CXXXVIII Roman Numerals: Rules, Solved Examples & Practice Questions

CXXXVIII Roman numeral represent the number 138 (one hundred thirty eight). Roman numerals CXXXVIII is a combination of four letters: C = 100, X = 10, V = 5  and I = 1. These letters are combined using addition rule of Roman numerals as: C + X + X + X + V + I + I + I = 100 + 10 + 10 + 10 + 5 + 1 + 1 + 1 = 138.

To convert CXXXVIII to numbers we must know the basic symbols and rules used in forming Roman numerals. On this page, we will explain the process of converting CXXXVIII Roman numerals into numbers comprehensively. Examples included on this page will help provide a better understanding of solving questions based on CXXXVIII Roman numerals. 

Table of Contents

• How to Write CXXXVIII Roman Numeral in Numbers?
• Numbers Related to CXXXVIII Roman Numerals
• Basic Rules to Write Roman Numerals
• Solved Examples on CXXXVIII Roman Numeral
• Practice Questions on CXXXVIII Roman Numeral

How to Write CXXXVIII Roman Numeral in Numbers?

To write CXXXVIII Roman numerals in numbers, we can use two different methods. 

I. Expansion Method

II. Grouping Method

Method 1: Expansion Method

• Break the CXXXVIII Roman numerals into individual letters.

• Replace each Roman numeral with its numerical value as per place value.

• Add all of these numbers together.

In this method, we have to first write CXXXVIII in expanded form as  C + X + X + X + V + I + I + I and then add each number individually. i.e., 100 + 10 + 10 + 10 + 5 + 1 + 1 + 1 = 138

Method 2: Grouping Method

In the second method, we can first pair symbols in groups, then replace each of them with numbers and consider them for addition as: CXXXVIII = C + XXX + VIII

By replacing each symbol pair with its numerical value we get: 100 + 30 + 8 = 138.

 

Numbers Related to CXXXVIII Roman Numerals

Basic Rules to Write Roman Numerals

There are important rules that should be followed to write and convert Roman numerals into numbers correctly. They involve understanding the placement and repetition of letters and symbols. As Roman numerals apply both addition and subtraction to represent numbers, it’s essential to follow the fundamental rules that govern Roman numeral construction to ensure accuracy. Here are 4 fundamental Roman numerals rules that we need to follow for writing or converting Roman numbers correctly.

• Addition Rule: When smaller numerals follow larger ones, their values are added.
  Example: VI = 5 + 1 = 6

• Subtraction Rule: When a smaller numeral comes before a larger one, it is subtracted.
  Example: IX = 10 − 1 = 9

• Repetition Rule: Symbols I, X, C, and M can be repeated up to three times.
  Example: XXX = 30

• Non-Repetition Rule: Symbols V, L, and D cannot be repeated.

 

Solved Examples on CXXXVIII Roman Numeral

Example 1. Write the numerical value of CXXXVIII Roman numeral.

Answer: To write CXXXVIII Roman numerals in numerical value, we first break and write it as a combination of single symbols as: C + X + X + X + V + I + I + I = 100 + 10 + 10 + 10 + 5 + 1 + 1 + 1 = 138.
 

Example 2. Determine the value of CXXX + IX.

Solution: We know that, 

CXXX = C + X + X + X = 100 + 10 + 10 + 10 = 130

And IX = X – I = 10 – 1 = 9

So, CXXX + IX = 130 + 9 = 139 

Therefore, CXXX + IX = CXXXIX

Example 3. What is the sum of CX + XXVIII?

Solution: CX = 110 and XXVIII = 28, 

So, 110 + 28 = 138 and 138 in Roman numerals is written as CXXXVIII

Therefore, CX + XXVIII = CXX

Example 4. Determine the value of CXXXVIII − X.

Solution: We know that, CXXXVIII = 100 + 10 + 10 + 10 + 5 + 1 + 1 + 1 = 138

X = 10

So, CXXXVIII − X = 138 − 10 = 128

128 in Roman numerals is CXXVIII

Therefore, CXXXVIII − X = CXXVIII

Example 5. What is the value of CXX + XVIII?

Solution: CXX = 120 and XVIII = 18

So, 120 + 18 = 138

138 in Roman numerals is CXXXVIII

Therefore, CXX + XVIII = CXXXVIII

Practice Questions on CXXXVIII Roman Numeral

1. Fill in the blank: CXXXVIII = ______ (in numbers).
2. Fill in the blank: ______ = CXXXVIII (in Roman numerals).
3. True or False: CXXXVIII represents 140.
4. Choose the correct option: The value of CXXXVIII is
   (a) 128
   (b) 138
   (c) 148
   (d) 158
5. Complete the sequence: CXXXVI, CXXXVII, CXXXVIII, ______.
6. Match the following:
   (i) CXXXVIII → (a) 138
   (ii) CXL → (b) 140
7. Fill in the blank: CXXXVIII + II = ______ (in Roman numerals).
8. True or False: CXXXVIII − VIII = CXXX.
9. Choose the correct Roman numeral for 133:
   (a) CXXX
   (b) CXXXIII
   (c) CXLIII
   (d) CXXIII
10. Fill in the blank: The number just before CXXXVIII is ______ (in Roman numerals).

 

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