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Comparing numbers represented different ways

CCSS.Math:

Video transcript

so as to compare these two numbers right over here and I just took a picture from the Khan Academy exercise but this isn't did it sell so I can't I can't click on this but if you did click on it on the exercise you would get to choose between one of these three but I'll just write it down so we're gonna compare two point seven two two and 17 hundredths so there's a bunch of ways you could do this you could convert both of them to mix numbers so for example two point seven two point seven you could rewrite this is the same thing as two and seven tenths two and seven tenths you could compare two and seven tenths to two this right over here which is two and 1700s two and 1700s so they both have a 2 so you want to compare the fraction part so what's larger seven tenths or 17 hundredths well if it doesn't jump out at you you could convert this to hundredths seven tenths is the same thing if you want to convert it to hundredths you can multiply the denominator by 10 which would make the 10 into 100 and then you would also have to multiply the numerator by 10 so two and seven tenths is the same thing as two and 70 hundredths and so 70 hundredths is for sure bigger than 1700s so this number two and seven tenths or two and 70 hundredths or two point seven is going to be greater than this number so it's going to be greater than we open the symbol to the larger number another way that we could have thought about this is we could have converted them both to decimals so we have two point seven which we could leave as a decimal two point seven but then two and 17 hundredths we could write as 2 point 1 7 this is 1700s over here and there's a bunch of ways that you could make this comparison you could just say well look two and seven tenths is the same thing as two and 70 hundredths over here I have 70 hundredths over here I only have 17 hundredths so this is going to be larger this one's going to be larger right over here another way you get a thought about is what like you start in the ones place they both have two ones so that doesn't tell you much but as soon as you go to the tenths place this number has seven tenths well this one only has one tenth so this number right over here is going to be greater than that number let's go to list to another example which of the following are less than two point zero three or two and three hundredths each big square represents one hole so one way we could do it and this is kind of the way that jumps out at me is let's let's write all of these as decimals so this one over here we have one hole another hole and then over here I don't have a full hole let's see I've taken a hole I've divided it into tenths and I have two tenths right over here so this number right over here is equal to two and two tenths you see that two one two and then two of the ten equal sections so two and two tenths which is the same thing as 2.2 and if we wanted to compare it to two point zero three well we just have to think about this well there's there's a bunch of ways you can think about this you could view this as two point two zero which would mean this is two and 20 hundredths and two and 20 hundredths is for sure greater than two and three hundredths so this is not less than two point zero three this one over here is greater than two point zero three so I'm going to rule that one out another way you could have thought about this is this is two and two tenths which is the same thing as two and 20 hundredths which is this is another way of representing that you say well this one over the number you're comparing against is two and three hundredths so 20 hundredths is greater than three hundredths so once again this is not less than two point zero three here we have two and 12 hundredths and actually this is useful because I already have our original number representatives two and three hundredths so the the whole number part the two is the same so you look at the fraction part 12 hundredths is greater than three hundredths so this one also is not less than two point zero three now what about 23 hundredths 23 hundredths we could write like this 23 hundredths or we could write it like this 2,300 and you might be tempted to say oh well hey 23 hundredths that's bigger than three hundredths but remember we have two holes over here we have two holes we have no holes over here we have over here one way to think that you have nothing in the ones place over here you have something in the ones place so when you look at the ones place here you have two ones you have zero ones over here it doesn't matter how many hundredths you have if you have less than 100 hundredths and so this one is for sure less than two point zero three this one is this is significantly less than even one so this one is the only of the three that is less than two point zero three let's do one more of these order the following values from least to greatest and once again I took a picture from the Khan Academy exercise so I'm not gonna be able to drag them around if you're doing the exercise you would be able to drag them around but I'm just going to I'm just going to think about the numbers and then write them in order so I want to write them all let's write them all in as decimals let's write them all as decimals I guess it's the easiest thing to do so here this one's already written as a decimal 2.59 2410 24 tenths so let's think about this that's 24 over 10 well 24 over 10 is the same thing this is equal to 20 over 10 plus 4 over 10 20 tenths this is two holes right over here so this is same thing as 2 & 4 tenths 2 & 4 tenths or the same thing as 2 point 4 2 & 4 tenths now if we want to make a comparison to two and fifty nine hundredths we could throw another zero right over here it's a okay we could view this as two and 40 hundredths so these are all different ways of representing this some of you all might have been able to go immediately Hey look 10 tenths is 1 20 tenths is 2 so 24 tenths is going to be 2 & 4 tenths or 2.4 or 2.40 now let's try this number 2 & 3 tenths can represent that is 2.3 if we want to think of it in terms of 2 if we want to think of in terms of hundredths you could say well this is the same thing as 2 and 30 hundredths which you could also represent as 2 two three zero and the reason why I'm adding the hundreds so we can more easily make the comparison so you're comparing you're comparing two and fifty nine hundredths to two and 4000s to two and 30 hundredths well they all have to in the ones place they all have to in the ones place so then we just have to go to the tenths place and you see this has the most tents five tenths this is the second most four tenths and this has the least tenths three tenths so ordering from least to greatest the least is two and three tenths the least is two and three tenths which is equal to two point three the next the one larger next larger than that is going to be twenty four tenths twenty four tenths which is equal to two point four and then the largest is two point five nine and once again this only they all have to in the ones place and then you go to the tenths this has 3/10 4/10 5/10