History of Hindu-Arabic Numbers
Zero to Nine
Our Number System
When we study mathematics, we do not often stop to think about our number system.
Where did it come from? How is it different from other number systems, past and present?
The number system we use was invented by the Hindus, and became known to the rest of the world through the Arabs. You may have read about the prophet Mohammed, the founder of the religion Islam. Mohammed lived in Arabia (now called Saudi Arabia). When he died in A.D. 632, he was succeeded by leaders called caliphs. The caliphs sent Arab horsemen out from Arabia in all directions, to invade lands and spread Islam. At the beginning of the eight century, Arab invaders came as far as north-west India. There they came in contact with Hindus, and learned many things from them. Among the things they learned was Hindu number system. When they went back to Arabia, they told their caliph, Harun-al-Rashid, what they had learnt. He was very interested, and he ordered Hindu mathematical books to be translated into Arabic. Later, the books were translated from Arabic into European languages. The Hindu number system is now widely used all over the world, because it is such a good one. Because the Arabs helped to spread it to the rest of the world, it is called the Hindu-Arabic System.
The Hindus decided on a different symbol for each number from one to nine. They numbers a place value, putting single numbers on the right, 10’s one place to the left, 100’s two places to the left, 1000’s three places to the left, etc. so 1888 could be written in only four numerals. Isn’t this easier than Egyptian and Roman systems?
One of the most important inventions of the Hindus in mathematics was the invention of zero. Zero allows us to leave an empty column when we write a number. If there were no zero, we couldn’t distinguish between 123, 1023, 1203, 1230 or 123,000,000. Zero keeps numbers in their places.
In our number system, we use ten as base. A number in one column has ten times the value of the same number in the next column to the right.
Why do you think we use ten as a base? This dictionary definition of the word ‘digit’ may help to explain:
Digit: a finger or toe, a figure used in arithmetic to represent a number. (Latin digitus, finger, toe)
If we all had twelve fingers and toes, the base would probably have been twelve. We naturally use our fingers for counting. The people of an American Indian tribes in California count in fours, because they count the spaces between their fingers instead of fingers themselves, but most people count their fingers.
It is very useful to have a base for counting. Using only the figures 0 to 9, and arranging them in different ways, we can write any possible number. Imagine how difficult it would be if there a different word or figure for every number up to a hundred.
This is the word for ninety-nine in the African Basuto language:
machoumearobilengmonoolemongametsoarobilengmonoolemong
Which is easier, that or 99?
A number system which uses ten as a base is called a decimal system.
A system which uses twenty (fingers and toes) as a base is called a vigesimal system.
In Dzongkha, both the decimal and vigesimal systems are used.
Primitive people, who did not have many possessions, or who did not have to make big calculations, did not need a developed number system. Some primitive tribes only used the number one and two. Here, for example, is the method of counting of one of the Papuan languages in the area of the Torres Straits between Papua New Guinea and Australia:
1 urapun
2 okosa
3 okosa urapun
4 okosa okosa
5 okosa okosa urapun
6 okosa okosa okosa
Any number above six is called simply called ‘a lot’.
This system is called a binary system, because it is based on two. A binary system is also used in modern computers.
As we have seen, the reason why ten is the base of our number system is probably because we have ten fingers. We often use our fingers as an aid to counting.
What aids can we use? Again, a dictionary definition of a word gives us a clue:
Calculate: to count; to think mathematically. (Latin calculare, to count with the help of little stones. Calculus, a small stone).
There are millions of numbers. So many to spare,
That if you could count every insect in air,
The moth, the mosquito, the bees and the gnat,
There still would be even more numbers than that!
There’s no end to numbers! But don’t be afraid!
There only are ten out of which they are made.
Learn from zero to nine, and the rest will come pat,
For the numbers of numbers all come out of that!
Eleanor Farjeon
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