4 in Roman Numerals - IV
The number 4 in Roman notation is IV. This is one of the examples of the subtraction rule in Roman numeral notation, which is a key element to understanding this ancient system.
Number 4 written in Roman numerals as IV
How do we write the number 4 in Roman numerals?
Four in Roman notation (IV) is an example of the subtraction rule. Instead of writing it as IIII (which would violate the rules), we use the notation IV, where I (1) stands before V (5), which means subtraction: 5-1=4.
The Roman system is based on two main principles:
Main principles of Roman numeral notation:
- Addition rule - when a smaller or equal symbol follows a larger one, the values are added (e.g., VI = 5 + 1 = 6)
- Subtraction rule - when a smaller symbol precedes a larger one, the smaller value is subtracted from the larger (e.g., IV = 5 - 1 = 4)
In the case of the number 4, we apply the subtraction rule by placing the symbol I (with a value of 1) before the symbol V (with a value of 5), which gives us the value 4.
Breaking down IV:
Step by step breakdown:
Correct notation:
Incorrect notations:
Historical curiosity:
In ancient Rome, 4 was initially written as IIII. Only later was the notation IV, which we know today, adopted. Interestingly, on clock faces, IIII is still often seen instead of IV, which is a reference to historical tradition!
Archaeological findings indicate that for many centuries both notations functioned in parallel. On coins from the Roman Republic period, you can find both IIII and IV notation, and only during the Empire did IV notation become dominant.
Evolution of the notation of number 4 in the Roman system
The history of writing the number 4 in the Roman system reflects the evolution of the system itself:
| Period | Dominant notation | Historical context |
|---|---|---|
| Early Republic (5th-3rd century BC) | IIII | Simple, additive number notations |
| Late Republic (2nd-1st century BC) | IIII and IV | Transitional period, both notations used |
| Empire (1st-5th century AD) | IV | Standardization of the subtraction rule |
| Middle Ages (5th-15th century) | IV (with exceptions) | IV notation dominates, but IIII returns in clockmaking |
Applications of number IV in culture and history
- In Roman timekeeping, Mercury was honored on Wednesday (dies Mercurii), which was the fourth day of the Roman week, not the fourth day of each month.
- In Christian symbolism, the number 4 refers to the four Gospels and the four evangelists.
- On clock faces, hour 4 is often marked as IIII instead of IV - this is a traditional exception used in clockmaking.
- Romans divided the day into 12 hours, and the night into 4 watches (vigiliae) - each watch lasted about 3 hours.
- In Roman architecture, proportions based on the number 4 were often used, especially in buildings of religious significance.
- The number 4 was also associated with the four seasons and the four elements, which were important in Roman natural philosophy.
Why is IIII used on clocks instead of IV?
There are several theories explaining why IIII is often used on clock faces instead of IV:
- • Pattern symmetry - IIII creates better visual balance with VIII (8) on the opposite side of the dial.
- • Respect for deity - IV is the beginning of the Latin notation IVPITER (Jupiter), so using IIII could stem from religious respect.
- • Royal tradition theory - some unverified legends claim Louis XIV preferred IIII notation, though this lacks historical documentation and IIII was used on clocks long before his reign.
- • Easier production - when casting numerals on clock faces, the notation IIII allowed for more economical use of molds.
IV and other notations using the subtraction rule
The subtraction rule, exemplified by the notation IV, is also used in the Roman system for other numbers:
| Arabic number | Roman number | Explanation |
|---|---|---|
| 4 | IV | 5 - 1 = 4 (I before V) |
| 9 | IX | 10 - 1 = 9 (I before X) |
| 40 | XL | 50 - 10 = 40 (X before L) |
| 90 | XC | 100 - 10 = 90 (X before C) |
| 400 | CD | 500 - 100 = 400 (C before D) |
| 900 | CM | 1000 - 100 = 900 (C before M) |
These examples show that the subtraction rule is applied consistently throughout the Roman system, not just for the number 4. Whenever a smaller symbol precedes a larger one, we subtract its value.
Rules for using Roman numerals in subtraction notation
The Roman system has strictly defined rules regarding the use of the subtraction rule:
Limitations when using the subtraction rule:
- Only symbols I, X, C can be used for subtraction (V, L, D are not used)
- Symbol I can only be subtracted from V and X
- Symbol X can only be subtracted from L and C
- Symbol C can only be subtracted from D and M
- You cannot subtract a symbol from another that has more than 10 times greater value
- Double subtraction cannot be used (e.g., IXC is incorrect, correctly it would be LXXXIX)
How to remember the Roman four notation?
To remember that 4 is written as IV, think of the rule: "smaller value before larger means subtraction". Since I (1) stands before V (5), we subtract 1 from 5, which gives 4.
Practical tip:
Numbers 1, 2 and 3 are written by adding I symbols (I, II, III). When we get to 4, instead of adding a fourth I symbol, we apply the subtraction rule and write IV (5-1). The same logic repeats with numbers 9 (IX = 10-1), 40 (XL = 50-10) etc.
To easily remember: when the value approaches a "threshold" marked by the next larger symbol (5, 10, 50, 100 etc.), we use the subtraction rule.
IV in the modern world
Book editions
Volume numbers, chapters and book parts (Volume IV, Part IV)
Monarch numbering
Designations of rulers (e.g., Charles IV, Henry IV, Pope Pius IV)
Film and entertainment
Numbering of movie sequels (Rocky IV, Rambo IV) and games (Final Fantasy IV)
Super Bowl IV:
One of the most famous examples of using Roman four in contemporary culture is Super Bowl IV - the fourth final of the professional American football league NFL, which took place in 1970. Since then, all Super Bowl finals have been numbered with Roman numerals, which has become a characteristic element of this sporting event.
IV in mathematics and science
The number 4 has special mathematical properties that make it interesting not only in the context of Roman notation:
- It is the first composite number (has more divisors than 1 and itself)
- It is the only number equal to its square root doubled (2² = 4)
- It is the smallest two-digit number in the ternary system (4 = 11₃)
- It is the base of a tetrahedron (regular tetrahedron) - a solid with four faces
- In the coordinate system, four quadrants define the plane
Did you know that:
In ancient Roman mathematics, the number 4 had special significance in geometry. Roman engineers and architects used proportions based on the number 4 when designing buildings, especially when determining right angles using the so-called Egyptian triangle (3-4-5).
Summary - IV in a nutshell
Notation rules
- IV = 5 - 1 = 4
- Uses the subtraction rule
- I stands before V, which means subtraction
- Is an alternative to the incorrect notation IIII
Modern applications
- Chapter designations in books
- Numbering of rulers and popes
- Designations of sporting events
- Product version numbering
- Quarter designations (Q-IV)
Writing the number 4 as IV is one of the fundamental examples of the subtraction rule in the Roman system. This rule, together with the addition rule, forms the basis of the entire system and enables efficient notation of numbers using a minimal number of symbols. Understanding the IV notation is key to mastering more complex Roman numerals.
Frequently Asked Questions about IV (4)
Why is 4 written as IV and not IIII?
IV follows the Roman subtraction rule: I (1) before V (5) means 5-1=4. While IIII was used in early Roman times, IV became standard during the Empire period because it's more efficient and follows the rule that no symbol should be repeated more than three times consecutively.
How do you break down IV step by step?
IV breaks down as: I = 1, V = 5. Since the smaller symbol (I) comes before the larger symbol (V), we apply the subtraction rule: V - I = 5 - 1 = 4. This is the key principle of Roman subtraction notation.
Why do some clocks show IIII instead of IV?
Many traditional clocks use IIII for visual balance and symmetry on the clock face. This creates better visual harmony with VIII (8) on the opposite side. Additionally, IIII was historically used before IV became standard, and clockmakers maintained this tradition.
When did Romans start using IV instead of IIII?
The transition occurred gradually. IIII was common in the early Roman Republic (5th-3rd century BC), both notations coexisted during the late Republic (2nd-1st century BC), and IV became dominant during the Empire period (1st-5th century AD) as the subtraction rule was standardized.
What other numbers use the same subtraction rule as IV?
The subtraction rule applies to: IV (4), IX (9), XL (40), XC (90), CD (400), and CM (900). The pattern is consistent: I can subtract from V and X, X can subtract from L and C, and C can subtract from D and M.
What comes before and after IV in the Roman sequence?
Before IV comes III (3), and after IV comes V (5). The sequence is: I (1), II (2), III (3), IV (4), V (5), VI (6). Notice how IV breaks the pattern of simply adding I symbols, introducing the subtraction principle.
How do you pronounce IV?
IV is pronounced as "four" in English. In classical Latin, it would have been "quattuor." When referring to the Roman numeral symbols themselves, you can say "I-V" (one-five) to indicate the individual letters.
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