128 LearnersLast updated on May 26th, 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
Students often make mistakes when writing numbers in Roman numerals. Here are some common mistakes and ways to avoid them:
Mistake 1
Errors in the repetition method
Beginners might find the repetition method confusing since certain Roman numerals cannot be repeated more than three times, while others, like V, L, and D, cannot be repeated at all.
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?
The total number of years is CLXIV.
Explanation
The first manuscript was written CL (150) years ago and the second one XIV (14) years ago. The total number of years between their writing and today is 150 + 14 = 164. 164 in Roman Numerals is CLXIV.
Problem 2
An artist created CLXIV paintings over a period of XX years. Find the average number of paintings created per year.
The average number of paintings per year is VIII.
Explanation
To find the average, divide the total number of paintings by the number of years: CLXIV / XX.
CLXIV = 164
XX = 20
164 / 20 = 8
8 in Roman Numerals is VIII.
Problem 3
A collector has a total of CCCXXVIII coins, of which CLXIV are ancient Roman coins. How many coins are not Roman?
The number of coins that are not Roman is CLXIV.
Explanation
Subtract the number of Roman coins from the total number of coins: CCCXXVIII - CLXIV.
CCCXXVIII = 328
CLXIV = 164
328 - 164 = 164
164 in Roman Numerals is CLXIV.
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?
The number of books remaining to be categorized is CLXIV.
Explanation
Subtract the number of categorized books from the total number of books: CCXXVIII - LXIV.
CCXXVIII = 228
LXIV = 64
228 - 64 = 164
164 in Roman Numerals is CLXIV.
Problem 5
Write the Roman Numeral for the sum of XLIV and CXX using the breakdown method.
The Roman Numeral for the sum is CLXIV
Explanation
First convert the numbers XLIV and CXX into Roman numerals:
XLIV = 44
CXX = 120
Add the numbers together: 44 + 120 = 164
Using the breakdown method: 164 = 100 + 50 + 10 + 4 = CLXIV
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.
7.How can children in Australia use numbers in everyday life to understand 164 in Roman Numerals?
8.What are some fun ways kids in Australia can practice 164 in Roman Numerals with numbers?
9.What role do numbers and 164 in Roman Numerals play in helping children in Australia develop problem-solving skills?
10.How can families in Australia create number-rich environments to improve 164 in Roman Numerals skills?
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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About BrightChamps in Australia
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.
