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 CLX.
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. CLX in Roman numerals can be written in number form by adding the values of each Roman numeral, i.e., CLX = 160.
Let us learn more about the Roman numeral CLX, 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, 100 is represented as C and not LL.
Let us learn about how to write CLX 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 CLX,
Step 1: First, we break the Roman numerals. CLX = 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 + L + X = 100 + 50 + 10 = 160. Therefore, the Roman Numeral CLX is 160.
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 CLX.
Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are C, L, and X. 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 L (50) and X (10) to C and we will get CLX. Therefore, the numeral of CLX is 160.
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 has CLX apples and sells XXX apples, how many apples does the merchant have left? Write the answer in Roman numerals.
The merchant has CXXX apples left.
Convert the Roman numerals into their decimal form:
CLX = 160
XXX = 30
Subtract the numbers:
160 - 30 = 130
Convert 130 into its Roman numeral:
130 = 100 (C) + 30 (XXX) = CXXX
A Roman engineer needs CLX bricks to complete a wall. He already has XC bricks. How many more bricks does he need? Write the answer in Roman numerals.
The engineer needs LXX bricks.
Convert the Roman numerals into their decimal form:
CLX = 160
XC = 90
Subtract the numbers:
160 - 90 = 70
Convert 70 into its Roman numeral:
70 = 50 (L) + 20 (XX) = LXX
A Roman scholar is writing a book and has completed XL pages. If the book needs to be CLX pages long, how many more pages does the scholar need to write? Write the answer in Roman numerals.
The scholar needs to write CXX pages.
Convert the Roman numerals into their decimal form:
CLX = 160
XL = 40
Subtract the numbers:
160 - 40 = 120
Convert 120 into its Roman numeral:
120 = 100 (C) + 20 (XX) = CXX
A Roman general receives CLX soldiers from another legion. If he divides them equally among V units, how many soldiers does each unit receive? Write the answer in Roman numerals.
Each unit receives XXXII soldiers.
Convert CLX into its decimal form:
CLX = 160
Divide by 5:
160 ÷ 5 = 32
Convert 32 into its Roman numeral:
32 = 30 (XXX) + 2 (II) = XXXII
Convert CLX into its decimal form.
In decimal form, CLX is 160.
Break CLX into components:
C = 100
L = 50
X = 10
Add values:
100 + 50 + 10 = 160
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.