Last updated on May 26th, 2025
Roman numerals are a way of expressing numbers using symbols. I, V, X, L, C, D, and M are the symbols we use. Roman numerals are used in royal titles, book names, sequences, and so on. Here we will be discussing Roman numerals, rules, and examples.
The royal titles, such as Henry I, Henry II, and so on, make use of Roman numerals. Have you noticed these titles and wondered what these symbols (I and II) represented?
Those are the Roman numerals. In ancient times, people used fingers, sticks, and bones to count. As life became more complex, a standard form was required for counting. Ancient Romans used the Roman numeral system, which includes symbols like I (1), V (5), X (10), L (50), D (100), and M (1000).
In Roman numerals, we use CCCXV to represent 315, where CCC is 300, X is 10, and V is 5. Let’s learn more about Roman numerals and how we write them.
There are certain basic rules for writing a number in Roman numerals. In this section, let’s discuss some basic rules that need to be remembered.
The addition method is used when a smaller number is placed after a larger number. For example, XV → X + V → 10 + 5 = 15
To write larger numbers, certain Roman numerals can be repeated up to three times. For example, CCC → 300.
If a smaller number precedes a larger number in Roman numerals, we subtract the smaller number from the larger number. For example, XL → L - X → 50 - 10 = 40
Symbols cannot be repeated more than three times, and some symbols like V, L, and D cannot be repeated. For example, instead of writing VVV for 15, we use XV.
Let’s now learn how to write 315 in Roman numerals using different methods.
In the expansion method, based on the place value, the number is broken down. Here's how to write 315 in Roman numerals using this method:
Step 1: Break the number based on place value: hundreds, tens, and ones. For 315, we write it as 300 + 10 + 5.
Step 2: Convert each part into Roman numerals:
300 in Roman numerals — CCC
10 in Roman numerals — X
5 in Roman numerals — V
Step 3: Combine these Roman numerals:
Therefore, 315 in Roman numerals is CCC (300) + X (10) + V (5) = CCCXV
When writing a large number as a Roman numeral, we can group the number. To write 315 in Roman numerals, we group it as 300 + 10 + 5:
300 in Roman numerals — CCC
10 in Roman numerals — X
5 in Roman numerals — V
So, 315 is written as CCCXV in Roman numerals.
some common mistakes with their solutions are given
A museum has CCCXV artifacts. They want to display them in groups of IX. How many complete groups can they make?
The number of complete groups is XXXV.
To find the number of complete groups, divide the total number of artifacts by the group size.
CCCXV = 315
IX = 9
315 ÷ 9 = 35
35 in Roman numerals is XXXV.
A library has a collection of books labeled with Roman numerals. They have CLXV and CL books in one section. How many books are there in total in Roman numerals?
The total number of books is CCCXV.
Add the number of books in each collection.
CLXV = 165
CL = 150
165 + 150 = 315
315 in Roman numerals is CCCXV.
A historian recorded the construction of a building in the year CCCXV. Calculate how many years have passed since the building was constructed if the current year is MCMXCIX in Roman numerals.
The number of years that have passed is MDCXCIV.
First, convert the years to Arabic numerals and find the difference.
CCCXV = 315
MCMXCIX = 1999
1999 - 315 = 1684
1684 in Roman numerals is MDCXCIV.
Convert the difference between CDL and CXXXV to Roman numerals.
The difference is CCCXV.
Subtract the smaller number from the larger number.
CDL = 450
CXXXV = 135
450 - 135 = 315
315 in Roman numerals is CCCXV.
Using Roman numerals, express the result of the sum of CC and CXV.
The sum is CCCXV.
Add the numbers together.
CC = 200
CXV = 115
200 + 115 = 315
315 in Roman numerals is CCCXV.
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.