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Current time:0:00Total duration:7:34

Reading and writing Roman numerals

Video transcript

if I'm a child and if I wanted to represent one of something I might just write hey one of that like one stick or one twig and then if I wanted to I might just write two twigs right one plus one three three twigs you know one next to another I'll just write them and say what I have is just one plus one plus one three and this is called additive way of writing things I just add what's there individually because I know this I like things stands for one and then I add III three ice which is just three so Roman numerals follows this idea of additive representation of numbers so I'm gonna look at one and what is one I'll go here I look at my table who won I write one as I and so it's just I and then two is I need two ones and I just have tried them next to each other so it's I and three is going to be that's right III food is going to be III I not really the force little so it seems right right to do this right three three eyes for three four eyes for four but then it turns out that this is not how we do it at least not anymore so I'm going to put four as controversial we're going to talk about four more so after this what about five I'm gonna go up here I can maybe put iiiii but then what what's going on it's already becoming hard to read and we've already made up a new alphabet for five so I will be putting five just because that's easier now what should I do for six it gets interesting for six because how do I write six so when I look at six I'll go up here and ask what is the largest thing that I have that's smaller than six so six lies between five and ten so I know that I can write 6 as five plus something so I'll first write my five which is V and then ask okay what is what is remaining here there's just one remaining and one I know how we can write it I'll just go write the one and the same thing happens for seven five plus two 8 is 5 plus 3 9 again I'm gonna put a question mark here because it's a different way of writing we do not write v iiiii with the four eyes right it becomes very long so you're gonna put it I'm gonna put a question mark here we're gonna learn how we're gonna write this and for 10 I'm gonna go up here it's exactly I already have an alphabet for it so I'm just gonna use that so let's look at an example if I had 23 with me and if I want to write 23 how should I think about it so in my head I'm going okay 23 is more than 10 it's less than 50 so I should write it as some times 10 and then I'll see what happens so how many tens are there and I see that there are two tens so I'm gonna write two tens maybe I should use a different color so two tens X X is that enough no no what I have is 20 so I've taken 23 and I've made it I've imagined it to be 20 plus 320 plus 3 and this 20 has already been written over here so now what about this 3 I treat this as a fresh problem as if I'm starting all over again I'll ask 3 where is 3 between it's between 1 and Phi and I already know how to write how to write 3 so just go up here and write 3 as 1 2 3 so xx III will give me 23 and as you can see the way if I had given this number if I had been given this number and asked what is this number how would I have read it I'll read it by going X is 10 X is 10 so 10 plus 10 is 20 is 1 III is 3 so this is 20 this is 3 so 20 plus 3 is 23 so that's exactly the backward process that I would have used and you can see that in all these cases the bigger number is what we write first and then the smaller numbers so X X comes and then III over here also you can see that V comes first and then D I so whenever we're writing usual numbers it comes in this format the bigger one first and then this but if you see in our unique case away oh so he said these two are controversial right four and nine so what what is it about four and nine how do we write four and nine so instead of thinking of four as four ones where we write I III which in fact people used to do back in the Roman times and then they stopped doing it because it just took too much space and in important documents where there's not much space we wanted a shorter way to write for so what is a shorter way to write for they thought of 4s hey I can write it as one less than five so I can put an AI and then I can write a V after that so this is the first time you're saying a smaller number come before a larger number so they said whenever you see this happening think of it as not 1 plus Phi equal to 6 don't do that but think of it as 5 minus 1 which is 4 the same thing goes for 9 think of it as 1 minus 10 actually 10 minus 1 or 1 less than 10 for 9 so we read IV 4 4 and IX 4 9 and when we do this this is called the subtractive notation I'm going to write it here sub attractive now this name is not that important it's just for you to realize that when we are writing it here in this way we are actually using a subtraction 5 minus 1 and 10 minus 1 now the most important thing to know about this subtractive notation is that it's super rare it very very rarely happens so I'm gonna fill in for 4 & 9 over here and then let's look at where the subtractive notation is used so 4 is IV and 9 is IX so where is the subtractive notation used so you will see that it's used very very very rarely in fact the only special cases are 4 & 9 you're asking me it doesn't don't we use this kind of thing anywhere else we do but just for the multiples of 4 & 9 4 and 940 9400 900 right only for these numbers do you use this subtractive notation in fact you can forget 400 900 there they're too big numbers we can just stick to four nine 40 and 90 so for you know how to write it iv9 you'll write it as I X what about 40 right now so instead of thinking of 40 as four tens and writing X X X X what we do is that we look at 40 is 10 minus 50 so what was me what must I do then 10 and I am again saying 10-50 what I really mean is 50 minus 10 I should stop doing this so 10 less than 50 so 10 less than 50 50 is l so I'll write XL I want you to stop and think about how to do 90 and when you try that and once you get the answer look at what I'm doing so how do you do 90 you will look at this number 100 and then subtract 10 from it so 10 less than a hundred that's 90