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108 LearnersLast updated on February 20th, 2025
164 in Roman Numerals
Roman numerals are a way of expressing numbers using symbols. I, V, X, L, C, D, and M are the symbols used. Roman numerals are often seen in royal titles, book names, sequences, and more. Here we will discuss Roman numerals, their rules, and examples.
What is 164 in Roman Numerals?
The royal titles, such as Henry I, Henry II, and so on, use Roman numerals. Have you noticed these names and wondered what the symbols (I and II) represent?
Those are Roman numerals. In ancient times, people counted using fingers, sticks, bones, etc. As life became more complex, a standard form was needed for counting. Ancient Romans used the Roman numeral system for this purpose. The symbols I (1), V (5), X (10), L (50), C (100), D (500), and M (1000) are used for counting.
In Roman numerals, we use CLXIV to represent 164. Here, C is 100, LX is 60, and IV is 4. Let’s learn more about Roman numerals and how we write them.
Basic Rules for 164 in Roman Numerals
Certain basic rules must be followed when writing a number in Roman numerals. Let's discuss some important rules to remember:
Rule 1: Addition Method
The addition method is used when a smaller numeral is placed after a larger numeral. For example, CLX → C + L + X → 100 + 50 + 10 = 160.
Rule 2: Repetition Method
Some Roman numerals can be repeated up to three times to represent numbers. III → 3.
Rule 3: Subtraction Method
If a smaller numeral precedes a larger numeral, we subtract the smaller one from the larger. For example, IV → V - I → 5 - 1 = 4.
Rule 4: Limitation Rule
Symbols cannot be repeated more than three times in succession, and certain symbols like V, L, and D cannot be repeated. For example, we don't write VV for 10; instead, we use X, and 8 is written as VIII, not IIIIIIII.
How to Write 164 in Roman Numerals
Let's now learn how to write 164 in Roman numerals. Follow these methods to write the number:
- By Expansion Method
- By Grouping Method
164 in Roman Numerals by Expansion Method
In the expansion method, a number is broken down based on its place value. Here's how to write 164 in Roman numerals using this method:
Step 1: Break down the number based on place value, such as ones, tens, and hundreds.
For 164, we write it as 100 + 60 + 4.
Step 2: Convert each part into Roman numerals:
100 in Roman numerals is C.
60 in Roman numerals is LX.
4 in Roman numerals is IV.
Step 3: Combine the Roman numerals.
Therefore, 164 in Roman numerals is C (100) + LX (60) + IV (4) = CLXIV.
164 in Roman Numerals by Grouping Method
When writing a large number in Roman numerals, we group the number. To write 164 in Roman numerals, group it as 100 + 60 + 4:
100 in Roman numerals is C.
60 in Roman numerals is LX.
4 in Roman numerals is IV.
So, 164 is written as CLXIV in Roman numerals.
Numbers Related to 164 in Roman Numerals
Roman numerals follow a certain pattern. Here are some numbers related to 164 in Roman numerals:
| Number | Roman Numeral | Breakdown |
|---|---|---|
| 160 | CLX | 100 + 50 + 10 = 160 |
| 161 | CLXI | 100 + 50 + 10 + 1 = 161 |
| 162 | CLXII | 100 + 50 + 10 + 1 + 1 = 162 |
| 163 | CLXIII | 100 + 50 + 10 + 1 + 1 + 1 = 163 |
Common Mistakes and How to Avoid Them in 164 Roman Numerals
164 in Roman Numerals Examples
Problem 1
A historian estimates that a manuscript was written CL years ago, and another was written XIV years ago. What is the total number of years between their writing and today?
Explanation
Problem 2
An artist created CLXIV paintings over a period of XX years. Find the average number of paintings created per year.
Explanation
Problem 3
A collector has a total of CCCXXVIII coins, of which CLXIV are ancient Roman coins. How many coins are not Roman?
Explanation
Problem 4
A librarian needs to categorize a collection of books. If there are CCXXVIII books and she has already categorized LXIV of them, how many remain to be categorized?
Explanation
Problem 5
Write the Roman Numeral for the sum of XLIV and CXX using the breakdown method.
Explanation
FAQs on 164 in Roman Numerals
1.What is 9 in Roman numerals?
2.How to write 164 in Roman numerals?
3.What is 160 in Roman numerals?
4.Is CLXIV a prime number?
5. What are the multiples of 164?
6.
Important Glossaries for 164 in Roman Numerals
- Addition rule: The addition method is used when a larger numeral is followed by a smaller numeral; the values are added. Example: CLXIV = C + LX + IV = 100 + 60 + 4 = 164.
- Grouping method: Numbers are grouped based on place value and converted into Roman numerals. Example: 164 = 100 + 60 + 4 = CLXIV.
- Repetition rule: Certain symbols (I, X, C, M) in Roman numerals can be repeated up to three times. Example: III = 3 (I is repeated three times).
- Subtraction rule: The subtraction method is used when a smaller numeral precedes a larger numeral. Example: IV = 5 - 1 = 4.
- Limitation rule: Symbols cannot be repeated more than three times consecutively, and some symbols like V, L, and D cannot be repeated.
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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.
Fun Fact
: She loves to read number jokes and games.
