118 in Roman Numerals - CXVIII
The Roman numeral for 118 is CXVIII. This number demonstrates straightforward additive notation, combining C (100), X (10), V (5), and three instances of I (1) to create one hundred eighteen.
How to write 118 in Roman numerals: CXVIII = 100 + 10 + 5 + 1 + 1 + 1
How to Write 118 in Roman Numerals
To write 118 in Roman numerals, we combine C (100), X (10), V (5), and III (3) using additive notation.
The Roman numeral system represents 118 as CXVIII, following the additive principle where symbols are placed in descending order of value.
Breaking Down 118 (CXVIII)
Step-by-Step Breakdown
The number 118 demonstrates classic Roman numeral construction using pure additive notation, building systematically from largest to smallest values.
✅ Correct Representation
❌ Incorrect Representations
Historical Curiosity
The year 118 AD (CXVIII) was significant in Hadrian's early reign. On July 9, 118 AD, Emperor Hadrian finally entered Rome, nearly a year after succeeding Trajan. He received a hostile reception from the Senate due to the execution of four consulars, which created political tensions.
To gain popular support, Hadrian took dramatic action by publicly burning debt records worth 900 million sestertii - an enormous sum representing uncollectable debts owed to the state. This gesture of financial clemency helped secure his position as emperor and demonstrated his commitment to starting his reign with a clean slate.
Evolution of 118 in Roman Numerals
The representation of 118 as CXVIII has remained consistent throughout history, demonstrating the stability of Roman numeral additive notation.
| Period | Notation | Context |
|---|---|---|
| Ancient Rome (753 BC - 476 AD) | CXVIII | Year 118 AD: Hadrian entered Rome and burned debt records |
| Medieval Period (476 - 1453 AD) | CXVIII | Manuscript pagination and historical documentation |
| Modern Era (1453 - Present) | CXVIII | Scientific nomenclature and formal numbering |
Cultural Applications
- Scientific notation for element 118 (Oganesson) - the heaviest known element
- Historical chronology marking year 118 AD (Hadrian's arrival in Rome)
- Academic course numbering and advanced curriculum levels
- Building addresses and architectural numbering systems
- Legal document section and clause numbering
Decimal System Comparison
The number 118 demonstrates how both Roman and decimal systems efficiently represent numbers in the second century.
- • Decimal 118: Three digits using positional notation (1 × 100 + 1 × 10 + 8 × 1)
- • Roman CXVIII: Six symbols using additive notation (100 + 10 + 5 + 1 + 1 + 1)
- • Mathematical property: 118 is a composite number
- • Prime factorization: 2 × 59
Addition Examples Around 118
Understanding how Roman numerals progress around 118 demonstrates the systematic additive construction pattern.
| Arabic | Roman | Explanation |
|---|---|---|
| 116 | CXVI | Simple addition: 100 + 10 + 5 + 1 |
| 117 | CXVII | Simple addition: 100 + 10 + 5 + 2 |
| 118 | CXVIII | Simple addition: 100 + 10 + 5 + 3 |
| 119 | CXIX | Mixed notation: 100 + 10 + (10 - 1) |
| 120 | CXX | Simple addition: 100 + 20 |
Notice how 118 (CXVIII) follows the predictable pattern of C + X + VIII, before transitioning to subtractive notation at 119 (CXIX).
Age and Year Calculation
If you are 118 years old, you are a supercentenarian with exceptional longevity. You would have been born in the year MCMVII (1907).
Additive Rules for CXVIII
The number 118 (CXVIII) demonstrates pure additive Roman numeral construction, building systematically from largest to smallest values.
Why CXVIII is Straightforward
- Pure addition: C + X + V + III with no subtraction needed
- Follows strict descending value order (C before X before V before I)
- Uses standard symbol repetition (III for 3)
- Easily readable as "one hundred, ten, five, and three"
Memory Tips for CXVIII
Remembering CXVIII is straightforward due to its logical additive construction.
Pattern Recognition
Think of CXVIII as "Century plus Eighteen" - the Roman C (100) combined with XVIII (18).
Remember the pattern: CXVII (117), CXVIII (118), CXIX (119) - notice the transition from additive to subtractive notation.
Break it into chunks: C (100) + XVIII (18) = CXVIII (118).
118 in the Modern World
Nuclear Science
Element 118 (Oganesson) - the heaviest known element
History
Year 118 AD: Hadrian's entry into Rome and debt forgiveness
Mathematics
Study of composite numbers and semiprimes
Special Significance of 118
The number 118 is the atomic number of Oganesson (Og), the heaviest known element in the periodic table. Discovered in 2002 at the Joint Institute for Nuclear Research in Dubna, Russia, and formally named in 2016, Oganesson honors nuclear physicist Yuri Oganessian. It completes the seventh row of the periodic table and is a member of group 18 (noble gases). Only five atoms have ever been produced, each with a half-life of 0.7 milliseconds.
Mathematical Properties of 118
The number 118 possesses several interesting mathematical properties that make it noteworthy in number theory.
- Semiprime: product of exactly two prime numbers (2 × 59)
- Even composite number with four total divisors: 1, 2, 59, 118
- Sum of all divisors equals 180
- Deficient number (sum of proper divisors 62 < 118)
- In binary: 1110110, in hexadecimal: 76
Did You Know?
Element 118 (Oganesson) is unique as it completes the seventh period of the periodic table, making it a "magic number" in nuclear physics. Despite being in the noble gas group, theoretical calculations suggest it might behave differently from lighter noble gases due to relativistic effects on its electrons.
Counting with Roman Numerals Around 118
Understanding the sequence around 118 demonstrates the systematic progression in Roman numeral construction.
- CXVII (117) → CXVIII (118) → CXIX (119) → CXX (120)
- The pattern shows transition from additive VIII to subtractive IX at 119
- Each number follows predictable addition: C (100) + X (10) + (units)
Frequently Asked Questions
Why is 118 written as CXVIII instead of other combinations?
CXVIII is the correct and standard way to write 118 in Roman numerals. It follows the additive principle with symbols in descending order: C (100) + X (10) + V (5) + III (3) = 118. This is the most efficient representation following Roman numeral rules.
What is the significance of element 118?
Element 118 is Oganesson (Og), the heaviest known element in the periodic table. Named after physicist Yuri Oganessian, it was discovered in 2002 and completes the seventh period. As a member of group 18, it would theoretically be a noble gas, though only five atoms have ever been produced, each lasting just 0.7 milliseconds.
What happened in the year 118 AD?
The year 118 AD (CXVIII) marked Hadrian's formal arrival in Rome on July 9, nearly a year after becoming emperor. He received a hostile reception from the Senate but gained popular support by dramatically burning records of 900 million sestertii in state debts, demonstrating financial clemency.
How do you continue counting from CXVIII?
After CXVIII (118), continue with CXIX (119) using subtractive notation, then CXX (120). The pattern transitions from additive VIII to subtractive IX at 119, showing the system's efficiency.
What makes 118 mathematically interesting?
118 is a semiprime, the product of exactly two prime numbers (2 × 59). It has four divisors (1, 2, 59, 118) with their sum equaling 180. As a deficient number, the sum of its proper divisors (62) is less than the number itself.
Can CXVIII be simplified or written differently?
No, CXVIII is already in its standard, most efficient form. Roman numeral rules require symbols to be arranged in descending order of value, and CXVIII follows this principle perfectly: C (100), X (10), V (5), III (3).
Summary
Key Points About CXVIII
- CXVIII represents 118 using straightforward additive notation
- Combines C (100) + X (10) + V (5) + III (3) in descending order
- No subtractive notation required
- Demonstrates the pattern before transition to IX at 119
Modern Usage
- Scientific notation for element 118 (Oganesson)
- Historical chronology marking year 118 AD
- Mathematical research in semiprimes
- Academic and professional numbering systems
The Roman numeral CXVIII (118) exemplifies the clarity and efficiency of additive notation in the second century. As the atomic number of Oganesson, the heaviest known element completing the periodic table, and the year marking Hadrian's dramatic debt forgiveness in Rome, 118 holds significance in both scientific and historical contexts. The straightforward construction of CXVIII demonstrates how Roman numerals effectively represent numbers through systematic combination of basic symbols.
Converting number 118 to Roman
This is the number 118 written in Roman numerals
Try the Roman numeral converter
Want to convert other numbers? Use our converter: