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 DCLVIII.
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. DCLVIII in Roman numerals can be written in number form by adding the values of each Roman numeral, i.e., DCLVIII = 658.
Let us learn more about the Roman numeral DCLVIII, 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 smaller symbol precedes a larger 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, 10 is represented as X and not VV.
Let us learn about how to write DCLVIII 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 DCLVIII,
Step 1: First, we break the Roman numerals. DCLVIII = D + C + L + V + I + I + I
Step 2: Write the Roman Numerals for each part The Roman Numeral D is 500 The Roman Numeral C is 100 The Roman Numeral L is 50 The Roman Numeral V is 5 The Roman Numeral I is 1
Step 3: Combine all the numbers D + C + L + V + I + I + I = 500 + 100 + 50 + 5 + 1 + 1 + 1 = 658. Therefore, the Roman Numeral DCLVIII is 658.
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 DCLVIII.
Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are D, C, L, and VIII. The numeral for DCL is 650.
Step 2: Now we need to either add or subtract the smaller number, depending on its place.
Here we add VIII to DCL and we will get DCLVIII. The Roman numeral VIII is 8. Therefore, the numeral of DCLVIII is 658.
Students can make mistakes when studying Roman numerals. Here are a few common mistakes students make, and ways to avoid them.
Calculate the combined total of DCLVIII and CCLII. Express the answer in Roman numerals.
The combined total is CMX.
Convert both Roman numerals into their decimal form:
DCLVIII = 658
CCLII = 252
Add the numbers together: 658 + 252 = 910
Convert 910 to Roman numerals: 910 = 900 (CM) + 10 (X) = CMX
Subtract CCCL from DCLVIII and provide the result in Roman numerals.
The result is CCCVIII.
Convert the Roman numerals into their decimal form:
DCLVIII = 658
CCCL = 350
Subtract the numbers: 658 - 350 = 308
Convert 308 into Roman numerals: 308 = 300 (CCC) + 8 (VIII) = CCCVIII
What is the result when you divide DCLVIII by VIII and write the answer in Roman numerals?
LXXXII
Convert DCLVIII into its decimal form:
DCLVIII = 658
Divide by 8: 658 ÷ 8 = 82
Convert 82 to Roman numerals: 82 = 80 (LXXX) + 2 (II) = LXXXII
Multiply DCLVIII by III. What is the product in Roman numerals?
The product is MCMXLIV.
Convert the Roman numerals into their decimal form:
DCLVIII = 658
III = 3
Multiply the numbers: 658 × 3 = 1974
Convert 1974 into Roman numerals: 1974 = 1000 (M) + 900 (CM) + 70 (LXX) + 4 (IV) = MCMXLIV
Convert DCLVIII into its decimal form.
In decimal form, DCLVIII is 658.
Break DCLVIII into components:
D = 500
CL = 100 + 50 = 150
VIII = 5 + 3 = 8
Add the values: 500 + 150 + 8 = 658
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.