View source for 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?  

{{Infobox person
| name               = Indian Number System
| image              = 100 Number Square.svg
}}

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 ==
[[File:Numerals.jpg|alt=Numerals - Sanskrit|thumb|Numerals - Sanskrit]]
India has a very ancient history dating back to thousands of years<ref>{{Cite book|last=|title=A Primer to Bhāratīya Gaṇitam , Bhāratīya-Gaṇita-Praveśa- Part-1|publisher=Samskrit Promotion Foundation|year=2021|isbn=978-81-951757-2-7}}</ref>. In those days Samskrit was commonly used. 
{| class="wikitable"
|+
!Numbers
!Sanskrit Name
!Numbers
!Sanskrit Name
|-
|1
|ekam 
|10+1 = 11
|ekādaśa 
|-
|2
|dve 
|10+5 = 15
|pañcadaśa 
|-
|3
|trīṇi 
|10+10 =20
|viṃśatiḥ 
|-
|4
|catvāri 
|50
|pañcāśat 
|-
|5
|pañca 
|100
|śatam
|-
|6
|ṣaṭ 
|
|
|-
|7
|sapta 
|
|
|-
|8
|aṣṭa 
|
|
|-
|9
|nava 
|
|
|-
|10
|daśa
|
|
|}
The Greeks, Romans, Persians, and Arabs had apparently no terminology for denominations above the thousand or at most the ''myriad'' (10<sup>4</sup>). In India there were eighteen specific denominations (10<sup>18</sup> ).<ref>{{Cite book|title=JAWAHARLAL  NEHRU ,  The Discovery of India|publisher=Oxford University Press|location=New Delhi|pages=116}}</ref>

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<ref>{{Cite book|last= Datta|first=Bibhutibhusan|title=History of Hindu Mathematics|last2=Narayan Singh|first2=Avadhesh|publisher=Asia Publishing House|year=1962|location=Mumbai}}</ref> . 

== Decimal Place Value System ==
[[File:Values of digits in the Decimal numeral system.svg|alt=Decimal Place Value System|thumb|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
{| class="wikitable"
|+
|5
|6
|7
|-
|↑
|↑
|↑
|-
|Hundreds
|Tens
|Units
|}
[[Aryabhata|Āryabhaṭa I]] (499) says on  the names of the position as "Eka (10<sup>0</sup> unit),  daśa ( 10<sup>1</sup> ten), śata (10<sup>2</sup>  hundred), sahasra (10<sup>3</sup>  thousand), ayuta (10<sup>4</sup> ten thousand), niyuta (10<sup>5</sup> hundred thousand), prayuta ( 10<sup>6</sup> million), koṭi (10<sup>7</sup> ten million), arbuda (10<sup>8</sup>  hundred million) and vṛnda ( 10<sup>9</sup> thousand million) are respectively from place to place each ten times the preceding".

[[Sridhara|Śrīdhara]] (750) has given the following names : Eka (10<sup>0</sup> Unit), daśa (10<sup>1</sup> ten), śata (10<sup>2</sup> hundred), sahasra (10<sup>3</sup> thousand), ayuta (10<sup>4</sup> ten thousand), lakṣa (10<sup>5</sup> lakh), prayuta (10<sup>6</sup> ten lakhs), koṭi (10<sup>7</sup> crore), arbuda (10<sup>8</sup> ten crore), abja (10<sup>9</sup> hundred crore),                        kharva (10<sup>10</sup> thousand crore), nikharva (10<sup>11</sup> ten thousand crore), mahāsaroja (10<sup>12</sup> one lakh crore) , Śaṅkhu (10<sup>13</sup> ten lakh crore),Saritā-pati (10<sup>14</sup>  crore of crore) , antya (10<sup>15</sup> ten crores of crore), madhya (10<sup>16</sup> hundred crores of crore), parārdha (10<sup>17</sup> thousand crores of crore).

[[Mahavira|Mahāvīra]] (850) gives twenty-four notational places: Eka (10<sup>0</sup> Unit), daśa (10<sup>1</sup> ten), śata (10<sup>2</sup> hundred), sahasra (10<sup>3</sup> thousand), daśa-sahasra (10<sup>4</sup> ten thousand), lakṣa (10<sup>5</sup> lakh),  daśa-lakṣa (10<sup>6</sup> ten lakhs), koṭi (10<sup>7</sup> crore),daśa-koṭi (10<sup>8</sup> ten crore), śata-koṭi (10<sup>9</sup> hundred crore), arbuda (10<sup>10</sup> thousand crore), nyarbuda (10<sup>11</sup> ten thousand crore), kharva  (10<sup>12</sup> one lakh crore) , mahākharva  (10<sup>13</sup> ten lakh crore), padma (10<sup>14</sup>  crore of crore) , mahā-padma(10<sup>15</sup> ten crores of crore), kṣoṇi (10<sup>16</sup> hundred crores of crore), mahā-kṣoṇi (10<sup>17</sup> thousand crores of crore), śaṅka (10<sup>18</sup>), mahā-śaṅka (10<sup>19</sup>), kṣiti (10<sup>20</sup>), mahā-kṣiti (10<sup>21</sup>), kṣobha (10<sup>22</sup>), mahā-kṣobha (10<sup>23</sup>).

== 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.<ref>{{Cite web|title=Valmiki Ramayana - Yuddha Kanda, Chapter (Sarga) 28,(Verses 33 – 38)|url=http://valmikiramayan.pcriot.com/utf8/yuddha/sarga28/yuddha_28_frame.htm}}</ref>
{| class="wikitable"
|+
!Name
!Indian Notation
!Power 
Notation
!Indian System
|-
|एक (''eka'')
|<small>1</small>
|10<sup>0</sup>
|One
|-
|दश (''daśa'')
|<small>10</small>
|10<sup>1</sup>
|Ten
|-
|शत (''śata'')
|<small>100</small>
|10<sup>2</sup>
|One hundred
|-
|सहस्र (''sahasra'')
|<small>1,000</small>
|10<sup>3</sup>
|One thousand
|-
|लक्ष (''lakṣa'')
|<small>1,00,000</small>
|10<sup>5</sup>
|One lakh
|-
|कोटि (''koṭi'')
|<small>1,00,000 ''śata''</small>
|10<sup>7</sup>
|One crore
|-
|शङ्कु (''śaṅku'')
|<small>1,00,000 ''koṭi''</small>
|10<sup>12</sup>
|One lakh crore
|-
|महाशङ्कु (''mahāśaṅku'')
|<small>1,00,000 ''śaṅku''</small>
|10<sup>17</sup>
|One thousand crore crore
|-
|वृन्द (''vr̥nda'')
|<small>1,00,000 ''mahāśaṅku''</small>
|10<sup>22</sup>
|
|-
|महावृन्द (''mahāvr̥nda'')
|<small>1,00,000 ''vr̥nda''</small>
|10<sup>27</sup>
|
|-
|पद्म (''padma'')
|<small>1,00,000 ''mahāvr̥nda''</small>
|10<sup>32</sup>
|
|-
|महापद्म (''mahāpadma'')
|<small>1,00,000 ''padma''</small>
|10<sup>37</sup>
|
|-
|खर्व (''kharva'')
|<small>1,00,000 ''mahāpadma''</small>
|10<sup>42</sup>
|
|-
|महाखर्व (''mahākharva'')
|<small>1,00,000 ''kharva''</small>
|10<sup>47</sup>
|
|-
|समुद्र (''samudra'')
|<small>1,00,000 ''mahākharva''</small>
|10<sup>52</sup>
|
|-
|ओघ (''ogha'')
|<small>1,00,000 ''samudra''</small>
|10<sup>57</sup>
|
|-
|महौघ (''mahaugha'')
|<small>1,00,000 ''ogha''</small>
|10<sup>62</sup>
|
|}

== See Also ==
[[भारतीय संख्या प्रणाली]]

== External Links ==

* [https://www.cuemath.com/numbers/decimal-number-system/ Decimal Number System]
* [https://www.isical.ac.in/~amartya/decimalsystem_springeronline%20(1).pdf Indian Numerals]

== References ==
[[Category:Mathematics]]
<references />
[[Category:Organic Articles English]]
[[Category:Vigyan Ready]]