Notational Places in Pāṭīgaṇitam: Difference between revisions

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[[Category:Mathematics in Pāṭīgaṇitam]]
[[Category:Mathematics in Pāṭīgaṇitam]]
[[Category:General]]
[[Category:General]]
==Introduction==
Here we will know the names used to denote the place value of digits as mentioned in Pāṭīgaṇitam.
Here we will know the names used to denote the place value of digits as mentioned in Pāṭīgaṇitam.
==Verse==
==Verse==
एकं दश शतमस्मात्सहस्रमयुतं ततः परं लक्षम् ।
एकं दश शतमस्मात्सहस्रमयुतं ततः परं लक्षम् ।

Latest revision as of 14:00, 1 September 2023

Here we will know the names used to denote the place value of digits as mentioned in Pāṭīgaṇitam.

Verse

एकं दश शतमस्मात्सहस्रमयुतं ततः परं लक्षम् ।

प्रयुतं कोटिमथार्बुदमब्ज खर्वं निखर्वं च ॥ ७ ॥

तस्मान् महासरोजं शङ्कुं सरितां पतिं ततस्त्वन्त्यम् ।

मध्यं परार्द्धमाहुर्यथोत्तरं दशगुणं तज्ज्ञाः ॥ ८ ॥

Translation

ekam , daśa , śatam , sahasram , ayutam , lakṣam , prayutam, koṭiḥ, arbudam , abjam , kharvaḥ, nikharvaḥ , mahāsarojam , śaṅku , saritapati , antyam , madhyam and parārdham are each stated to be ten times the preceding by those who have a knowledge of them.[1]

Name Indian Notation Power

Notation

Indian System
एकम् (ekam) 1 100 One
दश (daśa) 10 101 Ten
शतम् (śatam) 100 102 One hundred
सहस्रम् (sahasram) 1,000 103 One thousand
अयुतम् (ayutam) 10,000 104 Ten thousand
लक्षम् (lakṣam) 1,00,000 105 One Lakh
प्रयुतम् (prayutam) 10 lakṣam 106 Ten Lakhs
कोटिः (koṭiḥ) 10 prayutam 107 One crore
अर्बुदम् (arbudam) 10 koṭiḥ 108 Ten crore
अब्जम् (abjam) 10 arbudam 109 Hundred crore
खर्वः (kharvaḥ) 10 abjam 1010 Thousand crore
निखर्वः (nikharvaḥ) 10 kharvaḥ 1011 Ten thousand crore
महासरोजम् (mahāsarojam ) 10 nikharvaḥ 1012 One lakh crore
शङ्क़ुः (śaṅkuḥ) 10 mahāsarojam 1013 Ten lakh crore
सरिता-पति (sarita-pati) 10 śaṅkuḥ 1014 Crore of crore
अन्त्यम् (antyam) 10 sarita-pati 1015 Ten crores of crore
मध्यम् (madhyam) 10 antyam 1016 Hundred crores of crore
परार्द्धम् (parārdham) 10 madhyam 1017 Thousand crores of crore

Here each number is 10 times the previous number. daśa is 10 times of ekam. śatam is 10 times of daśa. sahasram is 10 times of śatam etc.

See Also

पाटीगणितम् में 'सांकेतिक स्थान'

References

  1. Shukla, Kripa Shankar (1959). The Pāṭīgaṇita of Śrīdharācārya. Lucknow: Lucknow University. p. 2.