's where we say how many tens we have. That's where we say how many tens. And we know how many tens we have, we have 4 tens. So the way that we would represent this in our number systems we would say that this was 4 tens and 2 ones. We call this right over here, we call this 42. Another way that you can think about this, is 4 tens, that's 10+10+10+10, that's going to be 40, but once again, we're using our number system to represent this, and then we have 2 ones but I like to write it this way, just to remind ourselves that this 4 which represents 4 tens also represents 40. Because 4 tens is 40.