31 in Roman Numerals

In Roman numerals, the symbol 'XXXI' is used to represent 31. Mentioned below are the seven symbols used in the ancient numeric system:

I - 1 
V - 5 
X - 10
L - 50
C - 100
D - 500 
M - 1000

According to the symbols given above, XXXI represents 31. As you can see, the number 0 does not appear anywhere in this numeric system. Let us now see the basic rules to write Roman numerals. 
 

Rule 1: Addition Method — In the addition method, you will combine different Roman numerals. When a smaller or the same number is placed after the larger number, we will simply add it -V(5) + I (1) = VI(6)

Rule 2: Repetition Method — In this method, a Roman numeral can only be used up to 3 times to get a larger value

I + I + I = III (3)
X + X + X = XXX (30)
But we can’t write XXXX for 40, it's XL (40)

Rule 3: Subtraction Method — In the above repetition method, we got to know that a symbol can’t be used more than 3 times, then how will we write 40? Here, we will use the subtraction method. If the smaller numeral is placed before the larger numeral, then you have to subtract the smaller numeral from the larger numeral. For example, if we take XL (40), the smaller numeral X (10) is subtracted from the larger numeral L (50). So, L (50) - X (10) = XL (40).

Rule 4: Limitation Rule - We can't repeat a number more than 3 times in Roman numerals. Instead of that, we will add and subtract. E.g. 4 is not to be written as IIII, instead write IV (subtraction method, i.e., 5-1=4). For ten (X), we can't use VV, as we have a specific letter for each value. For example, (V = 5, X = 10, L = 50, C = 100, D = 500, and M = 1000). As you can see, we have to use these symbols for specific values. Roman numeric system can be used easily by following these rules.
 

To write 31 in Roman numerals, we can simply write it using the symbol XXXI. It can be done using two methods :

Expansion Method: In this method, we will break the Roman numeral in smaller parts based on their values and then add them. Here, XXVIII (28) is made up of 2 parts that are 20 and 8. 20 can be written as XX which can also be written as X + X. 8 can be written as VIII which can also be written as V + III. Now if we add it, X + X + V + III = 28.

Grouping Method: We look at the numerals l and group them based on the rules of addition, subtraction, and repetition. We then add them together. Example, XIV 

X - 10, IV - 4 (since I came before V, we subtract 1 from 5). 

• Addition rule: When a smaller numeral is placed after a larger numeral or equal numeral, then it is said to be additive grouping. Example, VI = 5+1 = 6

• Subtractive rule: When a smaller numeral is placed before a larger numeral, then it is said to be subtractive grouping. Example: IV = 5-1 = 4

• Repetition: A numeral can be repeated thrice and not more than that. Examples: III = 1+1+1=3, XXX= 10+10+10= 30.

The method is about breaking the numbers according to the place values. Here are the steps for a better understanding.

Breaking down place values such as hundreds and tens. 

We are going to represent the value with a Roman numeral.

Now, we will add those values together to reach the right numerals.

For instance, 

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:

So we determine which Roman numerals are going to be added and which are going to be subtracted.

Add or subtract the symbols of the smaller numerals.

Then just add these values to represent 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.
 

Roman numerals may seem different, but they are quite similar. Take a look at Roman numerals that are related to 31:

• XX = 20
• XXI= 21
• XXIII = 23
• XXIV = 24
• XXV = 25
• XXV1 = 26
• XXVII = 27
• XXVIII = 28
• XXIX= 29
• XXX = 30

• Additive Principle: This principle means that when numerals are combined, their values are added together. For example, VI (5+1) = 6.

• Subtractive Principle: In Roman numerals, if a smaller number is placed before a larger number, it means we should subtract the smaller number from the larger number. For example:

XL is written as 40. Here, X is written before L, where X represents 10 and L represents 50  
The smaller number (X) is placed before the larger number (L). So we subtract it from the larger number L (50) - X(10) = 40 (XL)

• Grouping: Numbers starting from their larger numeral can be combined with a very small numeral to attain the total.

• Millennium: Every 1,000 years is a millennium. In Roman numerals 1,000 is written as M, where M means millennium.

• Consecutive Repetition: It is the process of repeating the same numeral continuously for three times to expand its value.