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Last updated on January 14th, 2025
We encounter Roman numerals in everyday life — on clocks, calendars, and books. Most of us know Arabic numerals well. So in this article, we will study the usages, and how to write Roman numerals.
Ancient Roman people introduced this numeric system for purposes like record-keeping. The unavailability of zero at that time and lack of other advanced mathematical operations made the Roman numerals popular. For example, we write 39 as XXXIX. A few rules we need to follow to represent numbers in Roman numerals are given below.
Rule 1: Addition - In Roman numerals, we add the values to get the numeric value. But you must make sure that the left value is equal or greater than the value on the right.
For example, XI = 11. We know that X = 10, and it comes before I (1). Therefore, according to the addition rule, we need to add 10 + 1 = 11 (XI).
Similarly, VII = 7. Once again, V (5) comes before I (1).
Rule 2: Repetition - Symbols should not be written together more than three times. And if it’s written 2 or 3 times, then the values are added. For instance, XXX = 30. In the above example, the symbol ‘X’ (10) repeats three times. Therefore, it’s added (X + X + X = 30).
Similarly, II = 2. The symbol I (1) is written 2 times continuously. Thus, the value will be added (I+I=2).
Rule 3: Subtraction - As the name suggests, we subtract the values. If the numeral on the left is smaller than its right counterpart, we subtract their values.
For example, IV = 4. Here, I (1) is of lesser value compared to that of V (5). So according to the subtraction rule, we need to subtract i.e., 5 (V) - 1 (I) = 4 (IV).
Similarly, IX = 9. In this case, the value of I (1) will be subtracted from X (10) to produce IX (9). So, [10 (X) - 1 (I) = IX (9)]
Rule 4: Limitation rule: According to this rule, symbols like V, L, and D are not repeated. And symbols like X, I, and C cannot be written more than thrice in a row. Instead, addition and subtraction methods are followed. For e.g., instead of writing 40 as XXXX, we write it as XL(50 - 10 = 40). Similarly, instead of writing 6 as IIIIII, write it as VI(5 + 1 = 6).
Refer to the above table and see the value of each symbol.
In Roman numerals, we write 39 as XXXIX. Remember to apply the addition, repetition, and subtraction rule when writing Roman numerals. Mentioned below are two methods used for the understanding of Roman numerals:
Let’s learn more about how these methods work and how we can use them in writing and understanding Roman numerals.
The expansion method is about breaking the numbers according to their place values. Whether it's thousands, hundreds, and so on. Follow the steps given below for better understanding.
Place values such as hundreds and tens are broken down first.
We will depict the value as a Roman numeral.
We will then combine the values to get the correct result.
For instance, 49 in Roman numeral can be represented as follows:
XLIX: X = 10
L = 50
IX = 9
We can represent this as,
XL = 50 - 10 = 40
IX = 10 - 1 = 9
So the expansion of XLIX is
40 + 9 = 49
In Roman numerals, large numbers are expressed through grouping methods. Here are a few grouping methods shown below:
First, we identify the Roman numerals that need to be added or subtracted.
Add or subtract the values of the smaller numerals.
Then add these values to get the desired Roman numeral.
For instance, XLIX:
XLIX = 49
XL = 50 - 10 = 40
IX = 10 - 1 = 9
Here we add: 40 + 9 = 49.
Combinations of numerals that represent specific values are what the grouping method focuses on.