62 in Roman Numerals

There are seven basic symbols in the system to represent particular numbers, which are as follows :

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

As per these symbols, LXII represents 62 in Roman numerals. In this numeral system, there is no symbol for zero (0). In this article, we will learn about the numeral LXII and different methods to represent it. 
 

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 - LXII(62) = L(50) + X (10) + II(2))

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

LXII(62) = L(50) + X (10) + II(2))
LXIII(63) = L(50) + X (10) + IIII(3))
We can’t write LXIIII for 64 , it's LXIV (64)

Rule 3: Subtraction Method — From the repetition method, we got to know that a symbol can’t be used more than 3 times, then how will we write LXIV ? Here in Roman numerals, 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, in LXIV (64), there are two parts: LX (60) and IV (4). 60 (L(50) + X(10)= LX(60)) and IV (V - I). Which results in LXIV (64) = L(50) + X (10)+IV(4)

Rule 4: Limitation Rule - In Roman Numerals we can't repeat a number more than 3 times. After that, we have to use different symbols. Here you will use addition and subtraction methods. For example - we can't write 4 as IIII, instead we write IV (subtraction method subtracting I(1) from V(5) to get IV(4). For 10, we use X. Here, we can't use VV because there are specific letters assigned to the values, for example (V - 5, X- 10, L - 50, C - 100, D - 500, M - 1000) we have to use these symbols for the specific values. These rules make it easy for us to use the numeral system.
 

To write 62 in Roman numerals, we can simply write it as LXII. It can be done using two methods :

Expansion Method: In this method, we will break the Roman numeral into smaller parts based on their values and then add them. For example, LXII is made up of 3 parts that are 50, 10 and 2. 60 can be written as LX(L(50) + X (10)). 2 can be written as II. Now if we add it LX(L(50) + X (10)) + II(2) = LXII(62).

Grouping method -  We look at the numerals and group them based on the rules of addition, subtraction, and repetition and add them. Example LXII

L (50), X - 10, II = 2 now if we add them (L (50)+X(10)+II(2))

• Addition rule: When a smaller numeral is placed after a larger numeral or equal numeral, then it is said to be additive grouping. Example: II = 1 +1 = 2 

• Subtractive rule: When a smaller numeral is placed before a larger numeral, then it is said to be subtractive grouping. Example: XL = 50-10 = 40

• Repetition: A numeral can be repeated up to 3 times, and not more than that. Example: III = 1+1+1=3, XXX= 10+10+10= 30.

The expansion method is about breaking the numbers according to their place values such as 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 express the value as a Roman numeral.

We will then combine the values to get the correct numerals.

For instance, 

LXII
L = 50(50 has a fixed symbol in Roman Numerals)
X = 10(10 has a fixed symbol in Roman Numerals)
II = 2

We can represent this as,

L = 50
X = 10
II = 2(I +I )

Therefore, the expansion of LXII is

50 +  10 + 2 = 62
 

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,LXII : 

LXII = 62
L = 50
X = 10
II = 2 

Here we add: 50 + 10 + 2 = 62.

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 62 : 

• LXI = 61
• LXII = 62
• LXIII = 63
• LXIV = 64
• LXV = 65
• LXVI =66
• LXVII = 67
• LXVIII = 68
• LXIX = 69
• LXX = 70
   

• Additive Principle: This principle means that when numerals are combined, their values are summed together. For example, XI (10+1) = 11.

• Subtractive Principle :  in Roman numerals , if a smaller number is placed before larger numbers it means we should subtract the smaller number from the larger number for example XL (40) so the X is before L and X represents 10 and L represents 50 .The smaller number is placed before the larger number, 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: A millennium is a time span of 1,000 years. In Roman numerals, 1,000 is represented as M, and hence a millennium is represented as M (1000).

• Consecutive Repetition: It refers to the process of repeating the same numeral up to three times to expand its value.