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 CMXII.
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. CMXII in Roman numerals can be written in number form by adding the values of each Roman numeral, i.e., CMXII = 912.
Let us learn more about the Roman numeral CMXII, 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.
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 CMXII 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 CMXII,
Step 1: First, we break the Roman numerals. CMXII = C + M + X + I + I
Step 2: Write the Roman Numerals for each part. The Roman Numeral C is 100 The Roman Numeral M is 1000 The Roman Numeral X is 10 The Roman Numeral I is 1
Step 3: Combine all the numbers. C + M + X + I + I = 100 + 900 + 10 + 1 + 1 = 912. Therefore, the Roman Numeral CMXII is 912.
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 CMXII.
Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are CM and XII. The numeral for CM is 900
Step 2: Now we need to either add or subtract the smaller number, depending on its place.
Here we add XII to CM, and we will get CMXII. The Roman numeral XII is 12 Therefore, the numeral of CMXII is 912.
Students can make mistakes when studying Roman numerals. Here are a few common mistakes students make, and ways to avoid them.
Find the sum of CMXII + LXXXVIII. Write the answer in Roman numerals.
The sum is M.
Convert both Roman numerals into their decimal form:
CMXII = 912
LXXXVIII = 88
Now add both numbers: 912 + 88 = 1000
Now convert the number into its Roman numeral: 1000 = M
What is the difference between MCMX - CMXII? Write in Roman numerals.
The difference is CMXCVIII.
Convert the Roman numerals into their decimal form:
MCMX = 1910
CMXII = 912
Now we subtract the numbers: 1910 - 912 = 998
Convert the number into its Roman numeral: 998 = 900 (CM) + 90 (XC) + 8 (VIII) = CMXCVIII
Divide CMXII by 4 and write the answer in Roman numerals.
CCXXVIII
Convert CMXII into its decimal form:
CMXII = 912
Divide by 4: 912 / 4 = 228
Write 228 in Roman numerals: 228 = 200 (CC) + 20 (XX) + 8 (VIII) = CCXXVIII
Find the product of CMXII and III.
MMMDXXXVI is the product of CMXII and III.
Write CMXII and III in numbers:
CMXII = 912
III = 3
Multiply the numbers: 912 × 3 = 2736
Convert 2736 into its Roman numerals: 2000 (MM) + 700 (DCC) + 30 (XXX) + 6 (VI) = MMMDXXXVI
Convert CMXII into its decimal form.
In decimal form, CMXII is 912.
Break CMXII into components:
CM = 900
X = 10
II = 2
Add values: 900 + 10 + 2 = 912
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.