How to say 40 in Roman numerals. Translation of Roman, Indian, Arabic numerals (numbers)

Roman numerals- numbers used by the ancient Romans in their non-positional number system.

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). The last rule applies only to avoid repeating the same number four times.

Roman numerals appeared around 500 BC among the Etruscans.

To fix in memory the letter designations of numbers in descending order, there is a mnemonic rule:

M s D arim WITH face-to-face L imons, X vatit V seven I X.

Respectively M, D, C, L, X, V, I

To correctly write large numbers in Roman numerals, you must first write the number of thousands, then hundreds, then tens, and finally units.

There is a "shortcut" for writing large numbers such as 1999. It is not recommended, but is sometimes used to simplify things. The difference is that to reduce a digit, any digit can be written to the left of it:

• 999. Thousand (M), subtract 1 (I), we get 999 (IM) instead of CMXCIX. Consequence: 1999 - MIM instead of MCMXCIX
• 95. One hundred (C), subtract 5 (V), get 95 (VC) instead of XCV
• 1950: Thousand (M), subtract 50 (L), get 950 (LM). Consequence: 1950 - MLM instead of MCML

It was only in the 19th century that the number “four” was written down as “IV”; before that, the number “IIII” was most often used. However, the entry “IV” can already be found in the documents of the Forme of Cury manuscript dating back to 1390. Watch dials have traditionally used "IIII" instead of "IV" in most cases, mainly for aesthetic reasons: this spelling provides visual symmetry with the "VIII" numerals on the opposite side, and an inverted "IV" is more difficult to read than "IIII".

Application of Roman numerals

In Russian, Roman numerals are used in the following cases:

• Century or millennium number: XIX century, II millennium BC. e.
• Serial number of the monarch: Charles V, Catherine II.
• The volume number in a multi-volume book (sometimes the numbers of parts of the book, sections or chapters).
• In some publications - the numbers of sheets with the preface to the book, so as not to correct the links within the main text when the preface is changed.
• Antique watch dial markings.
• Other important events or bullet points, for example: Euclid's V postulate, World War II, XXII Congress of the CPSU, etc.

In other languages, the scope of application of Roman numerals may have specific features; for example, in Western countries, the year number is sometimes written in Roman numerals.

Roman numerals and Unicode

The Unicode standard defines characters to represent Roman numerals as part of Number forms(English) Number Forms), in the area of ​​characters with codes U+2160 to U+2188. For example, MCMLXXXVIII can be represented in the form ⅯⅭⅯⅬⅩⅩⅩⅧ . This range includes both lowercase and uppercase numerals from 1 (Ⅰ or I) to 12 (Ⅻ or XII), including combination glyphs for composite numbers such as 8 (Ⅷ or VIII), primarily for compatibility with East Asian character sets in industry standards such as JIS X 0213, where these characters are defined. Combination glyphs are used to represent numbers that were previously composed of individual characters (for example, Ⅻ instead of its representation as Ⅹ and Ⅱ). In addition to this, glyphs exist for the archaic forms of 1000, 5000, 10,000, major reverse C (Ɔ), the late form of 6 (ↅ, similar to the Greek stigma: Ϛ), the early form of 50 (ↆ, similar to to the downward-pointing arrow ↓⫝⊥ ), 50,000, and 100,000. It should be noted that the backsmall small c, ↄ is not included in Roman numeral characters, but is included in the Unicode standard as the Claudian capital Ↄ.

Characters in the range U+2160-217F are present only for compatibility with other standards that define these characters. In everyday life, ordinary letters of the Latin alphabet are used. Displaying these characters requires software that supports the Unicode standard and a font that contains the glyphs corresponding to these characters.

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 are 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).

Roman numerals, invented more than 2,500 years ago, were used by Europeans for two millennia before being replaced by Arabic numerals. This happened because Roman numerals are quite difficult to write, and any arithmetic operations in the Roman system are much more difficult to perform than in the Arabic number system. Despite the fact that the Roman system is not often used today, this does not mean that it has become irrelevant. In most cases, centuries are denoted in Roman numerals, but years or exact dates are usually written in Arabic numerals.

Roman numerals are also used when writing the serial numbers of monarchs, encyclopedic volumes, and the valency of various chemical elements. The dials of watches also often use Roman numerals.

Roman numerals are certain signs with which decimal places and their halves are written. For this purpose, only seven capital letters of the Latin alphabet are used. The number 1 corresponds to the Roman numeral I, 5 – V, 10 – X, 50 – L, 100 – C, 500 – D, 1000 – M. When denoting natural numbers, these numbers are repeated. So 2 can be written using two times I, that is, 2 – II, 3 - three letters I, that is, 3 – III. If a smaller digit comes before a larger one, then the principle of subtraction is used (the smaller digit is subtracted from the larger one). So, the number 4 is depicted as IV (that is, 5-1).

In the case when a larger number comes in front of a smaller one, they are added, for example, 6 is written in the Roman system as VI (that is, 5+1).

If you are used to writing numbers in Arabic numerals, then some difficulties may arise when you need to write centuries in Roman numerals, a number or a date. You can convert any number from the Arabic system to the Roman number system and vice versa very easily and very quickly using the convenient converter on our website.

On your computer keyboard, just switch to English to easily write any number in Roman numerals.

Apparently, the ancient Romans preferred straight lines, which is why all their numbers are straight and strict. However, Roman numerals are nothing more than a simplified image of the fingers of a human hand. The numbers one to four resemble outstretched fingers, the number five can be compared to an open palm with the thumb protruding. And the number ten resembles two crossed hands. In European countries, when counting, it is customary to straighten your fingers, but in Russia, on the contrary, bend them.

Roman notation uses seven numerals - I, V, X, L, L, D, M. To represent the number n in Roman notation, we take the numbers of its units n 0, tens n 1, hundreds n 2 and thousands n 3. First, let's write down the number of units in Roman notation. For 0 ⩽ n 0 ⩽ 3, we simply write down the number I (one) n 0 times in a row. For 4 ⩽ n 0 ⩽ 8, we write down the number V (it means five), and add to it as many digits I as n 0 is more or less than five, and if more, then on the right, and if less, then on the left. Finally, we write n 0 = 9 as IX (X denotes ten, I on the left shows that the ten is missing one).

We will do the same with the number of tens n 1, only instead of the numbers I =1, V =5, C =10 we will use X =10, L =50, C =100.

The same rules apply to the number of hundreds n 2, the numbers C = 100, D = 500, M = 1000 are used for recording.

For thousands of Roman numerals it will only suffice for 0 ⩽ n 3 ⩽ 3, so you get either M, MM, or MMM.

All listed rules are summarized in the table.

Now let's put together the entries for n 3, n 2, n 1, n 0 in the order listed. The Roman number is ready.

For example, the number 1987 is written as MCMLXXXVII. Here 1000 = M, 900 = CM, 80 = LXXX and 7 = VII.

The disadvantage of Roman notation is visible: using six digits, it allows you to represent numbers no more than 3999.

An analysis of the rules for converting numbers into Roman notation shows that it is enough to write each of the decimal digits of a given number in Roman numerals, taking into account the number of its digit, and then put the resulting entries together. The rules for writing a decimal digit using Roman numerals are approximately the same - only the set of Roman numerals used for writing changes depending on the digit. For units it is I, V, X, for tens - X, L, C, for hundreds - C, D, M, for thousands - only M (since there are no digits for five and ten thousand).

Given this circumstance, it would be reasonable to implement in the form of a procedure (let's call it toRomanHelper) the conversion of a decimal digit to Roman notation. The procedure will take two parameters - a decimal digit and a decimal place number. The return value is the Roman notation of the decimal digit corresponding to its digit.

The toRoman procedure will handle the conversion of the number to Roman notation. She will parse the number into decimal digits. For each decimal digit, it will find a notation in Roman numerals in accordance with the digit in which it is located (toRomanHelper procedure will be called for this). The Roman notations for the decimal digits will be concatenated together and the resulting string will be returned from the procedure.

The reverse conversion will be done in reverse order. The string representing the Roman number must first be divided into decimal places, and then we find the decimal digits corresponding to these places.

The task of separating by ranks will now be more difficult. The point is that not every string composed of Roman numerals will be a valid Roman notation for a number (unlike decimal notation, in which any sequence of decimal digits will be valid).

In accordance with the rules for forming the Roman notation of numbers, the correct notation is four groups of Roman numerals composed together. The first (located on the left) is the group representing thousands, then there is the group of hundreds, then tens, and finally units. What each of these groups may consist of can be seen in the corresponding column of Table 31.1. "Writing decimal places in Roman numerals".

A good solution would be to use regular expressions to divide the Roman notation into groups of digits by digit. For each group, you need to create a template and enclose it in captivating brackets. The patterns for thousands, hundreds, tens, and ones, put together, will produce a regular expression that the entire Roman notation must match. Therefore, you should add anchors to the beginning and end of the string in your regular expression.

Let's start creating a template for the units digit. The solution that first comes to mind is to list all the alternatives: (|I|II|III|IV|V|VI|VII|VIII|IX) . Note the empty alternative with which the enumeration begins: the group of units in Roman notation can be empty. This decision can be made a little easier by using quantifiers. For numbers from 0 to 3 you can write I(0,3) instead of |I|II|III, for numbers from 5 to 8 you can write VI(0,3) instead of V|VI|VII|VIII. Thus, for the ones place we get the pattern (I(0,3)|IV|VI(0,3)|IX) . It can be further simplified by combining the first alternative with the third, and the second with the fourth: (V?I(0,3)|I) .

For tens and hundreds, exactly the same patterns are obtained, only composed of other Roman numerals: (L?X(0,3)|X) (tens) and (D?C(0,3)|C) (hundreds). For the thousands place the pattern is quite simple: (M(0,3)) .

So, for the whole Roman notation we get the following regular expression: ^(M(0,3))(D?C(0,3)|C)(L?X(0,3)|X)(V?I(0 ,3)|I)$ .