Last updated on May 26th, 2025
To meet their daily commerce and administration needs, the ancient Romans developed Roman Numerals. It used a combination of seven symbols — I, V, X, L, C, D, and M to represent numbers. Roman numerals were used to record transactions, keep track of data, and label military units. In this topic, we are going to learn about the Roman numeral MDCCLXIV.
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. MDCCLXIV in Roman numerals can be written in number form by adding the values of each Roman numeral, i.e., MDCCLXIV = 1764.
Let us learn more about the Roman numeral MDCCLXIV, 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.
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.
A symbol that is repeated three times in continuation increases the value of the numeral. For example, XXX = 30.
We use the subtraction method when a larger symbol follows a smaller symbol. For example, XL = 40 (which is 50 – 10).
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 MDCCLXIV in Roman numerals. There are two methods that we can use to write Roman numerals:
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 MDCCLXIV,
Step 1: First, we break the Roman numerals. MDCCLXIV = M + D + C + C + L + X + IV
Step 2: Write the Roman Numerals for each part. The Roman Numeral M is 1000 The Roman Numeral D is 500 The Roman Numeral C is 100 The Roman Numeral L is 50 The Roman Numeral X is 10 The Roman Numeral IV is 4
Step 3: Combine all the numbers. M + D + C + C + L + X + IV = 1000 + 500 + 100 + 100 + 50 + 10 + 4 = 1764. Therefore, the Roman Numeral MDCCLXIV is 1764.
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 MDCCLXIV.
Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are MD, CC, LX, and IV. The numeral for MD is 1500
Step 2: Now we need to either add or subtract the smaller number, depending on its place. Here we add CC, LX, and IV to MD, and we will get MDCCLXIV. The Roman numeral CC is 200 The Roman numeral LX is 60 The Roman numeral IV is 4 Therefore, the numeral of MDCCLXIV is 1764.
Students can make mistakes when studying Roman numerals. Here are a few common mistakes students make, and ways to avoid them.
A historian finds two ancient documents labeled MD and CXLIV. Find the total value of both documents in Roman numerals.
The total value is MDCXLIV
Convert the Roman numerals into their decimal form:
MD = 1500
CXLIV = 144
Add the values: 1500 + 144 = 1644
Convert 1644 into Roman numerals: 1000 (M) + 600 (DC) + 40 (XL) + 4 (IV) = MDCXLIV
A treasure map indicates two buried treasures marked as MM and CCLXIV. What is the difference between MM and CCLXIV in Roman numerals?
The difference is MDCCXXXVI
Convert the Roman numerals into their decimal form:
MM = 2000
CCLXIV = 264
Subtract the values: 2000 - 264 = 1736
Convert 1736 into Roman numerals: 1000 (M) + 700 (DCC) + 30 (XXX) + 6 (VI) = MDCCXXXVI
An ancient artifact is engraved with the numeral MCCC. Divide this number by 2 and express the result in Roman numerals.
DCLV
Convert MCCC into its decimal form:
MCCC = 1300
Divide by 2: 1300 / 2 = 650
Convert 650 into Roman numerals: 500 (D) + 100 (C) + 50 (L) = DCLV
Calculate the product of MMX and VIII.
The product is XVI,080
Convert MMX and VIII into numbers:
MMX = 2010
VIII = 8
Multiply the numbers: 2010 × 8 = 16080
Convert 16080 into Roman numerals: 10000 (X) + 6000 (MMMMMM) + 80 (LXXX) = XVI,080
Convert MDCXLIV into its decimal form.
In decimal form, MDCXLIV is 1644
Break MDCXLIV into components:
M = 1000
DC = 600 (D + C)
XL = 40
IV = 4
Add values: 1000 + 600 + 40 + 4 = 1644
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.