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Comparing decimals in different representations

CCSS.Math: ,

Video transcript

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 right over here on the Left we have 0.37 you could also view this as 37 hundredths and on the right we have 307 thousands 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 them 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 as I try to put them into a common representation so one way we could do it is we could try to rewrite this one on the right as a decimal so let's do that so we could rewrite this as it's expressing a certain number of thousands and so let me just make some blanks for our various places so let's say that's the ones place and that's our decimal that's going to be our tenths place that's going to be our hundredths place and that's going to be our thousandths place so one way to view three hundred and seven thousandths is that we have three hundred and seven 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 three hundred and seven 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 alright we have the same number of ones we have the same number of tenths and let me compare the like ones to 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 this number on the left is going to be larger so 37 hundredths is greater than three hundred and seven thousands another way that we could have done this is we could have re-expressed this left number in terms of thousandths we could have rewritten it as instead of 37 hundredths we could have just said zero point three seven and just put another zero on the right and this is 370 thousands I'll write it out 370 thousands 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 ways to represent them and really just try to get to a common representation and so I could rewrite six tenths as six times 1/10 six times 1/10 and this might be enough to be able to compare the two because six times 1/10 is that going to be greater than or less than or equal to six times one hundredths well a tenth is ten times larger than a hundredth so because this is ten times larger than that if you multiply it 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 hundred 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