Last updated on May 26th, 2025
To meet their daily commerce and administration needs, the ancient Romans developed Roman Numerals. They 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 CDXII.
Ancient Romans discovered that counting fingers could become complicated after 10. To overcome this complexity, the Roman numeric system was developed. This system 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.
CDXII in Roman numerals can be written as 412 in number form by adding and subtracting the values of each Roman numeral. Let us learn more about the Roman numeral CDXII, how to write it, the common mistakes, and ways to avoid these mistakes.
When writing Roman numerals, there are a few rules 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. 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.
A smaller symbol before a larger symbol indicates subtraction. 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 at all. For example, 10 is represented as X and not VV.
Let us learn about how to write CDXII 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 numbers is known as the expansion method. This 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 or subtract the numerals together.
For CDXII,
Step 1: First, we break the Roman numerals. CDXII = C + D + X + 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 X is 10.
The Roman Numeral I is 1.
Step 3: Combine all the numbers, accounting for subtraction where necessary. CDXII = 500 - 100 + 10 + 1 + 1 = 412.
Therefore, the Roman numeral CDXII is 412.
Using subtraction and addition rules, we will apply the grouping method. This involves breaking 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 CDXII.
Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are CD and XII. 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 XII to CD to get CDXII. The Roman numeral XII is 12.
Therefore, the numeral of CDXII is 412.
Students can make mistakes when studying Roman numerals. Here are a few common mistakes students make, and ways to avoid them.
If a Roman merchant had CDXII coins and gave away CXXIV, how many coins does he have left? Write the answer in Roman numerals.
The merchant has CCLXXXVIII coins left.
Convert the Roman numerals into their decimal forms:
CDXII = 412
CXXIV = 124
Subtract the numbers: 412 - 124 = 288
Convert 288 into Roman numerals: 200 (CC) + 80 (LXXX) + 8 (VIII) = CCLXXXVIII
A historian found a document mentioning CDXII years since the founding of a city. If the city was founded in 800 AD, in which year was the document written?
The document was written in 1212 AD.
Convert CDXII into its decimal form:
CDXII = 412
Add the number of years to the founding year: 800 + 412 = 1212
The document was written in 1212 AD.
Divide CDXII by IV and write the answer in Roman numerals.
CIII
Convert CDXII and IV into their decimal forms:
CDXII = 412
IV = 4
Divide: 412 ÷ 4 = 103
Write 103 in Roman numerals: 100 (C) + 3 (III) = CIII
Calculate the product of CDXII and II. Write the answer in Roman numerals.
The product is DCCCXXIV.
Convert CDXII and II into their decimal forms:
CDXII = 412
II = 2
Multiply the numbers: 412 × 2 = 824
Convert 824 into Roman numerals: 800 (DCCC) + 20 (XX) + 4 (IV) = DCCCXXIV
Convert CDXII into its decimal form.
In decimal form, CDXII is 412.
Break CDXII into components:
CD = 400
X = 10
II = 2
Add values: 400 + 10 + 2 = 412
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.