CXIII in Roman Numerals

Ancient Romans discovered that counting fingers could get very complicated after 10. So to overcome the complexity, the Roman numeric system was developed. This was widely used throughout Europe as a standard writing system until the late Middle Ages. Seven symbols are used to represent numbers in the Roman numeric system — I, V, X, L, C, D, and M. The numerals are made up of different combinations of these symbols. CXIII in Roman numerals can be written in number form by adding the values of each Roman numeral, i.e. CXIII = 113.

Let us learn more about the Roman numeral CXIII, how we write them, the mistakes we usually make, and ways to avoid these mistakes.

When writing Roman numerals, there are a few rules that we need to follow based on the Roman numerals we are trying to write. In this section, we will learn about the rules when writing Roman numerals and how to represent them.

Rule 1: Addition Method:

When a larger symbol is followed by a smaller symbol, we add the numerals to each other. For example, in XIII, we have 10 + 3 = 13.

Rule 2: Repetition Method:

A symbol that is repeated three times in continuation increases the value of the numeral. For example, CCC = 300.

Rule 3: Subtraction Method:

We use the subtraction method when a larger symbol follows a smaller symbol. For example, XC = 90 (which is 100 – 10).

Rule 4: Limitation Rule:

Symbols cannot be repeated more than three times, and some symbols, such as V, L, and D cannot be repeated more than once. For example, 100 is represented as C and not LL.

Let us learn about how to write CXIII in Roman numerals. There are two methods that we can use to write Roman numerals:

• By Expansion Method
• By Grouping Method

The breaking down of Roman numerals into parts and then converting them into numerals is what we call the expansion method. The expansion method is the breaking down of Roman numerals into numerical form and adding them to get the final number.

Step 1: Break the Roman numerals into parts.

Step 2: Now write each of the Roman numerals with its numerical digit in the place value.

Step 3: Add the numerals together.

For CXIII,

Step 1: First, we break the Roman numerals. CXIII = C + X + I + I + I

Step 2: Write the Roman Numerals for each part The Roman Numeral C is 100 The Roman Numeral X is 10 The Roman Numeral I is 1

Step 3: Combine all the numbers C + X + I + I + I = 100 + 10 + 1 + 1 + 1 = 113. Therefore, the Roman Numeral CXIII is 113.

Using subtraction and addition rules, we will apply the grouping method. This means we break the Roman numerals into smaller groups, which makes it easier to work with. This method groups the Roman numerals logically, and then we write the numbers for each group.

Step 1: Take the largest number and write the number for that Roman numeral.

Step 2: Write the Roman numeral using the subtraction and addition rules.

Example: Let’s take the Roman numeral CXIII.

Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are C, X, and III. The numeral for C is 100

Step 2: Now we need to either add or subtract the smaller number, depending on its place.

Here we add X and III to C and we will get CXIII. The Roman numeral X is 10 The Roman numeral III is 3 Therefore, the numeral of CXIII is 113.

We follow a pattern when it comes to writing Roman numerals. In this section, we will write some numbers related to the Roman numeral CXIII: 

• Limitation Rule: There are some symbols that cannot be repeated more than once (V, L, D). For example, LL for 100 is wrong, the correct answer is C.

• Place Value: The position of a digit in a number, this position determines its value. For example, the number 1 in 113 is the hundred's place.

• Prime Number: A number that has only two factors or multiples is called a prime number. For example, 113 is a prime number that has only two factors: 1 and itself.

• Subtraction Method: Used in Roman numerals when a smaller symbol precedes a larger symbol to indicate subtraction, such as in XC (90).

• Addition Method: The method of adding values of Roman symbols from left to right when a larger symbol precedes a smaller symbol, such as in XIII (13).