Continuing our counting, we have:
XV = 10 + 5 = 15
XVI = 10 + 5 + 1 = 16
XVII = 10 + 5 + 1 + 1 = 17
XVIII = 10 + 5 + 1 + 1 + 1 = 18
XIX = 10 + (10 – 1) = 10 + 9 = 19
XX = 10 + 10 = 20
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Eventually, we get to larger numbers. If we continue using these rules, we can create expressions for whatever values we are given.
Let's work some examples.
The biggest numeral smaller than 400 is the C for 100. But I can't do CCCC for the 400, because that's four of the same character in a row. Instead, I have to subtract 100 from 500: CD = 500 – 100 = 400.
The 50 is easy: that's just L. For the 3, I use three Is. Then my answer is:
453 = CDLIII
Note: This number is one that you might actually see expressed in Roman numerals "in real life" because, for some reason, the production dates on movies are written in Roman numerals.
The largest numbercharacter less than 1900 is 1000: M. After taking care of the thousand, I've got the 900 part of the number. I could start with a D for 500 and then add four Cs for the 400, but I can't use four of the same character in a row. So I'll instead use subtraction to get the 900: one hundred from one thousand is nine hundred, so 900 = CM.
The next part of the number is the 80; the largest numbercharacter smaller than this is L for 50. Then I'll add three Xs for the three tens: 80 = LXXX. I'm left then with the nine, which is written as "one from ten": IX. Putting it all together, I get:
1000 + (1000 – 100) + 50 + 30 + (10 – 1) = 1989 = MCMLXXXIX
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At the start of this Roman number is M which is 1000. Then comes D which is 500, followed by three Cs which is 300, for a total of 800. Then I've got an X which is 10, but that's followed by another C, which means that the 10 is subracted from the 100. In other words, the XC is a 100 – 10 = 90. After that comes VII which I recognize as being 5 + 1 + 1 = 7.
The year is 1,000 + 500 + 300 + 90 + 7 = 1897
Note: When your book or teacher or whatever refers to "Arabic numerals", that's just a fancy way of saying "the digits we normally use". Though our letters are Latin (that is, Roman), our numerals came to us in the MiddleAges from India via North Africans; that is, via Arabic scholars. Hence the name.
The first digit here is M, which stands for 1000. The next digit is a C, which stands for 100, but it's followed by an M, so this tells me that the C is actually subtracted from this second M. This means that the CM stands for 1000 – 100 = 900. Next come three X's, which is three tens, for 30. Then there's an I, but it's immediately followed by another X, which means that the I is subtracted from the X, giving me 10 – 1 = 9.
Putting it all together, I get:
1000 + (1000 – 100) + 3(10) + (10 – 1) = 1000 + 900 + 30 + 9 = 1939
You might think that I could just subtract one from five hundred: ID. But that's too much of a subtraction.
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In general, I can only subtract 1, 10, or 100 from the next one or two numerals bigger. That is, I can subtract 1 from 10 or 50, but not from anything bigger; I can subtract 10 from 50 or 100; and I can subtract 100 from 500 or 1,000, but that's it. (Why? "Because".) So I have to add up to 499, rather than subtracting down from 500.
The biggest numeral smaller than 499 is 100, but I can't add up to 100 by using four Cs; instead, I have to subtract 100 from 500 to get 400. This leaves me with the 99. While I can't subtract a 1 from a 100 to get 99, I can subtract a 10 from 100 to get 90. Then I can subtract a 1 from a 10 to get 9. Putting it all together, I get:
(500 – 100) + (100 – 10) + (10 – 1) = 400 + 90 + 9 = CDXCIX
To summarize:
← swipe to view full table →
Roman 

Arabic 

permitted 

Arabic 
I 

1 

IV 

5 – 1 = 4 
V 

5 

IX 

10 – 1 = 9 
X 

10 

XL 

50 – 10 = 40 
L 

50 

XC 

100 – 10 = 90 
C 

100 

CD 

500 – 100 = 400 
D 

500 

CM 

1,000 – 100 = 900 
M 

1,000 




Always build numbers starting with the biggestvalued character that you can squeeze into the number they've given you, and use subtractive forms wherever you can.
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