Hindu-Arabic Numerals

Hindu Numerals

Hindu system is a pure place value system, that is why you need a zero. Only the Hindus within the context of Indo-European civilisations have consistently used a zero.

Our decimal system is descendent from this system.

The earliest number symbols in India

In 3000BC the Hindus culture flourished and large numbers were used (inscriptions).

From the middle of 2000BC Indo-European tribes were making their way from the N.W. towards India. They introduced Sanskrit - earliest knowledge of maths from this time.

In Sanskrit there are number words for 1-9, 10, 100 and further powers of 10 - up to 10 - definitely a decimal system.

Brahmi Numerals

Brahmi inscriptions have been found all over the subcontinent of India - date from C3BC.

HUNDREDS(place value1002x1003x100......

The existence of special symbols for the figures 1 - 9 was a typical and important characteristic of Hindu arithmetic and provided the prerequisite for the rise of the decimal place - value system.

Tens were written with individual symbols - obstacle on the way towards a consistent place value system.

From 100 onwards numbers were represented according to another principle - 2 new symbols 100 and 1000 - named place value system.

Extending Hindu system towards a place value system

What was favourable to the development of a decimal place value system in India?

The later place - Value System

The most important as well as the most widely used place - value symbols are those belonging to the Nagari script numerals 1 - 9, very similar to the Brahmi numerals.

Nagari numerals are very similar to our own.

In books about AD570 they were writing


- digits arranged in normal way zero is used, place value notation is used for the numerator and denominator of the fraction.

This system quickly came into use - probably earliest symbol for zero was a dot and not a small circle.

Hindu Numerals among the Arabs

Knowledge of the Hindu decimal system was early in reaching the West (AD662).

On its way to the West the Hindu method of writing numerals soon became known to the Arabs who had established a world empire from the 7th Century. Many mathematical books from the Greeks and Hindus were translated in Baghdad and travelled the West.

The Arabs played an essential part in the dissemination of the numeral system - no number system of their own.

Al-Khouarizmi was the first Arab to explain the Hindu system of numerals. He wrote an "Algebra" and "Arithmetic" about AD820 - These have both come down to use via Latin translations.

Al-Khouarizmi's Arithmetic is the first Arabic work in which the decimal place value system and the computing operations based on it are explained. He explained in great detail how the value of the numeral changes when it is put in another place. He was also aware of zero.

In C8 a specific Arabic alphabetical style of writing numbers emerged based on the Greek. At about the same time a place value system appeared in which the numbers were represented by the so called East Arabic numerals with a special symbol for zero. They were a modification of the Brahmi numerals - some countries use them (Egypt).

The so called West Arabic numerals are contemporary with the East Arabic numerals and likewise stem from Hindu figures and are forerunners of our Western figures.

In the West Arabic numerals one dot indicates tens, 2 dots hundreds so it is not a complete place value system.

3 6 8 = 368and3 . 8 = 308

Later the symbol for zero (0) was introduced from the East.

As a consequence of trade between the Orient and Moorish Spain the Hindu figures came to North Africa. The merchants didn't understand the place value system but later the pure place value system from East Arabia gained acceptance. All that was needed then was for the zero to join the other 9 figures and dots to disappear.

Hindu-Arabic Numerals in the West

Counting Systems and Notations

History of Mathematics Module

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These pages are maintained by M.I.Woodcock.