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Last updated on March 17th, 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 CCCLX.
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. CCCLX in Roman numerals can be written in number form by adding the values of each Roman numeral, i.e. CCCLX = 360.
Let us learn more about the Roman numeral CCCLX, 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, CCC = 300.
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 CCCLX 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 CCCLX,
Step 1: First we break the Roman numerals. CCCLX = C + C + C + L + X
Step 2: Write the Roman Numerals for each part The Roman Numeral C is 100 The Roman Numeral L is 50 The Roman Numeral X is 10
Step 3: Combine all the numbers C + C + C + L + X = 100 + 100 + 100 + 50 + 10 = 360. Therefore, the Roman Numeral CCCLX is 360.
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 CCCLX.
Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are CCC, L, and X. The numeral for CCC is 300
Step 2: Now we need to add the smaller numbers, depending on their place. Here we add L and X to CCC and we will get CCCLX. The Roman numeral L is 50, and X is 10. Therefore, the numeral of CCCLX is 360.
Students can make mistakes when studying Roman numerals. Here are a few common mistakes students make, and ways to avoid them.
A museum exhibit lasts for CCCLX minutes. How many hours and minutes is this?
6 hours and 0 minutes
Convert CCCLX from Roman numerals to decimal form: CCCLX = 360
Divide 360 by 60 to convert minutes to hours: 360 ÷ 60 = 6 hours and 0 minutes
If a historian reads CCCLX pages over X days, how many pages does he read per day?
XXXVI pages per day
Convert the Roman numerals into decimal form: CCCLX = 360
X = 10
Divide the number of pages by the number of days: 360 ÷ 10 = 36
Convert 36 into Roman numerals: 36 = 30 (XXX) + 6 (VI) = XXXVI
A clock chimes every hour for a total of CCCLX chimes in a day. How many times does it chime each hour?
XV times
Convert CCCLX from Roman numerals to decimal form: CCCLX = 360
There are 24 hours in a day, so divide 360 by 24: 360 ÷ 24 = 15
Convert 15 into Roman numerals: 15 = 10 (X) + 5 (V) = XV
A marathon runner completes a circuit of CCCLX kilometers. If she runs IX kilometers per day, how many days will it take her to complete the circuit?
XL days
Convert the Roman numerals into decimal form: CCCLX = 360
IX = 9 Divide the total kilometers by the kilometers per day: 360 ÷ 9 = 40
Convert 40 into Roman numerals: 40 = XL
Convert CCCLX into its decimal form.
In decimal form, CCCLX is 360
Break CCCLX into components: CCC = 300
LX = 60
Add values: 300 + 60 = 360
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.