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Last updated on May 26th, 2025

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CXCVIII Roman Numerals

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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 CXCVIII.

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What is CXCVIII 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. CXCVIII in Roman numerals can be written in number form by adding the values of each Roman numeral, i.e., CXCVIII = 198.

 

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

 

cxcviii roman numerals

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Basic Rules for CXCVIII 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 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 more than once. For example, 10 is represented as X and not VV.

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How to Write CXCVIII in Roman Numerals?

Let us learn about how to write CXCVIII 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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CXCVIII in Roman Numerals 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 CXCVIII,

 

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

 

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 + XC + V + III = 100 + 90 + 5 + 3 = 198. Therefore, the Roman numeral CXCVIII is 198.

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CXCVIII in Roman Numerals 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 CXCVIII.

 

Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are C, XC, and VIII. The numeral for C is 100. 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 C + XC, and we will get CXCVIII. The Roman numeral VIII is 8. Therefore, the numeral of CXCVIII is 198.

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Common Mistakes and How to Avoid Them in CXCVIII 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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CXCIX in Roman Numerals Examples

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Problem 1

Find the sum of CXCIX + L. Write the answer in Roman numerals.

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The sum is CCXLIX

Explanation

Convert both Roman numerals into its decimal form:

CXCIX = 199

L = 50

Now add both numbers: 199 + 50 = 249

Now convert the number into its Roman numeral: 249 = 200 (CC) + 40 (XL) + 9 (IX) = CCXLIX

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Problem 2

What is the difference between CXCIX - LII? Write in Roman numerals.

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The difference is CXLVII

Explanation

Convert the Roman numerals into its decimal form:

CXCIX = 199

LII = 52

Now we subtract the numbers: 199 - 52 = 147

Convert the number into its Roman numeral: 147 = 100 (C) + 40 (XL) + 7 (VII) = CXLVII

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Problem 3

Divide CXCIX by 3 and write the answer in Roman numerals.

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LXVI

Explanation

Convert CXCIX into its decimal form:

CXCIX = 199

Divide by 3: 199 / 3 = 66 (rounded down)

Write 66 in Roman numerals: 66 = 60 (LX) + 6 (VI) = LXVI

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Problem 4

Find the product of CXCIX and II.

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CCCXCVIII is the product of CXCIX and II.

Explanation

Write CXCIX and II in numbers:

CXCIX = 199

II = 2

Multiply the numbers: 199 × 2 = 398

Convert 398 into its Roman numerals: 398 = 300 (CCC) + 90 (XC) + 8 (VIII) = CCCXCVIII

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Problem 5

Convert CXCIX into its decimal form.

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In decimal form, CXCIX is 199

Explanation

Break CXCIX into components: C = 100 XC = 90 (100 - 10) IX = 9 (10 - 1) Add values: 100 + 90 + 9 = 199

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FAQs on CXCVIII in Roman Numerals

1.What is CXVIII in Roman numerals?

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2.Is CXCVIII a prime number?

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3.What is CXCVIII + II?

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4.What is CCVIII?

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5.Subtract XVIII from CXCVIII

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6.How can children in Philippines use numbers in everyday life to understand CXCVIII Roman Numerals?

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7.What are some fun ways kids in Philippines can practice CXCVIII Roman Numerals with numbers?

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8.What role do numbers and CXCVIII Roman Numerals play in helping children in Philippines develop problem-solving skills?

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9.How can families in Philippines create number-rich environments to improve CXCVIII Roman Numerals skills?

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Important Glossaries for CXCVIII in Roman Numerals

  • Limitation Rule: There are some symbols that cannot be repeated more than once (V, L, D). For example, writing VV for 10 is wrong; the correct representation is X.

 

  • Place value: The position of a digit in a number; this position determines its value. For example, the number 9 in 198 is in the tens place.

 

  • Subtraction Method: A method used in Roman numerals where a smaller numeral precedes a larger numeral, indicating subtraction. For example, XC = 90 (100 - 10).

 

  • Repetition Method: A method where repeating a numeral increases its value. For example, III = 3.

 

  • Grouping Method: A method in which Roman numerals are grouped and calculated based on the addition and subtraction rules to simplify understanding.
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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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