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The Hindu-Arabic Number System

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    Imagine yourself in a grocery store, grabbing and taking hold of those precious items you wish to buy. You gathered the nicest things you have thought of, and you approach the counter for check-out. The cashier then carefully takes each item one by one, and by shock finds out that the machine doesn’t work out. So, with all fervor and passion, he starts to manually determine the total cost of your grocery items— first, by counting on the fingers the price of each item, and then writing on a piece of paper the numerical cost all written entirely in words. And so you wait for almost half a day, waiting on the payment aisle just to let the cashier finish with his ingenious method of counting.

    Thanks to the current system of counting numbers, people don’t have to consume much time performing calculations using spoken language itself. Using the current counting system, the Arabic Numeral System, counting things became easier through the use of separate symbols for each value. This minimizes the inconvenience of writing digits in whole words, which hampers manual calculations. Through the use of a glyphic system in counting values, there is a memory span advantage over the use of digit words, as values are only represented with a specialized and standardized set of symbols.

    Likewise, the use of the Arabic number system over other systems (such as the Roman numerals) provides a solution in handling empty powers of ten through the use of zero, as in “1005”. This modern system of numeration is based on place value, with the same symbol, such as 7, taking on different meaning (7, 70, 700, etc.) depending on its location within the representation of the number (Smith and Karpinski).


    The current system of counting numbers based on place value numeration was actually invented by Hindu mathematicians in India, with the full system emerging by the 8th to 9th century (O’Connor and Robertson). Although the system is usually credited to the Arabs, the system actually originated from the Hindus. Persian scholars based in Hindustan studying astronomy and mathematics particularly observed the Hindus’ system of counting, utilized and flourished its use within the Arab world, then later passed on to the European world through Arab scholars in North Africa and Spain (O’Connor and Robertson). The Europeans by that time call the numerical system as “Arabic”, as Arab scholars have introduced the system.

    However, the adoption of the Hindu numeric system by the Arabs since the latter’s exposure to it did not happen simply as is. Different number systems were used concurrently in the Arabic world over a long period of time. According to O’Connor,

    “there were at least three different types of arithmetic used in Arab countries in the eleventh century: a system derived from counting on the fingers with the numerals written entirely in words, this finger-reckoning arithmetic was the system used for by the business community; the sexagesimal system with numerals denoted by letters of the Arabic alphabet; and the arithmetic of the Indian numerals and fractions with the decimal place-value system” (O’Connor and Robertson).

    Arab scholars (particularly those in Northern Africa and Spain, which were areas dominated by the Arabs until 750 AD) introduced the use of the Hindu-Arabic numeral system to the European world. One of whom was the great Arab mathematician Mohammed ibn-Musa al-Khowarizmi, who shares the title of “Father of Algebra” with Diophantus. Al-Khowarizmi wrote a book on the Hindu number system known today in a translated book “De numero indorum”, which means “On the Hindu numbers” (Smith and Karpinski). However, it is worthy to note that the first sign that Indian numerals were moving west dates in the later part of 7th century (O’Connor and Robertson). Severus Sebokht, a Nestorian bishop based in Keneshra along the Euphrates River particularly wrote in 662 AD the convenience of the Indian numeral system over the prevailing systems in the Western world (i.e., Greece, Roman Empire).

    Although the Hindu-Arabic number system was introduced to the European world by 1000 AD, the Roman numerical system was still commonly used, either in finance, commerce, universities and even in everyday computing (Smith and Karpinski). By 1100’s, a renewed interest in Arab numerals emerged among European scholars, with several versions of Al-Khowarizmi’s Algebra interpreted into Latin versions (O’Connor and Robertson).  One particular European scholar, Leonardo of Pisa, published Liber abaci in 1202 explaining and “popularizing” the Hindu-Arabic system, the use of the zero, the horizontal fraction bar, and the various algorithms of the Algebra.

    Works Cited

    O’Connor, J J and E F Robertson. The Arabic numeral system. January 2001. 2 August 2009 <>.

    Rowlett, Russ. Roman and “Arabic” Numerals. 14 March 2001. 3 August 2009 <>.

    Smith, David Eugene and Louis Charles Karpinski. The Hindu-Arabic Numerals. Boston: Ginn and Company, 1911.

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    Frequently Asked Questions

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    How does the Hindu-Arabic number system work?
    Hindu-Arabic numerals are a decimal, or base-tenbase-tenHistory of decimal fractions Decimal fractions were first developed and used by the Chinese in the end of 4th century BCE, and then spread to the Middle East and from there to Europe. The written Chinese decimal fractions were non-positional. However, counting rod fractions were positional. › wiki › DecimalDecimal - Wikipedia, 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 based on?
    The system is based upon ten (originally nine) glyphs. The symbols (glyphs) used to represent the system are in principle independent of the system itself. The glyphs in actual use are descended from Brahmi numeralsBrahmi numeralsThe Brahmi numerals are a numeral system attested from the 3rd century BCE (somewhat later in the case of most of the tens). They are the direct graphic ancestors of the modern Indian and Hindu–Arabic numerals. › wiki › Brahmi_numeralsBrahmi numerals - Wikipedia and have split into various typographical variants since the Middle Ages.
    What are the 4 characteristics of the Hindu-Arabic number system?
    1) it uses 10 digits or symbols that can be used in combination to represent all possible numbers. 2) it groups by tens. 3) it uses a place value. 4) the system is additive and multiplicative.
    What is Hindu-Arabic system example?
    Hindu-Arabic numerals are defined as a number system based on the symbols for 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0. An example of Hindu-Arabic numerals is an ancient system of counting in India.

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