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 CMXLVI.
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. CMXLVI in Roman numerals can be written in number form by adding the values of each Roman numeral, i.e. CMXLVI = 946.
Let us learn more about the Roman numeral CMXLVI, 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 CMXLVI 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 CMXLVI,
Step 1: First, we break the Roman numerals. CMXLVI = C + M + XL + V + 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 XL is 40 The Roman Numeral V is 5 The Roman Numeral I is 1
Step 3: Combine all the numbers C + M + XL + V + I = 1000 - 100 + 50 - 10 + 5 + 1 = 946.
Therefore, the Roman Numeral CMXLVI is 946.
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 CMXLVI.
Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are CM, XL, and VI. The numeral for CM is 900 The numeral for XL is 40 The numeral for VI is 6
Step 2: Now we need to either add or subtract the smaller number, depending on its place.
Here, we add XL and VI to CM, and we will get CMXLVI. Therefore, the numeral of CMXLVI is 946.
Students can make mistakes when studying Roman numerals. Here are a few common mistakes students make, and ways to avoid them.
If a treasure map shows CMXLVI steps to reach a destination, and you have already walked DCC, how many more steps in Roman numerals do you need to walk?
CCXLVI
Convert the Roman numerals into decimal form:
CMXLVI = 946
DCC = 700
Subtract the number of steps already walked from the total steps: 946 - 700 = 246
Convert the result back to Roman numerals: 246 = 200 (CC) + 40 (XL) + 6 (VI) = CCXLVI
A clock shows the time CMXLVI in minutes since midnight. How many hours and minutes is that in standard time format (HH:MM)?
15:46
Convert CMXLVI into decimal form:
CMXLVI = 946
Convert minutes to hours and minutes: 946 ÷ 60 = 15 R 46 So, 15 hours and 46 minutes
Suppose a Roman army is divided equally into CMXLVI soldiers. If each legion consists of C soldiers, how many legions can be formed?
IX
Convert CMXLVI and C into decimal form:
CMXLVI = 946
C = 100
Divide the total soldiers by the number of soldiers per legion: 946 ÷ 100 = 9 R 46
Convert the quotient into Roman numerals: 9 = IX
You have a CMXLVI-page book. If you read XLVI pages per day, how many full days will it take you to read the book?
XX
Convert CMXLVI and XLVI into decimal form:
CMXLVI = 946
XLVI = 46
Divide the total number of pages by the number of pages read per day: 946 ÷ 46 = 20
Convert the result into Roman numerals: 20 = XX
Convert CMXLVI from Roman numeral to decimal form.
946
Break CMXLVI into components:
CM = 900 (1000 - 100)
XL = 40 (50 - 10)
VI = 6 (5 + 1)
Add values: 900 + 40 + 6 = 946
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.