The Hindu—Arabic Number System and Roman Numerals (2024)

Learning Objectives

  • Become familiar with the evolution of the counting system we use every day
  • Write numbers using Roman Numerals
  • Convert between Hindu-Arabic and Roman Numerals

The Evolution of a System

Our own number system, composed of the ten symbols {0,1,2,3,4,5,6,7,8,9} is called the Hindu-Arabic system. This is a base-ten (decimal) system since place values increase by powers of ten. Furthermore, this system is positional, which means that the position of a symbol has bearing on the value of that symbol within the number. For example, the position of the symbol 3 in the number 435,681 gives it a value much greater than the value of the symbol 8 in that same number. We’ll explore base systems more thoroughly later. The development of these ten symbols and their use in a positional system comes to us primarily from India.[1]

The Hindu—Arabic Number System and Roman Numerals (1)

Figure 10. Al-Biruni

It was not until the fifteenthcentury that the symbols that we are familiar with today first took form in Europe. However, the history of these numbers and their development goes back hundreds of years. One important source of information on this topic is the writer al-Biruni, whose picture is shown in figure 10.[2] Al-Biruni, who was born in modern day Uzbekistan, had visited India on several occasions and made comments on the Indian number system. When we look at the origins of the numbers that al-Biruni encountered, we have to go back to the third century BCE to explore their origins. It is then that the Brahmi numerals were being used.

The Brahmi numerals were more complicated than those used in our own modern system. They had separate symbols for the numbers 1 through 9, as well as distinct symbols for 10, 100, 1000,…, also for 20, 30, 40,…, and others for 200, 300, 400, …, 900. The Brahmi symbols for 1, 2, and 3 are shown below.[3]

The Hindu—Arabic Number System and Roman Numerals (2)

These numerals were used all the way up to the fourthcentury CE, with variations through time and geographic location. For example, in the first century CE, one particular set of Brahmi numerals took on the following form:[4]

The Hindu—Arabic Number System and Roman Numerals (3)

From the fourthcentury on, you can actually trace several different paths that the Brahmi numerals took to get to different points and incarnations. One of those paths led to our current numeral system, and went through what are called the Gupta numerals. The Gupta numerals were prominent during a time ruled by the Gupta dynasty and were spread throughout that empire as they conquered lands during the fourththrough sixthcenturies. They have the following form:[5]

The Hindu—Arabic Number System and Roman Numerals (4)

How the numbers got to their Gupta form is open to considerable debate. Many possible hypotheses have been offered, most of which boil down to two basic types.[6] The first type of hypothesis states that the numerals came from the initial letters of the names of the numbers. This is not uncommon . . . the Greek numerals developed in this manner. The second type of hypothesis states that they were derived from some earlier number system. However, there are other hypotheses that are offered, one of which is by the researcher Ifrah. His theory is that there were originally nine numerals, each represented by a corresponding number of vertical lines. One possibility is this:[7]

The Hindu—Arabic Number System and Roman Numerals (5)

Because these symbols would have taken a lot of time to write, they eventually evolved into cursive symbols that could be written more quickly. If we compare these to the Gupta numerals above, we can try to see how that evolutionary process might have taken place, but our imagination would be just about all we would have to depend upon since we do not know exactly how the process unfolded.

The Gupta numerals eventually evolved into another form of numerals called the Nagari numerals, and these continued to evolve until the eleventhcentury, at which time they looked like this:[8]

The Hindu—Arabic Number System and Roman Numerals (6)

Note that by this time, the symbol for 0 has appeared! The Mayans in the Americas had a symbol for zero long before this, however, as we shall see later in the chapter.

These numerals were adopted by the Arabs, most likely in the eighth century during Islamic incursions into the northern part of India.[9]It is believed that the Arabs were instrumental in spreading them to other parts of the world, including Spain (see below).

Other examples of variations up to the eleventh century include:[10]

The Hindu—Arabic Number System and Roman Numerals (7)

Figure 11. Devangari, eighth century

The Hindu—Arabic Number System and Roman Numerals (8)

Figure 12. West Arab Gobar, tenth century

The Hindu—Arabic Number System and Roman Numerals (9)

Figure 13. Spain, 976 BCE

Finally, figure 14[11]shows various forms of these numerals as they developed and eventually converged to the fifteenthcentury in Europe.

The Hindu—Arabic Number System and Roman Numerals (10)

Figure 14.

Roman Numerals

The numeric system represented by Roman numerals originated in ancient Rome (753 BC–476 AD)and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages (generally comprising the 14th and 15th centuries (c. 1301–1500)). Numbers in this system are represented by combinations of letters from the Latin alphabet. Roman numerals, as used today, are based on seven symbols:


The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced in most contexts by the more convenient Hindu-Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some minor applications to this day.

The numbers 1 to 10 are usually expressed in Roman numerals as follows:


Numbers are formed by combining symbols and adding the values, so II is two (two ones) and XIII is thirteen (a ten and three ones). Because each numeral has a fixed value rather than representing multiples of ten, one hundred and so on, according to position, there is no need for “place keeping” zeros, as in numbers like 207 or 1066; those numbers are written as CCVII (two hundreds, a five and two ones) and MLXVI (a thousand, a fifty, a ten, a five and a one).

Symbols are placed from left to right in order of value, starting with the largest. However, in a few specific cases,to avoid four characters being repeated in succession (such as IIII or XXXX), subtractive notation is used: as in this table:


In summary:

  • I placed before V or X indicates one less, so four is IV (one less than five) and nine is IX (one less than ten)
  • X placed before L or C indicates ten less, so forty is XL (ten less than fifty) and ninety is XC (ten less than a hundred)
  • C placed before D or M indicates a hundred less, so four hundred is CD (a hundred less than five hundred) and nine hundred is CM (a hundred less than a thousand)


Write the Hindu-Arabic numeral forMCMIV.

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Modern use

By the 11th century, Hindu–Arabic numerals had been introduced into Europe from al-Andalus, by way of Arab traders and arithmetic treatises. Roman numerals, however, proved very persistent, remaining in common use in the West well into the 14th and 15th centuries, even in accounting and other business records (where the actual calculations would have been made using an abacus). Replacement by their more convenient “Arabic” equivalents was quite gradual, and Roman numerals are still used today in certain contexts. A few examples of their current use are:

The Hindu—Arabic Number System and Roman Numerals (11)

Spanish Real using “IIII” instead of IV

  • Names of monarchs and popes, e.g. Elizabeth II of the United Kingdom, Pope Benedict XVI. These are referred to as regnal numbers; e.g. II is pronounced “the second”. This tradition began in Europe sporadically in the Middle Ages, gaining widespread use in England only during the reign of Henry VIII. Previously, the monarch was not known by numeral but by an epithet such as Edward the Confessor. Some monarchs (e.g. Charles IV of Spain and Louis XIV of France) seem to have preferred the use of IIII instead of IV on their coinage (see illustration).
  • Generational suffixes, particularly in the US, for people sharing the same name across generations, for example William Howard Taft IV.
  • In the French Republican Calendar, initiated during the French Revolution, years were numbered by Roman numerals – from the year I (1792) when this calendar was introduced to the year XIV (1805) when it was abandoned.
  • The year of production of films, television shows and other works of art within the work itself. It has been suggested – by BBC News, perhaps facetiously – that this was originally done “in an attempt to disguise the age of films or television programmes.”[23] Outside reference to the work will use regular Hindu–Arabic numerals.
  • Hour marks on timepieces. In this context, 4 is usually written IIII.
  • The year of construction on building faces and cornerstones.
  • Page numbering of prefaces and introductions of books, and sometimes of annexes, too.
  • Book volume and chapter numbers, as well as the several acts within a play (e.g. Act iii, Scene 2).
  • Sequels of some movies, video games, and other works (as in Rocky II).
  • Outlines that use numbers to show hierarchical relationships.
  • Occurrences of a recurring grand event, for instance:
    • The Summer and Winter Olympic Games (e.g. the XXI Olympic Winter Games; the Games of the XXX Olympiad)
    • The Super Bowl, the annual championship game of the National Football League (e.g. Super Bowl XXXVII; Super Bowl 50 is a one-time exception[24])
    • WrestleMania, the annual professional wrestling event for the WWE (e.g. WrestleMania XXX). This usage has also been inconsistent.
The Hindu—Arabic Number System and Roman Numerals (2024)


What is Hindu-Arabic numeral system and Roman numeral system? ›

The main differences between Roman and Hindu-Arabic numerals are that the Romans did not have a symbol for zero, and the placement of numerals within a number can sometimes indicate subtraction rather than addition. In the Hindu-Arabic number system, each digit in a number has a place value.

Where when and how digits 1 2 3 4 5 6 7 8 and 9 originated and were developed? ›

Hindu-Arabic numerals, set of 10 symbols—1, 2, 3, 4, 5, 6, 7, 8, 9, 0—that represent numbers in the decimal number system. They originated in India in the 6th or 7th century and were introduced to Europe through the writings of Middle Eastern mathematicians, especially al-Khwarizmi and al-Kindi, about the 12th century.

Why are 1 3 5 7 and 9 called Arabic numerals? ›

The numbers English speakers use every day, known as Arabic numerals, were developed in the Maghreb during the 10th century. They made their way into Europe through Arab scholars in Al-Andalus (modern-day Andalusia in Spain), hence they are called Arabic numerals.

How do you write 11 and 12 in Roman numerals? ›

After 10, the roman numerals are followed by XI for 11, XII for 12, XII for 13, … till XX for 20.

What is the name for 1 2 3 4 5 6 7 8 and 9? ›

Natural Numbers The numbers that we use when we are counting or ordering {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 …} Whole Numbers The numbers that include natural numbers and zero. Not a fraction or decimal.

What number systems has the digits 0 1 2 3 4 5 6 7 8 and 9? ›

The decimal number system uses ten digits: 0,1,2,3,4,5,6,7,8 and 9 with the base number as 10. The decimal number system is the system that we generally use to represent numbers in real life.

Where did our number system in us come from? ›

The Hindu–Arabic numeral system, which originated in India and is now used throughout the world, is a positional base 10 system.

Why is 0 9 called Arabic numerals? ›

Origins. The Hindu–Arabic or Indo–Arabic numerals were invented by mathematicians in India. Persian and Arabic mathematicians called them "Hindu numerals". Later they came to be called "Arabic numerals" in Europe because they were introduced to the West by Arab merchants.

Why is 7 used in Arabic? ›

The Roman numerals are used to symbolize the Arabic letters which don't exist, or rather, the ones that have no phonetic equivalent in English. For e.g., the Arabic letter “ح” (Haa) can't be accurately represented with Latin characters and it is, therefore, represented by the number “7”.

Why do Arabs use Hindu numerals? ›

Because the Arabs transmitted this system to the West after the Hindu numerical system found its way to Persia, the numeral system became known as Arabic numerals, though Arabs call the numerals they use “Indian numerals”, أرقام هندية, arqam hindiyyah.

How do you write 4 in Hindu-Arabic numerals? ›

In this context, 4 is usually written IIII.

How do you write XIV in Hindu-Arabic numerals? ›

∴XIV = 10 + 4 = 14.

How do you write XXVI in Hindu-Arabic numerals? ›

As none of the symbols is preceded by a step lower numeral, we will directly add the values of the symbols to convert it to Hindu-Arabic numerals. So, XXVI=10+10+5+1=26. Therefore, the Roman numeral XXVI is 26 in Hindu-Arabic system.

What is 1 2 3 4 5 6 7 8 9 10 in Arabic? ›

١ one, ٢ two, ٣ three, ٤ four, ٥ five, ٦ six, ٧ seven, ٨ eight, ٩ nine, ١٠ ten.

What is the symbol 3 in Arabic? ›

3 = ع ('ayn)

What is Z in roman numerals? ›

Use in the Middle Ages and Renaissance
NumberMedieval abbreviationNotes and etymology
500QRedundant with D; abbreviates quingenti, Latin for 500. Also sometimes used for 500,000.
800ΩBorrowed from Gothic.
900ϡBorrowed from Gothic.
16 more rows

What is roman numerals 1 to 100? ›

What are Roman numerals? Roman numerals are the symbols used in a system of numerical notation based on the ancient Roman system. The symbols are I, V, X, L, C, D, and M, standing respectively for 1, 5, 10, 50, 100, 500, and 1,000.

How do you write 2023 in roman numerals? ›

2023 is MMXXIII in Roman numerals.

What kind of sequence is 1 2 3 4 5 6 7 8? ›

Explanation: The given sequence is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. They are the first ten natural numbers.

What are numbers 1 2 3 4 5 6 called? ›

The correct option is A natural numbers. Natural numbers - All counting numbers except zero are natural numbers.

What are all numbers from 1 2 3 4 5 called? ›

Natural Numbers (N), (also called positive integers, counting numbers, or natural numbers); They are the numbers {1, 2, 3, 4, 5, …}

What uses ten digits 0 1 2 3 4 5 6 7 8 and 9 with the base number as 10? ›

decimal system, also called Hindu-Arabic number system or Arabic number system, in mathematics, positional numeral system employing 10 as the base and requiring 10 different numerals, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Which number system uses ten digits 0 1 2 3 4 5 6 7 8 and 9 with the base number as 10? ›

Lesson Summary. A number system's base is the number of digits used to represent numerals in the number system, and the base ten number system uses ten digits to create its numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The base ten number system is also known as the decimal number system.

Which numbering system uses 0 1 2 3 5 6 and 7? ›

Basics of Numbering Systems

There are many different numbering systems, each one based on a number of symbols. Each symbol represents a unique value. You are familiar with the decimal system, using the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The decimal system is based on the powers of 10.

What number system does USA use? ›

The U.S. is one of the few countries globally which still uses the Imperial system of measurement, where things are measured in feet, inches, pounds, ounces, etc.

What symbol was zero before it was 0? ›

The Babylonians displayed zero with two angled wedges (middle). The Mayans used an eyelike character [top left] to denote zero. The Chinese started writing the open circle we now use for zero. The Hindus depicted zero as a dot.

What number system do we use in America? ›

The most commonly used numeral system is the decimal positional numeral system, the decimal referring to the use of 10 symbols—0, 1, 2, 3, 4, 5, 6, 7, 8, 9—to construct all numbers.

What is 2 in Arabic? ›

2. Cardinal Numbers Zero to Ten
NumberEastern Arabic NumeralPronunciation
Two٢إثْنان (ʾiṯnān)
Three٣ثَلاثة (ṯalāṯah)
Four٤أربَعة (ʾarbaʿah)
Five٥خَمْسة (ḫamsah)
7 more rows
Oct 24, 2019

What is M in Arabic numerals? ›

here are the commonly used Roman numerals: I = 1. L = 50 M = 1000.

Does China use Arabic numerals? ›

Chinese numerals The Arabic numeral system used today in China was introduced to China by the Europeans in the early 17th century. But the Chinese character-based number systems are still in use. The financial numerals are used only when writing an amount on a form for remitting money at a bank.

What is the backwards 3 in Arabic? ›

For example, the numeral "3" is used to represent the Arabic letter ⟨ع⟩ (ʿayn)—note the choice of a visually similar character, with the numeral resembling a mirrored version of the Arabic letter.

What is the holy Arabic number? ›

In every religion, there are different rituals, customs, facts even certain numbers that hold a very important significance in defining that particular religion. One of them is the number “786” that is believed to be a Holy number in Islam.

What is a to z in Arabic? ›

أ,ب,ت,ث ج,ح,خ,د,ذ,ر,ز,س,ش,ص,ض,ط,ظ,ع,غ,ف,ق,ك,ل,م,ن,هـ,و,ي Shazly.

Why don't we use Roman numerals always? ›

There's one reason that the symbols from the ancient Roman system of numerical notation eventually gave way to the Arabic numeral system that is familiar to people around the world: Roman numerals can be rather impractical and cumbersome to use.

Does the whole world use Arabic numerals? ›

Some cultures still use other number systems or other bases, but Arabic numbers have become one of the few communication systems considered to be virtually universal among contemporary human cultures.

Why did Hindu-Arabic numerals replace Roman numerals? ›

Meanwhile, cultures that used the Hindu-Arabic system not only had an easier time with basic arithmetic, but they were also able to undertake more complex math. This enabled them to make big advances in algebra and geometry while Europeans toiled away with Roman numerals.

What is XL in Hindu-Arabic numerals? ›

XL = 40. Hence, the value of Roman Numerals XL is 40.

What is Xi in Hindu-Arabic numerals? ›

In Hindu Arabic numerals, XI is written as 9.

Are the 10 symbols which are used in Hindu-Arabic numerals? ›

Our own number system, composed of the ten symbols {0,1,2,3,4,5,6,7,8,9} is called the Hindu-Arabic system. This is a base-ten (decimal) system since place values increase by powers of ten.

What does 7 mean in Roman numerals? ›

A Roman numeral representing seven (7).

What does XIII mean? ›

13 in Roman Numerals is XIII.

What is Hindu-Arabic numerals XXIV? ›

So, XXIV stands for 24.

How do you write XXI in Hindu-Arabic numerals? ›

So, number corresponds to XXI in Hindu-Arabic numerals is 21. Q.

What is Hindu-Arabic numeration Xcix? ›

So, XCIX stands for 99.

What is meant by Hindu-Arabic system? ›

The Hindu–Arabic numeral system or Indo-Arabic numeral system (also called the Hindu numeral system or Arabic numeral system) is a positional decimal numeral system, and is the most common system for the symbolic representation of numbers in the world.

What does the Hindu-Arabic numeral system do? ›

The Hindu-Arabic numerals, as they are now known, greatly facilitated arithmetic computations, particularly multiplication and division.

What is the Hindu-Arabic number system based on? ›

Our own number system, composed of the ten symbols {0,1,2,3,4,5,6,7,8,9} is called the Hindu-Arabic system. This is a base-ten (decimal) system since place values increase by powers of ten.

How does Hindu-Arabic numerals work? ›

Hindu-Arabic numerals are a decimal, or base-ten, place-value number system with the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 as fundamental building blocks. Each digit in a number has a place value depending on its position.

What are Hindu Arabic numbers also called? ›

The Hindu–Arabic numeral system or Indo-Arabic numeral system (also called the Arabic numeral system or Hindu numeral system) is a positional decimal numeral system, and is the most common system for the symbolic representation of numbers in the world.

What is Arabic numerals in Word? ›

Arabic numeral. noun. : any of the number symbols 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0.

Are Arabic numbers the same as English? ›

Arabic numerals, also known as Western Arabic numerals, are numbers written exactly in the same way we write numbers in English. Hindi or Eastern Arabic numerals, on the other hand, use Arabic symbols.

Why is it called Hindu-Arabic numerals? ›

Because the Arabs transmitted this system to the West after the Hindu numerical system found its way to Persia, the numeral system became known as Arabic numerals, though Arabs call the numerals they use “Indian numerals”, أرقام هندية, arqam hindiyyah.

Why do we use the Arabic number system? ›

Although positional notation opened possibilities that were hampered by previous systems, late medieval Italian merchants did not stop using Roman numerals (or other reckoning tools). Rather, Arabic numerals became an additional tool that could be used alongside others.

How does the Roman numeral system work? ›

The Roman numeral system uses only seven symbols: I, V, X, L, C, D, and M. I represents the number 1, V represents 5, X is 10, L is 50, C is 100, D is 500, and M is 1,000. Different arrangements of these seven symbols represent different numbers.

Who invented Roman numerals? ›

Roman numerals are a number system that was invented by the ancient Romans for the purpose of counting and performing other day-to-day transactions. Roman numerals use just seven letters, with the quantity and order of these letters determining the value of the final number.

How many symbols are there in Roman system? ›

There are the 7 basic symbols in Roman numerals.

What are the four main attributes of Hindu-Arabic numeration system? ›

The Hindu-Arabic numeration system has several important features:
  • numbers created using a combination of ten digits.
  • Place value is used to determine the value of a digit.
  • base-ten place value relies groups of ten.
  • Uses zero as a placeholder.

How many 4 digit numbers are there in Hindu-Arabic numeration system? ›

There are ten thousand 4 digit numbers in the Hindu Arabic Numaral system. The series of 4 digit number starts from 1000 and ends at 9999.


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