128 LearnersLast updated on May 26th, 2025
CXXII in Roman Numerals
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 CXXII.
What is CXXII in Roman Numerals?
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. CXXII in Roman numerals can be written in number form by adding the values of each Roman numeral, i.e. CXXII = 122.
Let us learn more about the Roman numeral CXXII, how to write it, the mistakes we usually make, and ways to avoid these mistakes.
Basic Rules for CXXII in Roman Numerals
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.
Rule 1: Addition Method:
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.
Rule 2: Repetition Method:
A symbol that is repeated three times in continuation increases the value of the numeral. For example, XXX = 30.
Rule 3: Subtraction Method:
We use the subtraction method when a smaller symbol precedes a larger symbol. For example, XL = 40 (which is 50 – 10).
Rule 4: Limitation Rule:
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.
How to Write CXXII in Roman Numerals?
Let us learn about how to write CXXII in Roman numerals. There are two methods that we can use to write Roman numerals:
- By Expansion Method
- By Grouping Method
CXXII in Roman Numeral by Expansion Method
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 CXXII,
Step 1: First, we break the Roman numerals. CXXII = C + X + X + I + I
Step 2: Write the Roman Numerals for each part The Roman Numeral C is 100 The Roman Numeral X is 10 The Roman Numeral I is 1
Step 3: Combine all the numbers C + X + X + I + I = 100 + 10 + 10 + 1 + 1 = 122. Therefore, the Roman Numeral CXXII is 122.
CXXII in Roman Numeral by Grouping Method
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 CXXII.
Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are C, XX, and II. The numeral for C is 100 The numeral for XX is 20
Step 2: Now we need to either add or subtract the smaller number, depending on its place.
Here we add II to CXX and we will get CXXII. The Roman numeral II is 2 Therefore, the numeral of CXXII is 122.
Numbers Related to CXXII in Roman Numerals
We follow a pattern when it comes to writing Roman numerals. In this section, we will write some numbers related to the Roman numeral CXXII:
| Roman Numeral | Number | Breakdown |
|---|---|---|
| CXX | 120 | C + X + X |
| CXXI | 121 | C + X + X + I |
| CXXII | 122 | C + X + X + I + I |
| CXXIII | 123 | C + X + X + I + I + I |
| CXXIV | 124 | C + X + X + IV |
| CXXV | 125 | C + X + X + V |
| CXXVI | 126 | C + X + X + V + I |
| CXXVII | 127 | C + X + X + V + I + I |
| CXXVIII | 128 | C + X + X + V + I + I + I |
| CXXIX | 129 | C + X + X + IX |
Common Mistakes and How to Avoid Them in CXXII Roman Numerals
Students can make mistakes when studying Roman numerals. Here are a few common mistakes students make, and ways to avoid them.
Mistake 1
Mistakes when applying the repetition method
It can be quite confusing for beginners to remember that Roman Numerals cannot be repeated more than three times. Another thing to keep in mind is that Roman Numerals such as V, L, and D cannot be repeated.
For example, writing LL as 100 is incorrect, the correct answer is C.
CXXII Roman Numerals Examples
Problem 1
A historian finds a document fragment with the number CXXII. If this number represents the number of years since a treaty was signed, and the current year is 2023, in what year was the treaty signed?
The treaty was signed in 1901.
Explanation
Convert the Roman numeral CXXII into its decimal form:
CXXII = 122
Subtract 122 years from the current year, 2023: 2023 - 122 = 1901
Thus, the treaty was signed in the year 1901.
Problem 2
A museum exhibit features ancient coins, each stamped with the Roman numeral CXXII. If each coin is valued at $10 today, what is the total value of a collection containing 15 such coins?
The total value is $150.
Explanation
Each coin is valued at $10.
Multiply the value by the number of coins: 10 × 15 = 150
The total value of the collection is $150.
Problem 3
An archeologist discovers a series of stone tablets marked with Roman numerals, including CXXII and LXI. What is the sum of these numerals?
The sum is CLXXXIII.
Explanation
Convert the Roman numerals into their decimal form:
CXXII = 122
LXI = 61
Now add both numbers: 122 + 61 = 183
Convert 183 into its Roman numeral: 100 (C) + 80 (LXXX) + 3 (III) = CLXXXIII
Problem 4
A collector has a rare manuscript with the page numbers in Roman numerals. If a page is marked CXXII and another marked XCII, what is the difference in page numbers?
The difference is XXX.
Explanation
Convert the Roman numerals into their decimal form:
CXXII = 122
XCII = 92
Now subtract the numbers: 122 - 92 = 30
Convert 30 into its Roman numeral: 30 = XXX
Problem 5
A mathematician is analyzing sequences of numbers in Roman numerals. If she encounters a sequence starting with CXXII, followed by CXXIII, what is the next number in the sequence in Roman numerals?
The next number is CXXIV.
Explanation
Convert the sequence of Roman numerals into their decimal form:
CXXII = 122
CXXIII = 123
The next number in the sequence is one more than 123, which is 124.
Convert 124 into its Roman numeral: 100 (C) + 20 (XX) + 4 (IV) = CXXIV
FAQs on CXXII in Roman Numerals
1.What is XII in Roman numerals?
2.Is CXXII a prime number?
3.What is CXXII + CXXII?
4.What is CXXXIII?
5.Subtract LII from CXXII
Important Glossaries for CXXII in Roman Numerals
- Limitation Rule: There are some symbols that cannot be repeated more than once (V, L, D). For example, LVV for 60 is wrong, the correct answer is LX.
- Place value: The position of a digit in a number, this position determines its value. For example, the number 2 in 23 is in the ten's place.
- Repetition Method: A method where a symbol is repeated to increase its value, but not more than three times.
- Prime Number: A number that has only two factors or multiples is called a prime number. For example, 29 is a prime number that has only two factors: 1 and itself.
- Subtraction Method: A method where a smaller numeral is placed before a larger numeral to indicate subtraction. For example, IX is 9 (10 - 1).
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Hiralee Lalitkumar Makwana
About the Author
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.
Fun Fact
: She loves to read number jokes and games.
