Indian Number System

Introduction
Numbers are essential in our life. Counting with numbers is required in our day to day transactions. What is the population of our country?

How many members are affected with the pandemic? What is the temperature in the city ? What is the distance between two cities ? What is the cost of the daily essentials ? These are the questions coming as part of our life. Answers to these questions will be in numbers only.

Let us see what these numbers are and how did they originate?

Counting starts from the number One. Zero is a number which precedes number One. The Numbers from 0 to 9 which we use for counting have an interesting history.

The Indian Numerals
India has a very ancient history dating back to thousands of years. In those days Samskrit was commonly used. The Greeks, Romans, Persians, and Arabs had apparently no terminology for denominations above the thousand or at most the myriad (104). In India there were eighteen specific denominations (1018 ).

In modern times also, the numeral language of no other nation is as scientific and perfect as that of the Hindus.

In the Yajurveda Saṃhitā (Vājasaneyi) the following list of numeral 'denominations is given: Eka (1), daśa (10), śata (100), sahasra (1000), ayuta (10,000), niyuta (100,000), prayuta (1,000,000), arbuda (10,000,000), nyarbuda (100,000,000), samudra (1,000,000,000), madhya (10,000,000,000), anta (100,000,000,000), parārdha (1,000,000,000,000). The same list occurs at two places in the Taittirīya Saṃhitā.

Decimal Place Value System
Āryabhaṭa uses the phrase ' स्थानात् स्थानं दशगुणं स्यात् ' to explain the place value system. This means "the number from place to place is ten times the preceding one." To understand the place value system, the digits when placed from right to left occupy a certain position. Starting from right, the first digit will occupy the first position, the second digit will occupy the second position, the third digit will occupy the third position and so on. From the second position onwards the value of each place increases by ten. Hence every digit placed one place away from right side has its value increased by ten times. Since the value of the digits increases by ten, it is called the 'decimal' place value system.

For example consider the number 567 which is equal to 500 + 60 +7 = 5 X 100 + 6 X 10 + 7 X 1 Āryabhaṭa I (499) says on the names of the position as "Eka (100 unit),  daśa ( 101 ten), śata (102  hundred), sahasra (103  thousand), ayuta (104 ten thousand), niyuta (105 hundred thousand), prayuta ( 106 million), koṭi (107 ten million), arbuda (108  hundred million) and vṛnda ( 109 thousand million) are respectively from place to place each ten times the preceding".

Śrīdhara (750) has given the following names : Eka (100 Unit), daśa (101 ten), śata (102 hundred), sahasra (103 thousand), ayuta (104 ten thousand), lakṣa (105 lakh), prayuta (106 ten lakhs), koṭi (107 crore), arbuda (108 ten crore), abja (109 hundred crore),                       kharva (1010 thousand crore), nikharva (1011 ten thousand crore), mahāsaroja (1012 one lakh crore), Śaṅkhu (1013 ten lakh crore),Saritā-pati (1014  crore of crore) , antya (1015 ten crores of crore), madhya (1016 hundred crores of crore), parārdha (1017 thousand crores of crore).

Mahāvīra (850) gives twenty-four notational places: Eka (100 Unit), daśa (101 ten), śata (102 hundred), sahasra (103 thousand), daśa-sahasra (104 ten thousand), lakṣa (105 lakh), daśa-lakṣa (106 ten lakhs), koṭi (107 crore),daśa-koṭi (108 ten crore), śata-koṭi (109 hundred crore), arbuda (1010 thousand crore), nyarbuda (1011 ten thousand crore), kharva  (1012 one lakh crore), mahākharva  (1013 ten lakh crore), padma (1014  crore of crore) , mahā-padma(1015 ten crores of crore), kṣoṇi (1016 hundred crores of crore), mahā-kṣoṇi (1017 thousand crores of crore), śaṅka (1018), mahā-śaṅka (1019), kṣiti (1020), mahā-kṣiti (1021), kṣobha (1022), mahā-kṣobha (1023).

Numbering systems in Hindu epics
There are various systems of numeration found in various ancient epic literature of India (itihasas). The following table gives one such system used in the Valmiki Ramayana.