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Last updated on May 26th, 2025

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398 in roman numerals

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Roman numerals are a method of expressing numbers using specific symbols: I, V, X, L, C, D, and M. Roman Numerals are used in royal titles, book names, sequences, and more. Here we will discuss Roman Numerals, their rules, and examples.

398 in roman numerals for Vietnamese Students
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What is 398 in Roman Numerals?

Royal titles, such as Henry I, Henry II, etc., often use Roman Numerals. Have you ever wondered what these symbols (I and II) mean? They are Roman Numerals. In ancient times, people used fingers, sticks, and bones to count. As life became more complex, a standard counting system was needed. Ancient Romans used the Roman Numeral system to count. I (1), V (5), X (10), L (50), C (100), D (500), and M (1000) are the symbols used.

 

In Roman Numerals, we use CCCXCVIII to represent 398, where CCC is 300, XC is 90, and VIII is 8. Let’s learn more about Roman numerals and how we write them.

398 in roman numerals

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Basic Rules for 398 in Roman Numerals

There are certain basic rules to write a number in Roman Numerals. Let's discuss some of these rules.

 

Rule 1: Addition Method

The addition method is used when a smaller number is placed after a larger number. For example, VIII → V + III → 5 + 3 = 8

 

Rule 2: Repetition Method

To write a large number, certain Roman Numerals can be repeated up to three times. CCC → 300.

 

Rule 3: Subtraction Method

If a smaller number precedes a larger number in Roman Numerals, we subtract the smaller number from the larger number. For example, XC → C - X → 100 - 10 = 90

 

Rule 4: Limitation Rule

Symbols cannot be repeated more than three times, and certain symbols like V, L, and D cannot be repeated. For example, we don't write VV for 10; instead, we use X.

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How to Write 398 in Roman Numerals

Let’s learn how to write 398 in Roman Numerals by following these methods: Expansion Method and Grouping Method.

  • By Expansion Method

 

  • By Grouping Method
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398 in Roman Numerals by Expansion Method

In the expansion method, based on place value, the number is broken down. Here’s how to write 398 in Roman numerals using the expansion method:

 

Step 1: Break down the number based on place value: 300 + 90 + 8

 

Step 2: Convert each part into Roman Numerals:


300 in Roman Numerals — CCC


90 in Roman Numerals — XC


8 in Roman Numerals — VIII

 

Step 3: Combine the Roman Numerals together:


Therefore, 398 in Roman Numerals is CCC (300) + XC (90) + VIII (8) = CCCXCVIII

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398 in Roman Numerals by Grouping Method

When writing large numbers in Roman Numerals, we group the numbers. To write 398 in Roman Numerals, we group it as 300 + 90 + 8.

 

300 in Roman Numerals — CCC


90 in Roman Numerals — XC


8 in Roman Numerals — VIII

 

So, 398 is written as CCCXCVIII in Roman Numerals.

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Common Mistakes and How to Avoid Them in 398 Roman Numerals

Students often make mistakes when writing numbers in Roman Numerals. Here are some common mistakes and how to avoid them:

Mistake 1

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Errors in the repetition method  
 

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The repetition method can be confusing for beginners, as Roman Numerals cannot be repeated more than three times, and some symbols like V, L, and D cannot be repeated.

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398 in Roman Numerals Examples

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Problem 1

A historian discovers two ancient artifacts marked with the numbers CLXXX and CCXVIII in Roman numerals. What is the sum of these two numbers?

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The sum of CLXXX and CCXVIII is CCCXCVIII.

Explanation

CLXXX = 180  


CCXVIII = 218  


180 + 218 = 398  


398 in Roman numerals is written as CCCXCVIII.

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Problem 2

A museum has CCCXCVIII coins to be evenly distributed among XLIX display cases. How many coins will each display case receive?

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Each display case will receive VIII coins.
 

Explanation

To find the number of coins per display case, divide the total number of coins by the number of display cases.  


CCCXCVIII = 398  


XLIX = 49  


398 / 49 = 8  


8 in Roman numerals is written as VIII.

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Problem 3

An archaeologist finds a scroll detailing the construction of a Roman building with a height of CC and a width of CXCVIII. What is the total perimeter of the building?

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The total perimeter of the building is DCCXCVI.
 

Explanation

Perimeter is calculated by adding the lengths of all sides.  


Height = CC = 200  


Width = CXCVIII = 198

 
Perimeter = 2 × (Height + Width) = 2 × (200 + 198) = 2 × 398 = 796  


796 in Roman numerals is written as DCCXCVI.

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Problem 4

A scholar is translating ancient texts and needs to subtract the number CLXXXIX from CCCXCVIII. What is the result?

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The result of subtracting CLXXXIX from CCCXCVIII is CCIX.

Explanation

CCCXCVIII = 398  


CLXXXIX = 189  


398  189 = 209  


209 in Roman numerals is written as CCIX.

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Problem 5

Convert the following mathematical expression into Roman numerals: (CC + C) × II.

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The expression (CC + C) × II in Roman numerals is written as DC.
 

Explanation

First, convert the numbers to Roman numerals:  


CC = 200  


C = 100  


II = 2  

 

Now, solve the expression:  


(200 + 100) × 2 = 300 × 2 = 600  


600 in Roman numerals is written as DC.

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FAQs on 398 in Roman Numerals

1.What is 399 in Roman Numerals?

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2.How do you write 398 in Roman Numerals?

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3.What is 400 in Roman Numerals?

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4.Is CCCXCVIII a prime number?

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5.What are the multiples of 398?

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Important Glossaries for 398 in Roman Numerals

  • Addition method: Used when a smaller numeral follows a larger numeral, and their values are added. For example, VIII = V + III = 5 + 3 = 8.

 

  • Subtraction method: Used when a smaller numeral precedes a larger numeral, and the smaller is subtracted from the larger. For example, XC = C  X = 90.

 

  • Grouping method: The process of grouping numbers based on their place value and converting each group to Roman Numerals. For example, 398 = 300 + 90 + 8 = CCCXCVIII.

 

  • Repetition rule: Certain symbols (I, X, C, M) in the Roman numeric system can be repeated up to three times. For example, CCC = 300.

 

  • Limitation rule: Some symbols like V, L, and D cannot be repeated, and no symbol can be repeated more than three times consecutively.
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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.

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Fun Fact

: She loves to read number jokes and games.

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