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 DCCXXXII.
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. DCCXXXII in Roman numerals can be written in number form by adding the values of each Roman numeral, i.e., DCCXXXII = 732.
Let us learn more about the Roman numeral DCCXXXII, how we write it, 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 DCCXXXII 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 DCCXXXII,
Step 1: First we break the Roman numerals. DCCXXXII = D + CC + XXX + II
Step 2: Write the Roman Numerals for each part The Roman Numeral D is 500 The Roman Numeral C is 100 The Roman Numeral X is 10 The Roman Numeral I is 1
Step 3: Combine all the numbers D + CC + XXX + II = 500 + 100 + 100 + 10 + 10 + 10 + 1 + 1 = 732. Therefore, the Roman Numeral DCCXXXII is 732.
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 DCCXXXII.
Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are DCC, XXX, and II. The numeral for DCC is 700
Step 2: Now we need to either add or subtract the smaller number, depending on its place.
Here we add XXX and II to DCC and we will get DCCXXXII. The Roman numeral for XXX is 30 The Roman numeral for II is 2 Therefore, the numeral of DCCXXXII is 732.
Students can make mistakes when studying Roman numerals. Here are a few common mistakes students make, and ways to avoid them.
Combine the letters of DCC and XXXII into a single Roman numeral. What is the final numeral?
The combined numeral is DCCXXXII
Convert each part into its decimal form:
DCC = 700
XXXII = 32
Now add the numbers: 700 + 32 = 732
Convert 732 into Roman numerals: 700 (DCC) + 30 (XXX) + 2 (II) = DCCXXXII
Subtract CCCXC from DCCXXXII and express the result in Roman numerals.
The difference is CCCXLII
Convert the Roman numerals into decimal form:
DCCXXXII = 732
CCCXC = 390
Subtract the numbers: 732 - 390 = 342
Convert 342 into Roman numerals: 300 (CCC) + 40 (XL) + 2 (II) = CCCXLII
Divide DCCXXXII by IV and write the quotient in Roman numerals.
The quotient is CLXXXIII
Convert DCCXXXII into its decimal form:
DCCXXXII = 732
Divide by 4: 732 / 4 = 183
Convert 183 into Roman numerals: 100 (C) + 80 (LXXX) + 3 (III) = CLXXXIII
Multiply XX by XXXVI and provide the product in Roman numerals.
The product is DCCXX
Convert each numeral to decimal:
XX = 20
XXXVI = 36
Multiply the numbers: 20 × 36 = 720
Convert 720 into Roman numerals: 700 (DCC) + 20 (XX) = DCCXX
Convert DCCXXXII into its decimal form.
In decimal form, DCCXXXII is 732
Break down DCCXXXII into components:
DCC = 700 (D + CC)
XXX = 30 (X + X + X)
II = 2 (I + I)
Add the values: 700 + 30 + 2 = 732
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.