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# Arabic numerals

Arabic numerals are, by far, the most common form of symbolism used to represent numbers. The Arabic numeral system is a positional base 10 numeral system with 10 distinct glyphs representing the 10 digits. The leftmost digit of a number has the greatest value. In a more developed form, the Arabic numeral system also uses a decimal marker (usually a decimal point or a decimal comma) which separates the ones place from the tenths place, and also a symbol for "these digits repeat ad infinitum" (recur). In modern usage, this latter symbol is usually a vinculum. Historically, however, there has been much variation. In this more developed form, the Arabic numeral system can symbolize any rational number using only 12 glyphs.

The Arabic numeral system has used many different sets of glyphs. These glyph sets can be divided into two main families—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 picture below as "Arabic-Indic." "East Arabic-Indic" are a variety of East Arabic numerals. West Arabic numerals—which were developed in Spain and the Maghreb—are shown in the picture, labelled "European." Early varieties of West Arabic numerals often use the symbol "4" to represent the number five with some other symbol to represent five (often a loop), or had the glyph of the four digit rotated 90 degrees clockwise.

In Japan, Arabic numerals and the Roman alphabet are both 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 Japanese numerals). This translates as "Roman characters", and may sound confusing for those who know about Roman numerals.

## History

The Arabic numeral system is considered one of the most significant developments in mathematics, and, ergo, several theories have been advanced about its origin. These theories include

• the idea that it originated in China.
• the idea that it was invented by Al-Khwarizmi.
• the idea that it originated in the ancient Middle East and that the Arabic numeral system was simply an westward transmission of the Indian numeral system.

Although these theories contain varying amounts of truth, each is exaggerated in its thesis. Nevertheless, very few historians debate the Arabic numeral system was influenced by Indian mathematics.

Somewhat speculatively, the origin of a base-10 positional number system used in India can possibly be traced to China. Because the Chinese Hua Ma system (see Chinese numerals) is also a positional base-10 system, Hau Ma numerals—or some numeral system similar to it—may have been the inspiration for the base-10 positional numeral system that evolved in India. This hypothesis is made stronger by the fact that years from 400 to 700, during which a positional base-10 system emerged in India, were also the period during which the number of Buddhist pilgrims traveling between China and India peaked. What is certain is that by the time of Bhasakara I (i.e., the seventh century AD) a base 10 numeral system with 9 glyphs was being used in India, and the concept of zero (represented by a dot) was known (see the Vāsavadattā of Subandhu, or the definition by Brahmagupta).

This numeral system had reached the Middle East by 670. Muslim mathematicians working in what is now Iraq were already familiar with the Babylonian numeral system, which used the zero digit between nonzero digits (although not after nonzero digits), so the more general system would not have been a difficult step. In the tenth century AD, Arab mathematicians extended the decimal numeral system to include fractions, as recorded in a treatise by Abu'l-Hasan al-Uqlidisi in 952-3.

Fibonacci, an Italian mathematician who had lived in North Africa, introduced the Arabic numeral system to Europe and promoted it with his book Liber Abaci, which was published in 1202. It should be noted that in the Muslim World—until modern times—the Arabic numeral system was used only by mathematicians. Muslim scientists used the Babylonian numeral system, and merchants used a numeral system similar to the Greek numeral system and the Hebrew numeral system. Therefore, it was not until Fibonacci that the Arabic numeral system was used by a large population.