Last updated on May 26th, 2025
To meet their daily commerce and administration needs, the ancient Romans developed Roman numerals. This system used a combination of seven symbols — I, V, X, L, C, D, and M to represent numbers. Roman numerals were employed to record transactions, keep track of data, and label military units. In this topic, we are going to learn about the Roman numeral DCX.
The ancient Romans discovered that counting fingers could become cumbersome after 10. To address this complexity, the Roman numeric system was developed.
This was widely used throughout Europe as a standard writing system until the late Middle Ages. The Roman numeric system uses seven symbols — I, V, X, L, C, D, and M.
Numerals are made up of various combinations of these symbols. DCX in Roman numerals can be written in number form by adding the values of each Roman numeral, i.e., DCX = 600 + 100 + 10 = 710.
Let us learn more about the Roman numeral DCX, 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 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 up to three times in succession 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 DCX in Roman numerals. There are two methods that we can use to write Roman numerals:
Breaking down 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 DCX,
Step 1: First, we break the Roman numerals. DCX = D + C + X
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
Step 3: Combine all the numbers D + C + X = 500 + 100 + 10 = 610. Therefore, the Roman Numeral DCX is 610.
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 DCX.
Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are D, C, and X. The numeral for D is 500. The numeral for C is 100.
Step 2: Now we need to either add or subtract the smaller number, depending on its place. Here we add X to DC and we will get DCX. The Roman numeral X is 10. Therefore, the numeral of DCX is 610.
Students can make mistakes when studying Roman numerals. Here are a few common mistakes students make, and ways to avoid them.
Calculate the sum of DCX and CL. Give your answer in Roman numerals.
The sum is DCCLX
Convert both Roman numerals into their decimal form: DCX = 610
CL = 150
Now add both numbers: 610 + 150 = 760
Convert the number into its Roman numeral: 760 = 700 (DCC) + 60 (LX) = DCCLX
What is the difference between MCM and DCX? Write it in Roman numerals.
The difference is MCCXC
Convert the Roman numerals into their decimal form: MCM = 1900
DCX = 610
Subtract the numbers: 1900 - 610 = 1290
Convert the number into its Roman numeral: 1290 = 1000 (M) + 200 (CC) + 90 (XC) = MCCXC
Divide DCX by 5 and write the answer in Roman numerals.
CXXII
Convert DCX into its decimal form: DCX = 610
Divide by 5: 610 ÷ 5 = 122
Write 122 in Roman numerals: 122 = 100 (C) + 20 (XX) + 2 (II) = CXXII
Find the product of DCX and III.
MDCCCXXX is the product of DCX and III.
Write DCX and III in numbers: DCX = 610
III = 3
Multiply the numbers: 610 × 3 = 1830
Convert 1830 into its Roman numerals: 1000 (M) + 800 (DCCC) + 30 (XXX) = MDCCCXXX
Convert DCX into its decimal form.
In decimal form, DCX is 610
Break DCX into components: D = 500
C = 100
X = 10
Add values: 500 + 100 + 10 = 610
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.