Indian Number System - Revision history

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	== References ==		== References ==

			<references />

			[[Category:Articles using infobox templates with no data rows]]
			[[Category:Articles with hCards]]
	[[Category:Mathematics]]		[[Category:Mathematics]]
	~~<references />~~
	[[Category:Organic Articles English]]		[[Category:Organic Articles English]]
	~~[[Category:Vigyan Ready]]~~

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

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	== Numbering systems in Hindu epics ==		== 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.		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"		{\| class="wikitable"
	\|+		\|+
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	!Indian System		!Indian System
	\|-		\|-
	\|एक (''~~ēka~~'')		\|एक (''eka'')
	\|<small>1</small>		\|<small>1</small>
	\|10<sup>0</sup>		\|10<sup>0</sup>
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	\|One lakh		\|One lakh
	\|-		\|-
	\|कोटि (''~~kōṭi~~'')		\|कोटि (''koṭi'')
	\|<small>1,00,000 ''śata''</small>		\|<small>1,00,000 ''śata''</small>
	\|10<sup>7</sup>		\|10<sup>7</sup>
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	\|<small>1,00,000 ''koṭi''</small>		\|<small>1,00,000 ''koṭi''</small>
	\|10<sup>12</sup>		\|10<sup>12</sup>
	\|~~Ten kharab or~~ One lakh crore		\|One lakh crore
	\|-		\|-
	\|महाशङ्कु (''mahāśaṅku'')		\|महाशङ्कु (''mahāśaṅku'')
	\|<small>1,00,000 ''śaṅku''</small>		\|<small>1,00,000 ''śaṅku''</small>
	\|10<sup>17</sup>		\|10<sup>17</sup>
	\|~~One shankh or~~ One thousand crore crore		\|One thousand crore crore
	\|-		\|-
	\|वृन्द (''vr̥nda'')		\|वृन्द (''vr̥nda'')

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 |10<sup>2</sup>
 |One hundred
 |}

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	[[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>).		[[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.
			{\| class="wikitable"
			\|+
			!Name
			!Indian Notation
			!Power
			Notation
			!Indian System
			\|-
			\|एक (''ēka'')
			\|<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
			\|}

	== See Also ==		== See Also ==

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	\|		\|
	\|}		\|}
	~~While the~~ Greeks had no terminology for denominations above the ''myriad'' (10<sup>4</sup>) ~~and the Romans above the ''mille''~~ (10<sup>3</sup>) ~~, the ancient Hindus dealt freely with no less than eighteen denominations~~<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>~~. In modern times also, the numeral language of no other nation is as scientific and perfect as that of the Hindus.~~		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 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 .		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 ==		== Decimal Place Value System ==

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	== Introduction ==		== 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?		[[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		{{Infobox person
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	While the Greeks had no terminology for denominations above the ''myriad'' (10<sup>4</sup>) and the Romans above the ''mille'' (10<sup>3</sup>) , the ancient Hindus dealt freely with no less than eighteen denominations<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>. In modern times also, the numeral language of no other nation is as scientific and perfect as that of the Hindus.		While the Greeks had no terminology for denominations above the ''myriad'' (10<sup>4</sup>) and the Romans above the ''mille'' (10<sup>3</sup>) , the ancient Hindus dealt freely with no less than eighteen denominations<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>. 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 .		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 ==		== Decimal Place Value System ==

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	[[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".		[[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".

	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).		[[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>).		[[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>).

alpha>Ramamurthy S: /* The Indian Numerals */

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The Indian Numerals

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	While the Greeks had no terminology for denominations above the ''myriad'' (10<sup>4</sup>) and the Romans above the ''mille'' (10<sup>3</sup>) , the ancient Hindus dealt freely with no less than eighteen denominations<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>. In modern times also, the numeral language of no other nation is as scientific and perfect as that of the Hindus.		While the Greeks had no terminology for denominations above the ''myriad'' (10<sup>4</sup>) and the Romans above the ''mille'' (10<sup>3</sup>) , the ancient Hindus dealt freely with no less than eighteen denominations<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>. In modern times also, the numeral language of no other nation is as scientific and perfect as that of the Hindus.

	In the ~~Yaurveda~~ 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 .		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 ==		== Decimal Place Value System ==