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 larger than 6/12 was marked with an addition: S = 10\12. Another option is S::.

Origin

On at the moment doesn't exist unified theory 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 Latin or more ancient letter“and”, and a notch resembling 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 right hand, thrown out by the merchant when naming the price. V is set aside thumb, forming together with the palm 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 designate serial number monarch (Peter I), volume number of a multi-volume publication, sometimes a 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 English words eXtra (very), Small (small), Large (large).

The Roman numbering system using letters was common in Europe for two thousand years. Only in the late Middle Ages was it replaced by a more convenient decimal system of numbers, borrowed from the Arabs. But, to this day, Roman numerals are used to indicate dates on monuments, time on clocks, and (in the Anglo-American typographic tradition) pages of book prefaces. In addition, in Russian it is customary to use Roman numerals to denote ordinal numbers.

To designate numbers, 7 letters of the Latin alphabet were used: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000. Intermediate numbers were formed by adding several letters to the right or left. First thousands and hundreds were written, then tens and ones. Thus, the number 24 was depicted as XXIV. A horizontal line above the symbol meant multiplication by a thousand.

Natural numbers are written by repeating these numbers. At the same time, if big number stands in front of the smaller one, then they add up (the principle of addition), but if the smaller one is in front of the 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. For example, I, X, C are placed respectively before X, C, M to indicate 9, 90, 900 or before V, L, D to indicate 4, 40, 400. For example, VI = 5+1 = 6, IV = 5 - 1 = 4 (instead of IIII). XIX = 10 + 10 - 1 = 19 (instead of XVIIII), XL = 50 - 10 =40 (instead of XXXX), XXXIII = 10 + 10 + 10 + 1 + 1 + 1 = 33, etc.

Execution arithmetic operations dealing with multi-digit numbers in this entry is very inconvenient. The Roman numeral system is not currently used, with the exception, in some cases, of designating centuries (XV century, etc.), AD. e. (MCMLXXVII, etc.) and months when indicating dates (for example, 1. V. 1975), ordinal numbers, and sometimes derivatives of small orders, big three: yIV, yV, etc.

Roman numerals
I	1	XI	11	XXX	30	CD	400
II	2	XII	12	XL	40	D	500
III	3	XIII	13	L	50	DC	600
IV	4	XIV	14	LX	60	DCC	700
V	5	XV	15	LXX	70	DCCC	800
VI	6	XVI	16	LXXX	80	C.M.	900
VII	7	XVII	17	XC	90	M	1000
VIII	8	XVIII	18	C	100	MM	2000
IX	9	XIX	19	CC	200	MMM	3000
X	10	XX	20	CCC	300

>> Roman numeral system

§ 4.3. Roman number system

An example of a non-positional number system that has survived to this day is number systems, used more than two and a half thousand years ago in Ancient Rome.

The Roman number system is based on the signs I (one finger) for the number 1, V (open palm) for the number 5, X (two folded palms) for 10, and special signs to represent the numbers 50, 100, 500 and 1000.

The notation for the last four numbers has undergone significant changes over time. Scientists suggest that initially the sign for the number 100 looked like a bunch of three lines like the Russian letter Zh, and for the number 50 it looked like the upper half of this letter, which was later transformed into the sign L:

The first letters of the corresponding numbers began to be used to denote the numbers 100, 500 and 1000. Latin words(Centum - one hundred, Demimille - half a thousand, Mille - a thousand).

To write a number, the Romans used not only addition, but also subtraction of key numbers. The following rule was applied.

The value of each smaller sign placed to the left of the larger one is subtracted from the value of the larger sign.

For example, the entry IX represents the number 9, and the entry XI represents the number 11. Decimal number 28 is presented as follows:

XXVIII = 10 + 10 + 5 + 1 + 1 + 1.

The decimal number 99 is represented as follows:

The fact that when writing new numbers, key numbers can not only be added, but also subtracted, has a significant drawback: writing in Roman numerals deprives the number of unique representation. Indeed, in accordance with the above rule, the number 1995 can be written, for example, in the following ways:

MCMXCV = 1000 + (1000 - 100) + (100 -10) + 5,
MDCCCCLXXXXV = 1000 + 500 + 100 + 100 + 100 + 100 + 50 + 10 + 10 + 10 + 10 + 5,
MVM = 1000 + (1000 - 5),
MDVD = 1000 + 500 + (500 - 5) and so on.

There are still no uniform rules for recording Roman numerals, but there are proposals to adopt an international standard for them.

Nowadays, it is proposed to write any of the Roman numerals in one number no more than three times in a row. Built on this basis tables, which is convenient to use to denote numbers in Roman numerals:

This table allows you to write any integer from 1 to 3999. To do this, first write your number as usual (in decimal system). Then, for numbers in the thousands, hundreds, tens and units places, select the appropriate ones from the table.

In order to write down numbers greater than 3999, special rules are used, but familiarization with them is beyond the scope of our course.

Roman numerals have been used for a very long time. Even 200 years ago, in business papers, numbers had to be indicated by Roman numerals (it was believed that ordinary Arabic numerals easy to fake).

The Roman numeral system is used today mainly for naming significant dates, volumes, sections and chapters in books.

Bosova L. L. Computer Science: Textbook for 6th grade / L. L. Bosova. - 3rd ed., rev. and additional - M.: BINOM. Laboratory of Knowledge, 2005. - 208 pp.: ill.

Lesson content lesson notes supporting frame lesson presentation acceleration methods interactive technologies Practice tasks and exercises self-test workshops, trainings, cases, quests homework discussion questions rhetorical questions from students Illustrations audio, video clips and multimedia photographs, pictures, graphics, tables, diagrams, humor, anecdotes, jokes, comics, parables, sayings, crosswords, quotes Add-ons abstracts articles tricks for the curious cribs textbooks basic and additional dictionary of terms other Improving textbooks and lessonscorrecting errors in the textbook updating a fragment in a textbook, elements of innovation in the lesson, replacing outdated knowledge with new ones Only for teachers perfect lessons calendar plan for the year methodological recommendations discussion programs Integrated Lessons

| Lesson planning and lesson materials | 6th grade | Material for the curious | Roman number system

Material
for the curious

Roman number system

An example of a non-positional number system that has survived to this day is the number system used more than two and a half thousand years ago in Ancient Rome.

The Roman number system is based on the signs I (one finger) for the number 1, V (open palm) for the number 5, X (two folded palms) for 10, as well as special signs for the numbers 50, 100, 500 and 1000.

The notation for the last four numbers has undergone significant changes over time. Scientists suggest that initially the sign for the number 100 looked like a bunch of three lines like the Russian letter Zh, and for the number 50 it looked like the upper half of this letter, which was later transformed into the sign L:

To denote the numbers 100, 500 and 1000, the first letters of the corresponding Latin words began to be used (Centum - one hundred, Demimille - half a thousand, Mille - one thousand).

To write a number, the Romans used not only addition, but also subtraction of key numbers. The following rule was applied.

The value of each smaller sign placed to the left of the larger one is subtracted from the value of the larger sign.

For example, the entry IX represents the number 9, and the entry XI represents the number 11. The decimal number 28 is represented as follows:

XXVIII =10 + 10 + 5 + 1 + 1 + 1.

The decimal number 99 is represented as follows: XCIX = (-10 + 100) (- 1 + 10).

The fact that when writing new numbers, key numbers can not only be added, but also subtracted, has a significant drawback: writing in Roman numerals deprives the number of unique representation. Indeed, in accordance with the above rule, the number 1995 can be written, for example, in the following ways:

MCMXCV = 1000 + (1000 - 100) + (100 -10) + 5,
MDCCCCLXXXXV = 1000 + 500 + 100 + 100 + 100 + 100 + 50 + 10 + 10 + 10 + 10 + 5,
MVM = 1000 + (1000 - 5),
MDVD = 1000 + 500 + (500 - 5) and so on.

There are still no uniform rules for recording Roman numerals, but there are proposals to adopt an international standard for them.

Nowadays, it is proposed to write any of the Roman numerals in one number no more than three times in a row. Based on this, a table has been constructed that is convenient to use to designate numbers in Roman numerals:

This table allows you to write any integer from 1 to 3999. To do this, first write your number as usual (in decimal). Then, for numbers in the thousands, hundreds, tens and units places, select the appropriate code groups from the table.

In order to write down numbers greater than 3999, special rules are used, but getting to know them is beyond the scope of our course.

Roman numerals have been used for a very long time. Even 200 years ago, in business papers, numbers had to be denoted by Roman numerals (it was believed that ordinary Arabic numerals were easy to counterfeit).

The Roman numeral system is used today mainly for naming significant dates, volumes, sections and chapters in books.

The Roman numbering system using letters was common in Ancient Rome and Europe for two thousand years. Only in the late Middle Ages was it replaced by a more convenient decimal system of numbers, borrowed from the Arabs (1,2,3,4,5...).

But, until now, Roman numerals indicate dates on monuments, time on clocks and (in the Anglo-American typographic tradition) pages of book prefaces, clothing sizes, chapters of monographs and textbooks. In addition, in Russian it is customary to use Roman numerals to denote ordinal numbers. The Roman numeral system is currently used to designate centuries (XV century, etc.), AD. e. (MCMLXXVII, etc.) and months when indicating dates (for example, 1. V. 1975), in historical monuments of law as article numbers (Karolina, etc.)

To designate numbers, 7 letters of the Latin alphabet were used (the first letter of the words is five, ten, fifty, one hundred, five hundred, thousand):

I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000

C (100) is 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 Ф (1000)

The V sign (5) is the upper half of the X sign (10)

Intermediate numbers were formed by adding several letters to the right or left. Thousands and hundreds are written first, then tens and ones. So the number 24 is written as XXIV

Natural numbers are written by repeating these numbers.

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).

In other words, if a sign denoting a smaller number is to the right of a 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

The last rule applies only to avoid repeating the same number four times. To avoid repetition 4 times, the number 3999 is written as MMMIM.

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).

For example, I, X, C are placed respectively before X, C, M to indicate 9, 90, 900 or before V, L, D to indicate 4, 40, 400.

For example, VI = 5+1 = 6, IV = 5 - 1 = 4 (instead of IIII).

XIX = 10 + 10 - 1 = 19 (instead of XVIIII),

XL = 50 - 10 =40 (instead of XXXX),

XXXIII = 10 + 10 + 10 + 1 + 1 + 1 = 33, etc.

Roman numerals

MCMLXXXIV

Note:

Basic Roman numerals: I (1) - unus (unus) II (2) - duo (duo) III (3) - tres (tres) IV (4) - quattuor (quattuor) V (5) - quinque (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 XXIX (29) - undetriginta XXX (30) - triginta XL (40) - quadraginta L (50) - quinquaginta LX (60) - sexaginta LXX (70) - septuaginta LXXX (80) - octoginta XC (90) - nonaginta C (100) - centum CC (200) - 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 (1000000) - centum milia (centum milia) XI (1000000) - decies centena milia (decies centena milia)"