125 LearnersLast updated on May 26th, 2025
CMXCVIII 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 CMXCVIII.
What is CMXCVIII 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. CMXCVIII in Roman numerals can be written in number form by adding and subtracting the values of each Roman numeral, i.e., CMXCVIII = 998.
Let us learn more about the Roman numeral CMXCVIII, how we write them, the mistakes we usually make, and ways to avoid these mistakes.
Basic Rules for CMXCVIII 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 CMXCVIII in Roman Numerals?
Let us learn about how to write CMXCVIII in Roman numerals. There are two methods that we can use to write Roman numerals:
- By Expansion Method
- By Grouping Method
CMXCVIII 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 CMXCVIII,
Step 1: First, we break the Roman numerals. CMXCVIII = CM + XC + VIII
Step 2: Write the Roman Numerals for each part The Roman Numeral CM is 900 The Roman Numeral XC is 90 The Roman Numeral VIII is 8
Step 3: Combine all the numbers CM + XC + VIII = 900 + 90 + 8 = 998. Therefore, the Roman Numeral CMXCVIII is 998.
CMXCVIII 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 CMXCVIII.
Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are CM, XC, and VIII. 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 XC and VIII to CM, and we will get CMXCVIII. The Roman numeral XC is 90 The Roman numeral VIII is 8 Therefore, the numeral of CMXCVIII is 998.
Numbers Related to CMXCVIII 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 CMXCVIII:
| Number | Roman Numeral | Breakdown |
|---|---|---|
| 990 | CMXC | CM = 900 + XC = 90 = 990 |
| 991 | CMXCI | CM = 900 + XC = 90 + I = 1 = 991 |
| 992 | CMXCII | CM = 900 + XC = 90 + I = 2 = 992 |
| 993 | CMXCIII | CM = 900 + XC = 90 + I = 3 = 993 |
| 994 | CMXCIV | CM = 900 + XC = 90 + IV = 4 = 994 |
| 995 | CMXCV | CM = 900 + XC = 90 + V = 5 = 995 |
| 996 | CMXCVI | CM = 900 + XC = 90 + V = 5 + I = 1 = 996 |
| 997 | CMXCVII | CM = 900 + XC = 90 + V = 5 + I = 2 = 997 |
| 998 | CMXCVIII | CM = 900 + XC = 90 + V = 5 + I = 3 = 998 |
| 999 | CMXCIX | CM = 900 + XC = 90 + IX = 9 = 999 |
Common Mistakes and How to Avoid Them in CMXCVIII 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.
CMXCVIII Roman Numerals Examples
Problem 1
A museum has CMXCVIII artifacts. They acquired LII more. How many artifacts do they have now? Write the answer in Roman numerals.
The total number of artifacts is ML.
Explanation
Convert CMXCVIII and LII into decimal form: CMXCVIII = 998
LII = 52
Add the numbers: 998 + 52 = 1050
Convert 1050 into Roman numerals: 1050 = 1000 (M) + 50 (L) = ML
Problem 2
A historian found CMXCVIII pages of ancient manuscripts. If LXIV pages were damaged, how many usable pages remain? Write the answer in Roman numerals.
The number of usable pages is CMXXXIV.
Explanation
Convert CMXCVIII and LXIV into decimal form: CMXCVIII = 998
LXIV = 64
Subtract the numbers: 998 - 64 = 934
Convert 934 into Roman numerals: 934 = 900 (CM) + 30 (XXX) + 4 (IV) = CMXXXIV
Problem 3
Divide CMXCVIII by II and write the answer in Roman numerals.
The result is CDXCIX.
Explanation
Convert CMXCVIII into decimal form: CMXCVIII = 998
Divide by 2: 998 ÷ 2 = 499
Convert 499 into Roman numerals: 499 = 400 (CD) + 90 (XC) + 9 (IX) = CDXCIX
Problem 4
If CMXCVIII marbles are divided equally among VI children, how many marbles does each child get? Write the answer in Roman numerals.
Each child gets CLXVI marbles.
Explanation
Convert CMXCVIII into decimal form: CMXCVIII = 998
Divide by 6: 998 ÷ 6 = 166
Convert 166 into Roman numerals: 166 = 100 (C) + 50 (L) + 10 (X) + 6 (VI) = CLXVI
Problem 5
Convert CMXCVIII into its decimal form.
In decimal form, CMXCVIII is 998.
Explanation
Break CMXCVIII into components: CM = 900
XC = 90
VIII = 8
Add values: 900 + 90 + 8 = 998
FAQs on CMXCVIII in Roman Numerals
1.What is XCVIII in Roman numerals?
2.Is CMXCVIII a prime number?
3.What is CMXCVIII + I?
4.What is DCCC?
5.Subtract II from CMXCVIII
6.How can children in Vietnam use numbers in everyday life to understand CMXCVIII in Roman Numerals?
7.What are some fun ways kids in Vietnam can practice CMXCVIII in Roman Numerals with numbers?
8.What role do numbers and CMXCVIII in Roman Numerals play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve CMXCVIII in Roman Numerals skills?
Important Glossaries for CMXCVIII in Roman Numerals
- Subtraction Method: A method used in Roman numerals where a smaller numeral precedes a larger numeral, indicating subtraction. For example, XC is 90 (100-10).
- Addition Method: The process of adding values when a larger numeral precedes a smaller numeral. For example, VI is 6 (5+1).
- Limitation Rule: Symbols like V, L, and D cannot be repeated more than once. For example, 60 is represented as LX, not LVV.
- Place Value: The value of a digit based on its position within a number. For example, the number 9 in 998 is in the hundreds place.
- Roman Numerals: An ancient numeric system using combinations of letters from the Latin alphabet (I, V, X, L, C, D, M) to represent numbers.
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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.
