How to Convert Roman Numerals into Arabic Numerals

When you’re working with Roman numerals, you have to remember 3 things. You have to remember the value of each of the symbols, which I have written over there. You have to remember the rules for adding them, so for instance if you have the number CLV, you would just add these 3 up, you’d have 100 plus 50, plus 5, or 155.

Then, the third thing you have to remember is the exception to those rules, or to that rule. If you have a number, such as CXL, that goes from a higher number, to a lower number, back up to a higher number, then you have to treat this second 2 numbers here as a single number, so instead of being 100 plus 10, plus 50, you have this entity here, which is equal to 50 minus 10, so XL is only equal to 40, instead of 60, so this number would be 140.

Those are the 3 things you have to remember when you’re working with Roman numerals. Let’s look at the example here. Here we’re asked to convert from Roman numerals to Arabic numerals. The first one we have XLVI, so we have a 10, a 50, a 5, and a 1, because we went up from a 10 to a 50, we know that we have to treat this as a single unit, instead of adding 10 and 50, we have to subtract 10 from 50, so this is 40.

Then the V is on its own, so that’s a 5, and then a 1, so 40 plus 5, plus 1 is 46. The second example we have CCXCII. Once again, we go from a 10 up to a larger number, so we have 100, 100, 10, 100, 1,1, so instead of being 10 plus 100, we have to take this as a 100 minus 10, or 90, so we have 2 100s over here, this is worth 90, and this is worth 2, so this number here is 292.

The third one we have DCXLIV. Now, D is 500, C is 100, X is 10, L is 50—we went from a 10 to a 50—so this has to be treated as 50 minus 10, so this is 40, and then we have 1 and 5—so once again, we’re going from a lower to a higher—so we treat this as a single number, and that’s 5 minus 1, or 4.

Now the D and the C are worth 500 and 100, so this together is worth 600, and we can write this as 644. The final example we have MCMLI. 1000, 100, 1000, 50 and 1, so the only instance of going from lower to higher is C and M, so this becomes 1000 minus 100, so this is 900 here. This M is 1000, and this L and I is 51, so we have 1951.