Roman numerals often cause us confusion.
But it is they who are usually used when numbering centuries and book chapters, when designating clothing sizes and steps in music.
Roman numerals are present in our lives. So it’s too early to abandon them. Easier to learn, understand and learn. Moreover, it is not difficult.
So, to denote numbers in the Latin language, combinations of the following 7 characters are accepted: I (1), V (5), X (10), L (50), C (100), D (500), M (1000).
Why were Latin letters chosen to represent the numbers 5, 50, 100, 500 and 1000? It turns out that these are not Latin letters, but completely different characters. The fact is that the basis for the Latin alphabet (and it, by the way, exists in several versions - 23, 24 and 25 letters) was the Western Greek alphabet.
Thus, three signs L, C, and M go back to the Western Greek alphabet. Here they denoted aspirated sounds, which were not in the Latin language. When the Latin alphabet was drawn up, they turned out to be superfluous. And they were adapted to represent numbers in the Latin alphabet. Later they coincided in spelling with Latin letters. Thus, the sign C (100) became similar to the first letter of the Latin word centum (one hundred), and M - (1000) - the first letter of the word mille (thousand). As for the sign D (500), it was half of the sign F (1000), and then it became similar to a Latin letter. The V sign (5) was just the upper half of the X sign (10).
In this regard, by the way, the popular theory that the name of the church office of the Pope (Vicarius Filii Dei) when replacing the letters with Roman numerals in total gives the “devil's number” seems funny.
So, how do you understand Latin numbers?
If the sign denoting a smaller number is to the right of the sign denoting a larger number, then the smaller is added to the larger; if on the left, then subtract:
VI - 6, i.e. 5+1
IV - 4, i.e. 5-1
LX - 60, i.e. 50+10
XL - 40, i.e. 50-10
CX - 110, i.e. 100+10
XC - 90, i.e. 100-10
MDCCCXII - 1812, i.e. 1000+500+100+100+100+10+1+1.
Different designations for the same number are possible. Thus, the number 80 can be represented as LXXX (50+10+10+10) and as XXC(100-20).
Basic Roman numerals look like this:
I(1) - unus (unus)
II(2) - duo (duo)
III(3) - tres (tres)
IV(4) - quattuor (quattuor)
V(5) - quinque
VI(6) - sex (sex)
VII (7) - septem (septem)
VIII (8) - octo (octo)
IX (9) - novem (novem)
X (10) - decem (decem), etc.
XX (20) - viginti (viginti)
XXI (21) - unus et viginti or viginti unus
XXII (22) - duo et viginti or viginti duo, etc.
XXVIII (28) - duodetriginta (duodetriginta)
XXIX (29) - undetriginta (undetriginta)
XXX (30) - triginta (triginta)
XL (40) - quadraginta (quadraginta)
L (50) - quinquaginta (quinquaginta)
LX (60) - sexaginta (sexaginta)
LXX (70) - septuaginta (septuaginta)
LXXX (80) - octoginta (octogintna)
XC (90) - nonaginta (nonaginta)
C (100) - centum (centum)
CC (200) - ducenti (ducenti)
CCC (300) - trecenti (trecenti)
CD (400) - quadrigenti (quadrigenti)
D (500) - quingenti (quingenti)
DC (600) - sexcenti (sexcenti)
DCC (700) - septigenti (septigenti)
DCCC(800) - octingenti (octigenti)
CM (DCCCC) (900) - nongenti (nongenti)
M (1000) - mille (mille)
MM (2000) - duo milia (duo milia)
V (5000) - quinque milia (quinque milia)
X (10000) - decem milia (decem milia)
XX (20000) - viginti milia (viginti milia)
C (1,000,000) - centum milia (centum milia)
XI (1000000) - decies centena milia (decies centena milia)"
Elena Dolotova.
We all use Roman numerals - we use them to mark the numbers of centuries or months of the year. Roman numerals are found on clock dials, including the chimes of the Spasskaya Tower. We use them, but we don't know much about them.
How do Roman numerals work?
The Roman counting system in its modern version consists of the following basic signs:
I 1
V 5
X 10
L 50
C 100
D 500
M 1000
To remember numbers that are unusual for us who use the Arabic system, there are several special mnemonic phrases in Russian and English:
We Give Juicy Lemons, That's Enough
We Give Advice Only to Well-Educated Individuals
I Value Xylophones Like Cows Dig Milk
The system for arranging these numbers relative to each other is as follows: numbers up to three inclusive are formed by adding units (II, III) - repeating any number four times is prohibited. To form numbers greater than three, the larger and smaller digits are added or subtracted, for subtraction the smaller digit is placed before the larger one, for addition - after, (4 = IV), the same logic applies to other digits (90 = XC). The order of thousands, hundreds, tens and units is the same as what we are used to.
It is important that any number should not be repeated more than three times, so the longest number up to a thousand is 888 = DCCCLXXXVIII (500+100+100+100+50+10+10+10+5+1+1+1).
Alternative options
The ban on the fourth use of the same number in a row began to appear only in the 19th century. Therefore, in ancient texts one can see variants IIII and VIII instead of IV and IX, and even IIII or XXXXXX instead of V and LX. Remnants of this writing can be seen on the clock, where four is often marked with four units. In old books, there are also frequent cases of double subtractions - XIIX or IIXX instead of the standard XVIII.
Also in the Middle Ages, a new Roman numeral appeared - zero, which was denoted by the letter N (from the Latin nulla, zero). Large numbers were marked with special signs: 1000 - ↀ (or C|Ɔ), 5000 – ↁ (or |Ɔ), 10000 – ↂ (or CC|ƆƆ). Millions are obtained by double underlining standard numbers. Fractions were also written in Roman numerals: ounces were marked using symbols - 1/12, half was marked with the symbol S, and everything greater than 6/12 was marked with an addition: S = 10\12. Another option is S::.
Origin
At the moment there is no single theory of the origin of Roman numerals. One of the most popular hypotheses is that Etruscan-Roman numerals originated from a counting system that uses notched strokes instead of numbers.
Thus, the number “I” is not the Latin or more ancient letter “i”, but a notch reminiscent of the shape of this letter. Every fifth notch was marked with a bevel - V, and the tenth was crossed out - X. The number 10 in this count looked like this: IIIIΛIIIIX.
It is thanks to this recording of numbers in a row that we owe a special system of adding Roman numerals: over time, the recording of the number 8 (IIIIΛIII) could be reduced to ΛIII, which convincingly demonstrates how the Roman counting system acquired its specificity. Gradually, the notches turned into graphic symbols I, V and X, and acquired independence. Later they began to be identified with Roman letters - since they were similar in appearance to them.
An alternative theory belongs to Alfred Cooper, who suggested looking at the Roman counting system from a physiological point of view. Cooper believes that I, II, III, IIII is a graphical representation of the number of fingers of the right hand that the trader throws out when calling the price. V is the extended thumb, which together with the palm forms a figure similar to the letter V.
That is why Roman numerals add up not only ones, but also add them with fives - VI, VII, etc. - this is the thumb thrown back and the other fingers of the hand extended. The number 10 was expressed by crossing the hands or fingers, hence the symbol X. Another option was to simply double the number V, getting an X. Large numbers were transmitted using the left palm, which counted tens. So gradually the signs of ancient finger counting became pictograms, which then began to be identified with the letters of the Latin alphabet.
Modern Application
Today in Russia, Roman numerals are needed, first of all, to record the number of the century or millennium. It is convenient to place Roman numerals next to Arabic ones - if you write the century in Roman numerals, and then the year in Arabic, then your eyes will not be dazzled by the abundance of identical signs. Roman numerals have a certain connotation of archaism. They are also traditionally used to indicate the serial number of the monarch (Peter I), the volume number of a multi-volume publication, and sometimes the chapter of a book. Roman numerals are also used in antique watch dials. Important numbers, such as the year of the Olympiad or the number of a scientific law, can also be recorded using Roman numerals: World War II, Euclid's V postulate.
In different countries, Roman numerals are used slightly differently: in the USSR it was customary to indicate the month of the year using them (1.XI.65). In the West, the year number is often written in Roman numerals in the credits of films or on the facades of buildings.
In parts of Europe, especially in Lithuania, you can often find the days of the week designated in Roman numerals (I – Monday, and so on). In Holland, Roman numerals are sometimes used to denote floors. And in Italy they mark 100-meter sections of the route, marking, at the same time, every kilometer with Arabic numerals.
In Russia, when writing by hand, it is customary to emphasize the Roman numerals below and above at the same time. However, often in other countries, the underscore meant increasing the case of the number by 1000 times (or 10,000 times with a double underscore).
There is a common misconception that modern Western clothing sizes have some connection with Roman numerals. In fact, the designations are XXL, S, M, L, etc. have no connection with them: these are abbreviations of the English words eXtra (very), Small (small), Large (large).
To designate numbers in Latin, combinations of the following seven characters are accepted: I (1), V (5), X (10), L (50), C (100), D (500), M (1000).
To remember the letter designations of numbers in descending order, a mnemonic rule was invented:
We Give Juicy Lemons, Vsem Ix (respectively M, D, C, L, X, V, I) will be enough.
If the sign denoting a smaller number is to the right of the sign denoting a larger number, then the smaller number should be added to the larger one, if on the left, then subtract, namely:
VI - 6, i.e. 5+1
IV - 4, i.e. 5 - 1
XI - 11, i.e. 10 + 1
IX - 9, i.e. 10 - 1
LX - 60, i.e. 50 + 10
XL - 40, i.e. 50 - 10
CX - 110, i.e. 100 + 10
XC - 90, i.e. 100-10
MDCCCXII - 1812, i.e. 1000 + 500 + 100 + 100 + 100 + 10 + 1 + 1.
Different designations for the same number are possible. For example, the number 80 can be written as LXXX (50 + 10 + 10 + 10) and as XXX (100 - 20).
To write numbers in Roman numerals, you must first write the number of thousands, then hundreds, then tens, and finally units.
I (1) - unus (unus)
II (2) - duo (duo)
III (3) - tres (tres)
IV (4) - quattuor (quattuor)
V (5) - quinque
VI (6) - sex (sex)
VII (7) - septera (septem)
VIII (8) - octo (octo)
IX (9) - novem (novem)
X (10) - decern (decem)
XI (11) - undecim (undecim)
XII (12) - duodecim (duodecim)
ХШ (13) - tredecim (tradecim)
XIV (14) - quattuordecim (quattuordecim)
XV (15) - quindecim (quindecim)
XVI (16) - sedecim (sedecim)
XVII (17) - septendecim (septendecim)
XVIII (18) - duodeviginti (duodeviginti)
XIX (19) - undeviginti (undeviginti)
XX (20) - viginti (viginti)
XXI (21) - unus et viginti or viginti unus
XXII (22) - duo et viginti or viginti duo, etc.
XXVIII (28) - duodetriginta (duodetriginta)
XXIX (29) - undetriginta (undetriginta)
XXX (30) : triginta (triginta)
XL (40) - quadraginta (quadraginta)
L (5O) - quinquaginta (quinquaginta)
LX (60) - sexaginta (sexaginta)
LXX (70) - septuaginta (szltuaginta)
LXXX180) - octoginta (octoginta)
KS (90) - nonaginta (nonaginta)
C (100) centum (centum)
CC (200) - ducenti (ducenti)
CCC (300) - trecenti (trecenti)
CD (400) - quadrigenti (quadrigenti)
D (500) - quingenti (quingenti)
DC (600) - sescenti (sescenti) or sexonti (sextonti)
DCC (700) - septigenti (septigenti)
DCCC (800) - octingenti (octingenti)
CV (DCCC) (900) - nongenti (nongenti)
M (1000) - mille (mille)
MM (2000) - duo milia (duo milia)
V (5000) - quinque milla (quinque milia)
X (10,000) - decem milia (decem milia)
XX (20000) - viginti milia (viginti milia)
C (100000) - centum milia (centum milia)
XI (1,000,000) - decies centena milia (decies centena milia).
If suddenly an inquisitive person asks why the Latin letters V, L, C, D, M were chosen to denote the numbers 50, 100, 500 and 1000, then we will immediately say that these are not Latin letters at all, but completely different signs.
The fact is that the basis for the Latin alphabet was the Western Greek alphabet. It is to him that the three signs L, C and M go back. Here they denoted aspirated sounds, which were not in the Latin language. When the Latin alphabet was drawn up, they turned out to be superfluous. They were adapted to represent numbers in the Latin alphabet. Later they coincided in spelling with Latin letters. Thus, the sign C (100) became similar to the first letter of the Latin word centum (hundred), and M (1000) - to the first letter of the word mille (thousand). As for the sign D (500), it was half of the sign F (1000), and then it began to look like a Latin letter. The sign V (5) was just the upper half of the sign X (10).
Roman numerals are the numerals used by the ancient Romans in their non-positional number system.
Natural numbers are written by repeating these numbers: I (1), V (5), X (10), L (50), C (100), D (500), M (1000). Moreover, if a larger number is in front of a smaller one, then they are added (the principle of addition), but if a smaller number is in front of a larger one, then the smaller one is subtracted from the larger one (the principle of subtraction). The last rule applies only to avoid repeating the same number four times.
To correctly write large numbers in Roman numerals, you must first write the number of thousands, then hundreds, then tens, and finally units. In this case, some of the numbers (I, X, C, M) can be repeated, but no more than three times in a row; thus, they can be used to write any integer up to 3999 (MMMCMXCIX).
The smaller number can be written to the left of the larger one, then it should be subtracted from the larger one. In this case, only numbers denoting 1 or powers of 10 can be subtracted, and only the two digits closest in the number series to the subtrahend (that is, the subtrahend multiplied by 5 or 10) can be used as a minuend. Repetitions of a smaller number are not allowed. Thus there is only six options using the “subtraction rule”:
- IV = 4
- IX = 9
- XL=40
- XC = 90
- CD = 400
- CM = 900
Converting a number written in Roman numerals to a decimal number
Converting a Decimal Number to Roman Numerals
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