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Comparing decimals visually

CCSS Math: 4.NF.C.7

Video transcript

- [Voiceover] The goal of this video is to try to compare these two quantities. I have 0.17 and I have 0.2, and I wanna figure out which of these two is larger or maybe they're equal, and I encourage you to pause the video to try to figure that out. One way to do it is to try to visualize these. Each of these large squares you can view as a whole. And this one on the left, I have it split into 100 smaller sections 'cause you notice we have 10 rows, and each row has 10 squares, so we have 100 squares here. So, each of these squares represents 1/100 of the whole. And so this number up here, 0.17, we could view that as 17/100. So let's color in 17/100. 17/100 is going to be, so that's 1/100, two, three, four, five, six, seven, eight, nine, 10/100. And notice 10/100, I filled in one out of the 10 rows, so this is the same thing as 1/10. So that's 10/100, 11/100, 12/100, 13, 14, 15, 16, 17. So, one way to visualize 0.17, which is 17/100, is the fraction of this whole that is filled in magenta. Now what about 0.2? 0.2 is the same thing as 2/10. So we could take our whole and divide it into 1/10, divide it into 10 equal sections which we've done here. Notice each of these sections is equal to 10/100. And that makes sense, 1/10 is equal to 10/100. Let's fill in two of them now 'cause we're dealing with 2/10. So let's fill in two of them. We have 1/10 and 2/10. Which of these is larger? We see we're filling in more of the whole when we're doing 2/10 than when we're doing 17/100. And that makes sense because 2/10 is the same thing. 2/10 is the same thing. Another way of me saying 2/10 is you could write it as 20/100. 20/100 is greater than 17/100. To get the 20/100, you'd have to fill in these three as well. Notice when you fill out those three, you're filling out the same fraction of your whole. So, which one's larger? 2/10 is. And how do we write that down? When we write it in equality, we wanna open to the larger number. You want to open to that one. So we have 0.17 or 17/100, is less than 2/10. Now, another way that we could've tackled this, even without having to draw all of this, is we could've just gone to the largest place value. So if you went to the one's place, we have zero ones. And we have zero ones here, so that doesn't help us. Then you go to the next largest, so you go to the 1/10 place. Here you have 1/10, here you have 2/10. So immediately, without even looking at what comes after this, this could be 0.17358, it could keep going, but the bottom line is you have more 1/10 here than you have 1/10 here, which tells you that this one over here is going to be larger. So the general thing is, look at the largest place value. If one of the numbers has a larger digit in the largest place value, it's gonna be larger. If they're equal, go to the next larger place value. And you could keep going like that, but another way to think about it is just to visualize it, just like we did over here.