CDLXVIII 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. CDLXVIII in Roman numerals can be broken down by adding and subtracting the values of each Roman numeral: CDLXVIII = 468.

Let us learn more about the Roman numeral CDLXVIII, how we write it, 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 three times in continuation increases the value of the numeral. For example, XXX = 30.

Rule 3: Subtraction Method:

We use the subtraction method when a smaller symbol precedes a larger 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 CDLXVIII 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 involves breaking down 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 CDLXVIII,

Step 1: First we break the Roman numerals. CDLXVIII = C + D + L + X + V + I + I + I

Step 2: Write the Roman Numerals for each part The Roman Numeral C is 100 The Roman Numeral D is 500 The Roman Numeral L is 50 The Roman Numeral X is 10 The Roman Numeral V is 5 The Roman Numeral I is 1

Step 3: Combine all the numbers C + D + L + X + V + I + I + I = 100 + 500 - 100 + 50 + 10 + 5 + 3 = 468. Therefore, the Roman Numeral CDLXVIII is 468.

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 CDLXVIII.

Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are CD, LX, and VIII. 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 LX to CD and then add VIII, and we will get CDLXVIII. The Roman numeral L is 50 and X is 10, making LX 60. The Roman numeral VIII is 8. Therefore, the numeral of CDLXVIII is 468.

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

• Limitation Rule: There are some symbols that cannot be repeated more than once (V, L, D). For example, LVV for 60 is wrong; the correct answer is LX.
   
• Subtraction Method: The method of subtracting a smaller numeral that precedes a larger numeral, such as IV for 4.
   
• Place Value: The position of a digit in a number, this position determines its value. For example, the number 4 in 468 is in the hundreds place.
   
• Addition Method: The method of adding numerals where larger numerals precede smaller ones, such as VI for 6.
   
• Grouping Method: A way to break down and structure numerals using the addition and subtraction methods to simplify solving.