178 LearnersLast updated on May 26th, 2025
CMXC 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 CMXC.
What is CMXC 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. CMXC in Roman numerals can be written in number form by adding and subtracting the values of each Roman numeral, i.e. CMXC = 900 + 90 = 990.
Let us learn more about the Roman numeral CMXC, how we write it, the mistakes we usually make, and ways to avoid these mistakes.
Basic Rules for CMXC 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 VI, we have 5 + 1 = 6.
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, IV = 4 (which is 5 – 1).
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 CMXC in Roman Numerals?
Let us learn about how to write CMXC in Roman numerals. There are two methods that we can use to write Roman numerals:
- By Expansion Method
- By Grouping Method
CMXC 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 CMXC,
Step 1: First we break the Roman numerals. CMXC = CM + XC
Step 2: Write the Roman Numerals for each part The Roman Numeral CM is 900 The Roman Numeral XC is 90
Step 3: Combine all the numbers CM + XC = 900 + 90 = 990. Therefore, the Roman Numeral CMXC is 990.
CMXC 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 CMXC.
Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are CM and XC. 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 to CM and we will get CMXC. The Roman numeral XC is 90 Therefore, the numeral of CMXC is 990.
Numbers Related to CMXC 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 CMXC:
| 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 CMXC 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 VV for 10 is incorrect, the correct answer is X.
CMXC Roman Numerals Examples
Problem 1
What is the result of adding CMXC to LX? Write the answer in Roman numerals.
The result is ML
Explanation
Convert both Roman numerals into their decimal form: CMXC = 990
LX = 60
Now add both numbers: 990 + 60 = 1050
Now convert the number into its Roman numeral: 1050 = 1000 (M) + 50 (L) = ML
Problem 2
Subtract CXL from CMXC and provide the answer in Roman numerals.
The difference is DCCL
Explanation
Convert the Roman numerals into their decimal form: CMXC = 990
CXL = 140
Now subtract the numbers: 990 - 140 = 850
Convert 850 into its Roman numeral: 850 = 500 (D) + 300 (CCC) + 50 (L) = DCCL
Problem 3
Divide CMXC by V and express the result as a Roman numeral.
CXCVIII
Explanation
Convert CMXC into its decimal form: CMXC = 990
Divide by 5: 990 / 5 = 198
Convert 198 into Roman numerals: 100 (C) + 90 (XC) + 8 (VIII) = CXCVIII
Problem 4
Find the product of CMXC and IV.
The product is MMMDLX
Explanation
Write CMXC and IV in numbers: CMXC = 990
IV = 4
Multiply the numbers: 990 × 4 = 3960
Convert 3960 into Roman numerals: 3000 (MMM) + 900 (CM) + 60 (LX) = MMMDLX
Problem 5
Convert CMXC into its decimal form.
In decimal form, CMXC is 990
Explanation
Break CMXC into components: CM = 900 (1000 - 100)
XC = 90 (100 - 10)
Add values: 900 + 90 = 990
FAQs on CMXC in Roman Numerals
1.What is XC in Roman numerals?
2.Is CMXC a prime number?
3.What is CMXC + CMXC?
4.What is CMXX?
5.Subtract X from CMXC
6.How can children in Vietnam use numbers in everyday life to understand CMXC in Roman Numerals?
7.What are some fun ways kids in Vietnam can practice CMXC in Roman Numerals with numbers?
8.What role do numbers and CMXC 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 CMXC in Roman Numerals skills?
Important Glossaries for CMXC in Roman Numerals
- Limitation Rule: There are some symbols that cannot be repeated more than once (V, L, D). For example, LL for 100 is wrong, the correct answer is C.
- Place value: The position of a digit in a number, this position determines its value. For example, the number 9 in 990 is in the hundred's place.
- Subtraction Method: A method used in Roman numerals where a smaller numeral is placed before a larger numeral to indicate subtraction. For example, IV stands for 4.
- Addition Method: A method in Roman numerals where numerals are added together based on their values. For example, VI stands for 6.
- Grouping Method: A way to simplify Roman numerals by breaking them into smaller, manageable groups to ensure accurate numerical conversion.
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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.
