## Reading and writing Roman numerals | Class 6 (India) | Math | Khan Academy

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- [Instructor] If I'm a child,
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and if I wanted to
represent one of something,
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I might just write, hey, one of that.
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Like one stick or one twig.
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And then if I wanted two,
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I might just write two
twigs, right, one plus one.
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Three, three twigs.
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One next to another.
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I just write them and say what I have
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is just one plus one plus one, three.
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way of writing things.
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I just add what's there individually
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because I know this I-like
thing stands for one.
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And then I add I, I, I, three
Is, which is just three.
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So Roman numerals follows this idea
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So I'm gonna look at one, and what is one?
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I'll go here, I'll look at my table.
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Oh, one, I write one as I.
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And so it's just I.
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And then two is, I need two ones,
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and I just have to write them
next to each, so it's II.
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And three is going to
be, that's right, III.
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Four is going to be IIII.
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Not really. (chuckles)
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So it seems right, right, to do this.
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Write three Is for
three, four Is for four.
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But then it turns out that
this is not how we do it,
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at least not anymore.
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So I'm gonna put four as controversial.
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We're gonna talk about four more.
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So after this, what about five?
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I'm gonna up here.
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I can maybe put IIIII.
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But then, what's going on?
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a new alphabet for five.
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So I'll be putting five
just because that's easier.
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Now, what should I do for six?
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It gets interesting for six
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because how do I write six?
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So when I look at six,
I'll go up here and ask,
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"What is the largest thing that I have
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"that's smaller than six?"
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So six lies between five and 10.
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So I know that I can write
six as five plus something.
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So I'll first write my five, which is V.
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what is remaining here?"
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There's just one remaining.
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And one, I know how I can write it.
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I'll just go write the one.
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And the same thing happens
for seven, five plus two.
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Eight is five plus three.
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Nine, again, I'm gonna
put a question mark here
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because it's a different way of writing.
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We do not write VIIII with the four Is.
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Right, it becomes very long.
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So I'm gonna put a question mark here.
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I'm gonna learn how
we're gonna write this.
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And for 10, I'm gonna go up here.
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have an alphabet for it,
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so I'm just gonna use that.
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So let's look at an example.
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If I had 23 with me, and
if I want to write 23,
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how should I think about it?
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So in my head, I'm going,
"Okay, 23 is more than 10.
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"It's less than 50.
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"So I should write it as sum times 10,
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"and then I'll see what happens."
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So how many 10s are there?
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And I see that there are two 10s.
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So I'm gonna write two 10s.
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Maybe I should use a different color.
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So two 10s, XX.
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Is that enough?
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No, now what I have is 20.
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So I've taken 23, and I've made it,
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imagined it to be 20 plus three.
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20 plus three.
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been written over here.
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I treat this as a fresh problem,
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as if I'm starting all over again.
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I'll ask, "Three, where is three between?"
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It's between one and five.
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I already know how to write
that, how to write three.
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So I just go up here and write
three as one, two, three.
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So XXIII will give me 23.
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And as you can see,
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if I had been given this number
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and asked, "What is this number?"
how would I have read it?
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going X is 10, X is 10.
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So 10 plus 10 is 20.
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I is one, III is three.
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So this is 20, this is three.
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So 20 plus three is 23.
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So that's exactly the backward process
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that I would have used.
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And you can see that in all these cases
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the bigger number is what we write first
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and then the smaller numbers.
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So XX comes and then II.
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Over here we can see that V
comes first and then the I.
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So whenever we're writing usual numbers
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it comes in this format,
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the bigger one first and
then the smaller ones.
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But if you see, in our unique as well.
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So we said these two are
controversial, right.
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Four and nine.
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So what is it about four and nine?
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How do we write four and nine?
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of four as four ones
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where we write IIII.
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Which in fact, people used to
do back in the Roman times,
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and then they stopped doing it
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because it just took too much space.
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And in important documents
where there's not much space,
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we want a shorter way to write four.
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So what is a shorter way to write four?
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They thought of four as,
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"Hey, I can write it
was one less than five."
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So I can put an I, and then
I can write a V after that.
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So this is the first time
you're seeing a smaller number
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come before a larger number.
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So they said, "Whenever
you see this happening,
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"think of it as not one
plus five equal to six.
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"Don't do that.
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"But think of it as five
minus one, which is four."
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The same thing goes for nine.
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Think of it as one minus 10.
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Actually, 10 minus one, or
one less than 10 for nine.
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So we had an IV for four and IX for nine.
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And when we do this,
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this is called the subtractive notation.
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I'm gonna write it here as subtractive.
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Now this name is not that important,
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it's just for you to realize
that when we're writing it here
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in this way, we're actually
using a subtraction.
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Five minus one and 10 minus one.
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Now, the most important thing to know
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is that it's super rare.
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It very, very rarely happens.
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So I'm gonna fill in for
four and nine over here.
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And then let's look at where
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the subtractive notation is used.
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So four is IV, and nine is IX.
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So where is the subtractive notation used?
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So you can see that it's
used very, very, very rarely.
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In fact, the only special
cases are four and nine.
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"Don't we use this kind
of thing anywhere else?"
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We do.
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But just for the multiples
of four and nine.
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Four and nine, 40, 90, 400, 900.
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Only for these numbers do you
use this subtractive notation.
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And in fact, you can forget 400 and 900,
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they're two big numbers.
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We can just take the
four, nine, 40, and 90.
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So four, you know how to write it, IV.
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Nine, you'll write it as IX.
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So instead of thinking of 40
as four 10s and writing XXXX,
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what we do is that we
look at 40 as N minus 50.
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So what must I do then?
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And I'm again saying 10 minus 50,
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what I really mean is 50
minus 10. (chuckling softly)
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I should stop doing this.
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So 10 less than 50.
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So 10 less than 50, 50 is L.
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So I'll write XL.
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I want you to stop and
think about how to do 90.
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And when you try that, and
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look at what I'm doing.
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So how do you do 90?
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You will look at this number, 100,
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and then subtract N from it.
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So 10 less than 100, that's 90.
Title:
Reading and writing Roman numerals | Class 6 (India) | Math | Khan Academy
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