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# Comparing decimals visually

CCSS.Math:

## Video transcript

so the goal of this video is to try to compare these two quantities I have zero point one seven and I have zero point two and I want to figure out which of these two is larger or maybe they are equal and I encourage you to pause the video to try to figure that out well one way to do it is to try to visualize these and so each of these large squares you can view as a whole and this one on the left I haven't split into a hundred smaller sections because you notice we have ten rows and each row has ten squares so we have a hundred squares here so each of these squares represents a hundredth of the whole and so this number up here 0.17 we could do that as 17 hundredths so let's color in 17 hundredths so 1700s is going to be so that's one hundredth 2 3 4 5 6 7 8 9 10 hundredths and notice 10 hundredths I filled in 1 out of the 10 rows so this is the same thing as 1/10 so that's 10 hundredths 1,100 1,200 13 14 15 16 17 so one way to visualize 0.17 which is 17 hundredths is the fraction of this hole that is filled in in magenta now what about 0.2 well 0.2 is the same thing as 2 tenths and so we can take our hole and divide it into tenths divided into ten equal equal sections which we've done here notice each of these sections is equal to ten hundredths and that makes sense 1/10 is equal to ten hundredths now let's fill in two of them now because we're dealing with two tenths so let's fill in two of them so we have one tenth and two tenths so which of these which of these is larger well we see we're filling in more of the hole and we're doing two tenths than were doing when we're doing 17 hundredths and that makes sense because two tenths is the same thing two tenths is the same thing another way of think saying two tenths is you could write it as 20 hundredths 20 hundredths is greater than 17 others to get to 20 hundredths you would have to fill in these three as well notice when you fill out those three you're filling out the same fraction of your hole so which ones larger well two tenths is and how do we write that down well when we write an inequality we want to open to the larger number so you want to open to that one so we have zero point one seven or 17 hundredths is less than two tenths now another way that we could have tackled this even without kind of having to draw all of this is we could have just gone to the largest place value so if you go to the if you go went to the ones place you've got okay we have zero ones now we have zero ones here alright so that doesn't help us then you go to the next largest so then you go to the tenths place here you have one tenth here you have two tenths so immediately without even looking at what comes after this this could be zero point one seven three five eight it could keep going but the bottom line is you have more tenths here then you have tents here which tells you that this one over here is going this one is going to be larger so the general thing is look at the largest place value if one of one of the numbers has a larger digit in the largest place value is going to 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