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 DCCXXIV.
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. DCCXXIV in Roman numerals can be written in number form by adding the values of each Roman numeral, i.e., DCCXXIV = 724.
Let us learn more about the Roman numeral DCCXXIV, 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 smaller symbol precedes a larger 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 DCCXXIV 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 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 DCCXXIV,
Step 1: First, we break the Roman numerals. DCCXXIV = D + C + C + X + X + IV
Step 2: Write the Roman Numerals for each part. The Roman Numeral D is 500 The Roman Numeral C is 100 The Roman Numeral X is 10 The Roman Numeral IV is 4
Step 3: Combine all the numbers. D + C + C + X + X + IV = 500 + 100 + 100 + 10 + 10 + 4 = 724. Therefore, the Roman Numeral DCCXXIV is 724.
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 DCCXXIV.
Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are DCC, XX, and IV. The numeral for DCC is 700
Step 2: Now, we need to either add or subtract the smaller number, depending on its place.
Here we add XX and IV to DCC, and we will get DCCXXIV. The Roman numeral XX is 20 The Roman numeral IV is 4 Therefore, the numeral of DCCXXIV is 724.
Students can make mistakes when studying Roman numerals. Here are a few common mistakes students make, and ways to avoid them.
A historian finds an ancient tablet with the inscription DCCXXIV + CXL. Calculate the sum and write it in Roman numerals.
The sum is DCCCLXIV
Convert both Roman numerals into their decimal form:
DCCXXIV = 724
CXL = 140
Now add both numbers: 724 + 140 = 864
Now convert the number into its Roman numeral: 864 = 800 (DCCC) + 60 (LX) + 4 (IV) = DCCCLXIV
An artifact shows two dates: DCCC and DCCXXIV. What is the difference between these dates in Roman numerals?
The difference is LXXVI
Convert the Roman numerals into their decimal form:
DCCC = 800
DCCXXIV = 724
Now we subtract the numbers: 800 - 724 = 76
Convert the number into its Roman numeral: 76 = 70 (LXX) + 6 (VI) = LXXVI
A manuscript details a division of land marked as DCCXXIV acres to be divided by 4 among heirs. How many acres does each heir receive? Write the answer in Roman numerals.
Each heir receives CLXXXI acres
Convert DCCXXIV into its decimal form:
DCCXXIV = 724
Divide by 4: 724 / 4 = 181
Write 181 in Roman numerals: 181 = 100 (C) + 80 (LXXX) + 1 (I) = CLXXXI
A scroll describes a battle involving DCCXXIV soldiers, multiplied by the morale factor of II. Calculate the effective soldier count in Roman numerals.
The effective count is MCDXLVIII
Write DCCXXIV and II in numbers:
DCCXXIV = 724
II = 2
Multiply the numbers: 724 × 2 = 1448
Convert 1448 into its Roman numerals: 1448 = 1000 (M) + 400 (CD) + 40 (XL) + 8 (VIII) = MCDXLVIII
Convert DCCXXIV into its decimal form.
In decimal form, DCCXXIV is 724
Break DCCXXIV into components:
DCC = 700 (D + CC)
XX = 20 (X + X)
IV = 4 (V - I)
Add values: 700 + 20 + 4 = 724
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.