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Last updated on February 26th, 2025

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CCXCVIII in Roman Numerals

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Foundation
Intermediate
Advance Topics

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 CCXCVIII.

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What is CCXCVIII in Roman Numerals?

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. CCXCVIII in Roman numerals can be written in number form by adding the values of each Roman numeral, i.e., CCXCVIII = 298.

 

Let us learn more about the Roman numeral CCXCVIII, how we write them, the mistakes we usually make, and ways to avoid these mistakes.

ccxcviii roman numerals

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Basic Rules for CCXCVIII in Roman Numerals

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 three times in continuation increases the value of the numeral. For example, XXX = 30.

 

Rule 3: Subtraction Method:

We use the subtraction method when a smaller symbol precedes a larger 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 more than once. For example, 10 is represented as X and not VV.

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How to Write CCXCVIII in Roman Numerals?

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

 

  • By Expansion Method
  • By Grouping Method
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CCXCVIII in Roman Numeral by Expansion 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 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 CCXCVIII,

Step 1: First, we break the Roman numerals. CCXCVIII = C + C + XC + V + I + I + I

Step 2: Write the Roman Numerals for each part. The Roman Numeral C is 100 The Roman Numeral XC is 90 The Roman Numeral V is 5 The Roman Numeral I is 1

Step 3: Combine all the numbers. C + C + XC + V + I + I + I = 100 + 100 + 90 + 5 + 1 + 1 + 1 = 298. Therefore, the Roman Numeral CCXCVIII is 298.

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CCXCVIII in Roman Numeral by Grouping Method

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 CCXCVIII.

Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are CC, XC, and VIII. The numeral for CC is 200. The numeral for XC is 90.

Step 2: Now we need to either add or subtract the smaller number, depending on its place.

 

Here we add VIII to CCXC, and we will get CCXCVIII. The Roman numeral VIII is 8. Therefore, the numeral of CCXCVIII is 298.

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Common Mistakes and How to Avoid Them in CCXCVIII Roman Numerals

Students can make mistakes when studying Roman numerals. Here are a few common mistakes students make, and ways to avoid them.

Mistake 1

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Mistakes when applying the repetition method

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It can be quite confusing for beginners to remember that Roman Numerals cannot be repeated more than three times. Another thing to keep in mind is that Roman Numerals such as V, L, and D cannot be repeated.

 

For example, writing LL as 100 is incorrect; the correct answer is C.

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CCXCVIII Roman Numerals Examples

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Problem 1

A historian finds two ancient artifacts labeled as CC and XCVIII. Calculate the total value of both artifacts in Roman numerals.

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The total value is CCXCVIII

Explanation

Convert each Roman numeral into its decimal form:

CC = 200

XCVIII = 98

Add both values: 200 + 98 = 298

Convert the sum back into Roman numerals: 298 = 200 (CC) + 90 (XC) + 8 (VIII) = CCXCVIII

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Problem 2

A collection of ancient coins is split into two groups: one with a value of CCC and another with CCII. Find the difference between the two groups in Roman numerals.

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The difference is XCVIII

Explanation

Convert the Roman numerals into their decimal forms:

CCC = 300

CCII = 202

Subtract the numbers: 300 - 202 = 98

Convert 98 into Roman numerals: 98 = 90 (XC) + 8 (VIII) = XCVIII

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Problem 3

An ancient scroll mentions a division of wealth among three siblings with a total of DCCXCIV. Calculate the share of each sibling in Roman numerals.

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Each sibling receives CCXCVIII

Explanation

Convert DCCXCIV into its decimal form:

DCCXCIV = 794

Divide by 3: 794 / 3 = 264.67 (round down to 264 for whole number in Roman numerals)

Convert 264 into Roman numerals: 264 = 200 (CC) + 60 (LX) + 4 (IV) = CCLXIV

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Problem 4

A sculpture is inscribed with the number CCXCVIII as part of a series. If the series multiplies each number by II, what is the result in Roman numerals?

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The result is DXCVI

Explanation

Convert CCXCVIII into its decimal form:

CCXCVIII = 298

Multiply by 2: 298 × 2 = 596

Convert 596 into Roman numerals: 596 = 500 (D) + 90 (XC) + 6 (VI) = DXCVI

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Problem 5

Express the Roman numeral CCXCVIII in its decimal form.

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In decimal form, CCXCVIII is 298

Explanation

Break CCXCVIII into components:

CC = 200

XC = 90

VIII = 8

Add the values: 200 + 90 + 8 = 298

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FAQs on CCXCVIII in Roman Numerals

1.What is XCVIII in Roman numerals?

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2.Is CCXCVIII a prime number?

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3.What is CCXCVIII + CCXCVIII?

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4.What is CCC?

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5.Subtract XCVIII from CCXCVIII

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Important Glossaries for CCXCVIII in Roman Numerals

  • Limitation Rule: There are some symbols that cannot be repeated more than once (V, L, D). For example, LL for 100 is wrong; the correct answer is C.
     
  • Place value: The position of a digit in a number, this position determines its value. For example, the number 9 in 298 is in the ten's place.
     
  • Subtraction Method: In Roman numerals, a smaller numeral before a larger numeral indicates subtraction. For example, IX is 9.
     
  • Prime Number: A number that has only two factors is called a prime number. For example, 7 is a prime number with only two factors, 1 and itself.
     
  • Expansion Method: A method in Roman numerals where each numeral is broken down into its basic components and summed to find the total value.
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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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