The Decimal System in Mathematics
 Today even a child knows the decimal system in arithmetic, but few people know its historical significance
The invention of the decimal system by Indians was perhaps the most revolutionary and greatest scientific achievement in the ancient world, and without it, progress in science would have been extremely slow.
The numbers in the decimal system were called Arabic numerals by the Europeans, but surprisingly the Arab scholars called them Hindu numerals. Were they really Arabic or Hindu?
 In this connection it may be mentioned that the languages Urdu, Persian, Arabic and Hebrew are written from right to left, but if you ask any speaker of these languages to write any number selected at random, e.g. 257 or 1096, he will write the number from left to right. What does this show ? This shows that these numbers were taken from a language which was written from left to right and not from right to left, and it is accepted universally now that these numbers came from India, and they were copied by the Arabs from us, who then passed them over to the Europeans.
I would like to explain the revolutionary significance of the decimal system.
 As we all know, ancient Rome was a great civilization, the civilization of Caesar and Augustus, but if one would have asked an ancient Roman to write the number one million he would have almost gone crazy. This is because the ancient Romans felt very uncomfortable with numbers above 1000. And that is because the ancient Romans wrote their numbers in alphabets, I denoting 1, II denoting 2, V denoting 5, X denoting 10, L denoting 50, C denoting 100, D denoting 500, and M denoting 1000.
 In the Roman numerals there is no single alphabet denoting a number greater than  M, which stands for millenium or one thousand. So to write 2000 an ancient Roman had to write MM, to write 3000 he had to write MMM, and to write one million he had to write M one thousand times, which would have driven him crazy.
On the other hand, under our system to express one million we have just to write the number one followed by six zeros.
In the Roman numerals there is no zero. Zero was an invention of ancient India and progress was not possible without this invention.
 Here I may explain that these numbers 1,2,3, etc do not really exist in the objective universe. What exists is 1 man, 2 trees, 3 tables, 4 houses, etc. The numbers 1,2,3,4, etc are pure abstractions having no actual physical existence in the objective universe. It required a flight of imagination to conceive of numbers in the abstract. This flight was no doubt achieved by the ancient Greeks and Romans.
  But it required a further flight of imagination, to imagine the number 0, and this the ancient Europeans never achieved on their own, but could get only from Indians ( through the Arabs, as mentioned before ).
I am not going into details about the great contributions of our renowned mathematicians like Aryabhatta, Brahmagupta, Bhaskar, Varahamihira etc. One can read about it in the Google Website. Also, see books on ancient Indian mathematics, e.g. ' History of Hindu Mathematics ' by B.Datta and A. N. Singh, ' History of Science and Technology in Ancient India ' by D.P. Chattopadhyaya, etc.
Aryabhatta in his famous book called the Aryabhatiya wrote about algebra, arithmetic, trigonometry, quadratic equations and the sine table. He calculated the value of Pi at 3.1416, which is close to the actual value which is about 3.14159. Aryabhatta's works were later adopted by the Arabs and others.
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 However, I may just give two simple illustrations in this connection.

The number 1,00,000 is called a lakh in the Indian numeral system.  100 lacs is called one crore, 100 crores is called one arab, 100 arabs is called one kharab, 100 kharabs is called one neel, 100 neels is called one padma, 100 padmas is called one shankh, 100 shankh is called one mahashankh, etc. Thus one mahashankh will be the number 1  followed by 19 zeros (for further details you may see V.S. Apte's Sanskrit English Dictionary in Google). On the other hand the ancient Romans could not express any number larger than one thousand except by repeating M and the other alphabets again and again.

Take another illustration.  According to the Vishnu Purana, the Kaliyuga in which we are living consists of 4, 32, 000 years. The preceding Yuga is known as the Dwapar Yug ( in which Lord Krishna lived ), and was said to be twice as long as the Kaliyuga.   Preceding the Dwapar Yug, was the Treta Yug ( in which Lord Rama lived ), which is thrice the duration of the Kaliyuga. The Yuga preceding Treta Yug is the Satyug which was said to be four times longer than the Kaliyuga.
 One Kaliyuga, one Dwapar Yug, one Treta Yug and one Satyug are collectively known as one Chaturyugi (or 43 lacs 20 thousand years). Fifty Six Chaturyugis are known as one Manovantar. Fourteen Manovantars is known as one Kalpa.  Twelve Kalpas make one day of Brahma.  Brahma is believed to have lived for billions or trillions of years.

When Hindus do the sankalp, which is to be done everyday by orthodox people, they have to mention the exact day, month and year of the Kaliyug as well as the Chaturyugi, Manovantar and Kalpa in which we are living.   It is said that we are living today in the 28th Chaturyugi in our present Manovantar, that is to say half the Manovantar of our Kalpa is over, but the remaining Manovantar is yet to be completed.  We are living presently  in the  Vaivasvata Manuvantar.
One may or may not believe the above system, but one can only marvel at the flight of imagination of our ancestors who could conceive of billions or trillions of years in history.