XXXIII in Roman Numerals

The ancient Romans discovered that counting fingers could get very complicated after 10. To overcome this 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. XXXIII in Roman numerals can be written in number form by adding the values of each Roman numeral, i.e., XXXIII = 33.

Let us learn more about the Roman numeral XXXIII, how to 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.

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 up to three times in sequence 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. For example, 10 is represented as X and not VV.

Let us learn about how to write XXXIII in Roman numerals. There are two methods that we can use to write Roman numerals:

• By Expansion Method
• By Grouping 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 involves breaking down 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 XXXIII,

Step 1: First, we break the Roman numerals. XXXIII = X + X + X + I + I + I

Step 2: Write the Roman Numerals for each part The Roman Numeral X is 10. The Roman Numeral I is 1.

Step 3: Combine all the numbers X + X + X + I + I + I = 10 + 10 + 10 + 1 + 1 + 1 = 33. Therefore, the Roman Numeral XXXIII is 33.

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 XXXIII.

Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are XXX and III. The numeral for XXX is 30.

Step 2: Now we need to either add or subtract the smaller number, depending on its place. Here we add III to XXX and we will get XXXIII. The Roman numeral III is 3. Therefore, the numeral of XXXIII is 33.

We follow a pattern when it comes to writing Roman numerals. In this section, we will write some numbers related to the Roman numeral XXXIII:

• Addition Method: A rule where values are added when a smaller numeral follows a larger numeral. For example, XII = 10 + 1 + 1 = 12.
   
• Subtraction Method: A rule where a smaller numeral precedes a larger numeral, indicating subtraction. For example, IX = 10 - 1 = 9.
   
• Repetition Rule: Roman numerals can be repeated up to three times to increase their value. For example, XXX = 30.
   
• Prime Number: A number that has only two factors: 1 and itself. For example, 11 is a prime number.
   
• Place Value: The value of the position of a digit in a numeral. For example, the number 3 in 33 is in the ten's place.