128 LearnersLast updated on May 26th, 2025
CDXLVIII 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 CDXLVIII.
What is CDXLVIII 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. CDXLVIII in Roman numerals can be written in number form by adding or subtracting the values of each Roman numeral, i.e. CDXLVIII = 448.
Let us learn more about the Roman numeral CDXLVIII, how we write them, the mistakes we usually make, and ways to avoid these mistakes.
Basic Rules for CDXLVIII 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 larger symbol follows a smaller 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 CDXLVIII in Roman Numerals?
Let us learn about how to write CDXLVIII in Roman numerals. There are two methods that we can use to write Roman numerals:
- By Expansion Method
By Grouping Method
CDXLVIII 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 or subtract the numerals accordingly.
For CDXLVIII,
Step 1: First we break the Roman numerals. CDXLVIII = C + D + XL + V + I + I + I
Step 2: Write the Roman Numerals for each part The Roman Numeral C is 100 The Roman Numeral D is 500 The Roman Numeral XL is 40 The Roman Numeral V is 5 The Roman Numeral I is 1
Step 3: Combine all the numbers D (500) - C (100) + XL (40) + V (5) + I (1) + I (1) + I (1) = 448. Therefore, the Roman Numeral CDXLVIII is 448.
CDXLVIII 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 CDXLVIII.
Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are CD, XL, and VIII. The numeral for CD is 400 The numeral for XL is 40 The numeral for VIII is 8
Step 2: Combine all the numbers according to the rules. Here we add them all together: CD (400) + XL (40) + VIII (8) = 448. Therefore, the numeral of CDXLVIII is 448.
Numbers Related to CDXLVIII 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 CDXLVIII:
| Roman Numeral | Number | Breakdown |
|---|---|---|
| CDXLVIII | 448 | CD + XL + VIII |
| CDXLVII | 447 | CD + XL + VII |
| CDXLVI | 446 | CD + XL + VI |
| CDXLV | 445 | CD + XL + V |
| CDXLIV | 444 | CD + XL + IV |
Common Mistakes and How to Avoid Them in CDXLVIII 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.
CDXLVIII Roman Numerals Examples
Problem 1
If a hiker climbs CDXLVIII meters and then descends C meters, how many meters has the hiker gained? Write the answer in Roman numerals.
The hiker has gained CCCXLVIII meters.
Explanation
Convert the Roman numerals into their decimal form:
CDXLVIII = 448
C = 100
Subtract the meters descended from the meters climbed: 448 - 100 = 348
Convert the number into its Roman numeral: 348 = 300 (CCC) + 40 (XL) + 8 (VIII) = CCCXLVIII
Problem 2
A collector has CDXLVIII stamps and decides to give away L stamps. How many stamps does the collector have left? Write the answer in Roman numerals.
The collector has CCCXCVIII stamps left.
Explanation
Convert the Roman numerals into their decimal form:
CDXLVIII = 448
L = 50
Subtract the given away stamps from the total: 448 - 50 = 398
Convert the number into its Roman numeral: 398 = 300 (CCC) + 90 (XC) + 8 (VIII) = CCCXCVIII
Problem 3
A Roman merchant sold CDXLVIII pieces of cloth in a month and then sold another half of that amount the next month. How many pieces were sold in the second month? Write in Roman numerals.
CCXXIV pieces were sold in the second month.
Explanation
Convert the Roman numeral into its decimal form:
CDXLVIII = 448
Calculate half of 448: 448 / 2 = 224
Convert 224 into its Roman numeral: 224 = 200 (CC) + 20 (XX) + 4 (IV) = CCXXIV
Problem 4
A historian finds that an ancient text mentions a treasure of CDXLVIII gold coins, which were divided equally among VIII people. How many coins did each person receive? Write the answer in Roman numerals.
Each person received LVI coins.
Explanation
Convert the Roman numerals into their decimal form:
CDXLVIII = 448
VIII = 8
Divide the total coins by the number of people: 448 / 8 = 56
Convert 56 into its Roman numeral: 56 = 50 (L) + 6 (VI) = LVI
Problem 5
Convert CDXLVIII into its decimal form.
In decimal form, CDXLVIII is 448.
Explanation
Break CDXLVIII into components:
CD = 400 (500 - 100)
XL = 40 (50 - 10)
VIII = 8 (5 + 3)
Add values: 400 + 40 + 8 = 448
FAQs on CDXLVIII in Roman Numerals
1.What is CDL in Roman numerals?
2.Is CDXLVIII a prime number?
3.What is CDXLVIII + II?
4.What is CD?
5.Subtract XL from CDXLVIII
6.How can children in Vietnam use numbers in everyday life to understand CDXLVIII in Roman Numerals?
7.What are some fun ways kids in Vietnam can practice CDXLVIII in Roman Numerals with numbers?
8.What role do numbers and CDXLVIII 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 CDXLVIII in Roman Numerals skills?
Important Glossaries for CDXLVIII in Roman Numerals
- Subtraction Rule: Only certain symbols can be subtracted, such as I from V and X, and X from L and C.
- Addition Rule: When a smaller numeral follows a larger numeral, add the smaller numeral to the larger one.
- Place Value: In Roman numerals, the sequence of symbols determines their value; numerals like I, X, C, and M can be combined with others to adjust value.
- Repetition Rule: Symbols like I, X, C, and M can be repeated up to three times in succession.
- Grouping Method: A technique used to simplify writing Roman numerals by breaking them down into logical groups, facilitating easier calculations.
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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.
