Comparing decimals in different representations

- [Instructor] So what we're going to do in this video is build our muscles at comparing numbers that are represented in different ways. So, for example, over here on the left we have 0.37, you could also view this as thirty-seven hundredths, and on the right we have 307 thousandths. And so, what I want you to do is pause this video, and figure out, are these equal to each other? Or is one of the larger than the other? And if one of them is, which one is larger, and which one is smaller? Pause this video and try to figure that out. All right, now let's try to do this together, and the way that my brain works is, I try to put them into a common representation. So, one way we could do it is we could try to re-write this one on the right as a decimal. So let's do that. So, we could re-write this as, it's expressing a certain number of thousandths, so let me just make some blanks for our various placeS. So let's say that's the one's place, and that's our decimal, that's going to be our tenth's place, that's going to be our hundredth's place, and that's going to be our thousandth's place. So, one way to view 307 thousandths is that we have 307 of this place, right over there. So, we could just write the seven there, the zero there, and the three over there. This over here would be 307 thousandths, and so we would have no ones. And so when you look at it this way, it's a little bit easier to compare. You can say, "all right, we have the same number of ones, we have the same number of tenths, let me compare the like one to the like ones." So, our tenths are equal, but what happens when we get to the hundredths? Here, we have seven hundredths, and here we have zero hundredths. So, this number on the left is going to be larger. So, 37 hundredths is greater than 307 thousandths. Another that we could have done this is we could have re-expressed this left number in terms of thousandths. We could've re-written it as, instead of 37 hundredths, we could've just said zero point three seven, and just put another zero on the right, and this is 370 thousandths. I'll write it out. 370 thousandths. And when you look at it this way, once again it's clear that 370 of something is more than 307 of that something. So, this quantity on the left is larger. Let's do another example, but I'll use different formats. So, let's say on the left, I'll use decimal format, I'll have zero point six, or six tenths, and then on the right, I'm going to have six times one over a hundred. Pause this video and tell me, which of these quantities, if either, are greater, or are they equal to each other? All right, so once again, in order to tackle this, you really just have to think about what are different way to represent them? And really just get to a common representation. And so, I could re-write six tenths and six times one tenth. Six times one tenth. And this might be enough to be able to compare the two, because six times one tenth, is that going to be greater than, or less than, or equal to six times a hundredth? Well, a tenth is ten times larger than a hundredth, so because this is ten times larger than that, if you multiply is by six, well, this is going to be a larger quantity. So we could go and say, "Hey, this is greater than that." Another way that you might have realized that is if you were to express this right quantity as a decimal like this. So, this is six times a hundredth, or six hundredths. So, we could write that's our ones, that's our tenths, and then in our hundredths place, you would have six. And if it isn't obvious that this is less than that, you could add a zero here, and this, we would read as 60 hundredths, and 60 hundredths is for sure larger than six hundredths. So, these are all very reasonable ways of re-representing these numbers and putting them in the same format so we can make the comparison and realize the one on the left, actually in both scenarios, is larger than the one on the right.