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# Arabic numerals

By far the most common form of symbolism used to represent numbers. Arabic numerals are a positional base 10 numeral system with 10 distinct glyphs representing the 10 digits. The leftward most digit of a number has the greatest value; this is the most logical arrangement if the number is read from right to left which is how Arabic is read. However for those accustomed to reading from left to right it is less than ideal. In a more developed form Arabic numeral also contain a decimal marker (usually a decimal point or a decimal comma) that separates the ones place from the tenths place and a symbol for "these digits repeat ad infinitum". In modern usage this latter symbol is usually a vinculum although historically there has been much variation. In this more developed form Arabic numerals can describe any rational number using only 12 glyphs.

Arabic numerals have been represented using many different sets of glyphs. These glyph sets can be divided into two families and these two families can be used to create two different types of Arabic numerals - namely the West Arabic numerals and the East Arabic numerals. East Arabic numerals which were developed primarily in what is now Iraq are shown in the below picture as "Arabic-Indic". West Arabic numeral which were developed in Spain and the Maghreb countries are shown as "European". "East Arabic-Indic" can be considered a variation of East Arabic numerals. Early varieties of West Arabic numerals often had the glyphs of the digit four and the digit five reversed or the glyph of the four digit rotated 90 degrees.

In Japan, Western European numerals and alphabet are used under the name of "romaji". So, if a number is written in Arabic numerals, they would say "it is written in romaji" (as opposed to native Japanese numbers). This translates as "Roman characters" and may sound confusing for those who know "Roman numbers".

## History

Because they are considered one of the most significant developments in mathematics several theories have been advanced about the origin of Arabic numerals. These theories include that Arabic numerals originated in China, that Arabic numerals were invented by Al-Khwarizmi, that Arabic numerals originated in the ancient Middle East and that Arabic numerals were simply an westward transmission of Indian numerals. Although these theories contain varying amounts of truth each is somewhat exaggerated in its thesis. Nevertheless very few historians debate that Arabic numerals were influence by Indian mathematics. Somewhat speculatively Indian numerals can be traced to China. Chinese merchants or Buddhist pilgrims may have introduced into India a numeral system similar to the Chinese Hua Ma system (see Chinese numerals). It is certain though that by the middle of the 1st Millennium AD a base 10 numeral system with 9 glyphs was being used in India. This numeral system was introduced to the Middle East by the 7th Century AD. Significantly however the numerals lack a zero digit. Muslim mathematicians working in what is now Iraq were familiar with the Babylonian numerals which used the zero digit between nonzero digits although not after nonzero digits. However by 874 AD at the latest Muslim mathematicians were using a base 10 positional number system which used the zero digit both between and after nonzero digits. Mathematicians in India took the same step at essentially the same time (by 876 AD at the latest). The two groups apparently derived analogous numeral systems independently. In the early 12th Century AD Arab mathematicians in North Africa extended the Arabic numeral system to include decimals. Fibonacci and Italian mathematician who had lived in North Africa introduced the Arabic numerals to Europe and promoted them with his book Liber Abaci which was published in 1202. It should be noted that until modern times in the Muslim world Arabic numerals were known solely to mathematicians. Muslim scientist used Babylonian numerals and merchants used a numeral system similar to the Greek numerals and Hebrew numerals. Therefore it was not until Fibonacci that Arabic numerals were used by a large population.