CMLXIV 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. CMLXIV in Roman numerals can be written in number form by adding the values of each Roman numeral, i.e., CMLXIV = 964.

Let us learn more about the Roman numeral CMLXIV, 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 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 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 CMLXIV 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 CMLXIV,

Step 1: First we break the Roman numerals. CMLXIV = CM + LX + IV

Step 2: Write the Roman Numerals for each part The Roman Numeral CM is 900 The Roman Numeral LX is 60 The Roman Numeral IV is 4

Step 3: Combine all the numbers CM + LX + IV = 900 + 60 + 4 = 964. Therefore, the Roman Numeral CMLXIV is 964.

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 CMLXIV.

Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are CM, LX, and IV. The numeral for CM is 900 The numeral for LX is 60

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

Here we add LX and IV to CM and we will get CMLXIV. The Roman numeral IV is 4 Therefore, the numeral of CMLXIV is 964.

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

• Subtraction Method: When a smaller numeral precedes a larger numeral, it is subtracted. For example, IX is 9 (10 - 1).

• Addition Method: When a larger numeral precedes a smaller numeral, it is added. For example, VI is 6 (5 + 1).

• Limitation Rule: There are some symbols that cannot be repeated more than once (V, L, D). For example, VV for 10 is wrong, the correct answer is X.

• Numerical Value: The value assigned to a Roman numeral based on the symbols used, such as C = 100.

• Place Value: The position of a digit in a number, which determines its value. For example, the number 6 in 964 is in the tens place.