Numbers & Operations - The Real & Complex Number Systems 176-188
Sal shows how to turn numbers from expanded form to number form. Created by Sal Khan.
- [Instructor] Let's say that I had the following number. And I'm just gonna write it out so I have this number. And what I wanna do is think about how many hundreds, how many tens, and how many ones do I have. Well, to figure that out, we can just look at the place value. So we know this right over here is the ones place. We know this tells us how many tens we have, so we have three tens. And this tells us how many hundreds, hundreds we have. So you can view this number 832 as being the same thing as eight hundreds, so eight hundreds is the same thing as 800, plus three tens, well, three tens is the same thing as 30, 10 plus 10 plus 10, 10, 20, 30. And then two ones, well, that's just the same thing as two. And so you could write 832 as 800 plus 30 plus 2. And this form right over here is called expanded form. And that makes sense 'cause in a lot of ways it looks like you've expanded this number out. You're writing it in terms of a certain number of hundreds, tens, and ones. So let me give you another example. I want you to tackle that by yourself. So let's say I had this number right over here. pause this video and see if you can write this in expanded form. Okay, now let's do this together. Well, it's the same idea. How many hundreds do I have here? Well, I could go to the hundreds place and see that there are four hundreds, four hundreds is the same thing as 400. And then in the tens place, I have one ten. Well, one ten is the same thing as just 10. And then last but not least, in the ones place I have five. I have five ones. So this is the same thing as 400 plus 10 plus 5 in expanded form. Now what if you were to go the other way around? What if I were to give you something in expanded form, say the following like this. How would you write that as a number and sometimes people would just call this, standard form. Well, some of you might just say, "Well, if I add 700 to four, I'm gonna get 704." And that's right. Or you could think about them in terms of place values. If we think about hundreds place, a tens place, and ones place, how many hundreds do we have? Well, we can see right over here we have seven hundreds. So you put a seven right over there. How many tens do we have? Well, we have nothing expressed in terms of tens here, so we can write it as zero tens. And then last but not least, how many ones do we have? We see that right over here, four ones. So you can write it just like that.