CDXVIII in Roman Numerals

The ancient Romans discovered that counting on fingers could get very complicated after 10. To overcome this complexity, the Roman numeric system was developed. This system 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.

CDXVIII in Roman numerals can be written in number form by adding and subtracting the values of each Roman numeral, i.e. CDXVIII = 418. Let us learn more about the Roman numeral CDXVIII, 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 VIII, we have 5 + 3 = 8.

Rule 2: Repetition Method:

A symbol that is repeated increases the value of the numeral. For example, XXX = 30.

Rule 3: Subtraction Method:

We use the subtraction method when a larger symbol follows a smaller symbol. For example, XL = 40 (which is 50 – 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, 10 is represented as X and not VV.

Let us learn about how to write CDXVIII 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 or subtracting 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 or subtract the numerals together.

For CDXVIII,

Step 1: First, we break the Roman numerals. CDXVIII = CD + X + V + III

Step 2: Write the Roman Numerals for each part

The Roman Numeral CD is 400

The Roman Numeral X is 10

The Roman Numeral V is 5

The Roman Numeral I is 1

Step 3: Combine all the numbers CD + X + V + III = 400 + 10 + 5 + 3 = 418.

Therefore, the Roman Numeral CDXVIII is 418.

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 CDXVIII.

Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are CD, X, V, and III. The numeral for CD is 400

Step 2: Now we need to either add or subtract the smaller number, depending on its place. Here we add X, V, and III to CD and we will get CDXVIII.

The Roman numeral X is 10

The Roman numeral V is 5

The Roman numeral III is 3

Therefore, the numeral of CDXVIII is 418.

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

• Limitation Rule: Some symbols cannot be repeated more than once (V, L, D). For example, writing 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 4 in 418 is in the hundred's place.

• Subtraction Method: A Roman numeral rule where a smaller numeral before a larger numeral means subtracting the smaller from the larger. For example, IV for 4.

• Addition Method: A Roman numeral rule where numerals are added if a smaller numeral follows a larger numeral. For example, VI for 6.

• Numerical Expansion: The breaking down of a number into its constituent parts for easier calculation or understanding. For example, CDXVIII as CD + X + V + III.