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Template:Table Numeral Systems

The Template:IAST numeration is a system of numerals based on Sanskrit phonemes. It was introduced in the early 6th century by [[Aryabhata|Template:IAST]], in the first chapter titled Gītika Padam of his Aryabhatiya. It attributes a numerical value to each syllable of the form consonant+vowel possible in Sanskrit phonology, from Template:IAST = 1 up to Template:IAST = 1018.

## History

The basis of this number system is mentioned in the second stanza of the first chapter of Aryabhatiya.

The Varga (Group/Class) letters Ka to Ma are to be placed in the varga (square) places (1st,100th,10000th ...etc. places) and Avarga letters like Ya, Ra , La .. have to be placed in Avarga places (10th,1000th,...etc. places).

The Varga letters 'Ka' to 'Ma' have value from 1,2,3 .. up to 25 and Avarga letters 'Ya' to 'Ha' have value 30,40,50.. up to 100.In the Varga and Avarga letters, beyond the ninth vowel (place), new symbols can be used.

The values for vowels are as follows : i= 100 ; u = 10000, ru = 1000000 and so on.

Aryabhata used this number system for representing both small and large numbers in his mathematical and astronomical calculations. This system can even be used to represent fractions and mixed fractions. For example nga is 1/5, nja is 1/10 and Jhardam (jha=9; its half) = 4½

## Example

 Example:  299,792,458 100 101 102 103 104 105 106 107 108 85, 42, 97, 99, 2 Template:Script Template:Script Template:Script Template:Script Template:Script Template:IAST Template:IAST Template:IAST Template:IAST Template:IAST

The traditional Indian digit order is reversed compared to the modern way. By consequence, ĀryabhaTemplate:IASTa began with the ones before the tens; then the hundreds and the thousands; then the myriad and the lakh (= 105) and so on. (cf. Indian numbering system)

## Numeral table

Here is the complete table:

 The   33 × 9  =  297   Sanskrit alphabetic numerical syllables Nine vowels or syllabics -Template:IPA -Template:IPA -Template:IPA -Template:IAST -Template:IAST -Template:IPA -Template:IPA -Template:IPA -Template:IPA अ इ उ ऋ ऌ ए ऐ ओ औ × 10 0 10 2 10 4 10 6 10 8 1010 1012 1014 1016 Five velar plosives Template:IPA - क 1 क Template:IPA कि Template:IPA कु Template:IPA कृ Template:IAST कॢ Template:IAST के Template:IPA कै Template:IPA को Template:IPA कौ Template:IPA Template:IPA - ख 2 ख Template:IPA खि Template:IPA खु Template:IPA खृ Template:IAST खॢ Template:IAST खे Template:IPA खै Template:IPA खो Template:IPA खौ Template:IPA Template:IPA - ग 3 ग Template:IPA गि Template:IPA गु Template:IPA गृ Template:IAST गॢ Template:IAST गे Template:IPA गै Template:IPA गो Template:IPA गौ Template:IPA Template:IPA - घ 4 घ Template:IPA घि Template:IPA घु Template:IPA घृ Template:IAST घॢ Template:IAST घे Template:IPA घै Template:IPA घो Template:IPA घौ Template:IPA Template:IAST - ङ 5 ङ Template:IAST ङि Template:IAST ङु Template:IAST ङृ Template:IAST ङॢ Template:IAST ङे Template:IAST ङै Template:IAST ङो Template:IAST ङौ Template:IAST Five palatal plosives Template:IPA - च 6 च Template:IPA चि Template:IPA चु Template:IPA चृ Template:IAST चॢ Template:IAST चे Template:IPA चै Template:IPA चो Template:IPA चौ Template:IPA Template:IPA - छ 7 छ Template:IPA छि Template:IPA छु Template:IPA छृ Template:IAST छॢ Template:IAST छे Template:IPA छै Template:IPA छो Template:IPA छौ Template:IPA Template:IPA - ज 8 ज Template:IPA जि Template:IPA जु Template:IPA जृ Template:IAST जॢ Template:IAST जे Template:IPA जै Template:IPA जो Template:IPA जौ Template:IPA Template:IPA - झ 9 झ Template:IPA झि Template:IPA झु Template:IPA झृ Template:IAST झॢ Template:IAST झे Template:IPA झै Template:IPA झो Template:IPA झौ Template:IPA Template:IPA - ञ 10 ञ Template:IPA ञि Template:IPA ञु Template:IPA ञृ Template:IAST ञॢ Template:IAST ञे Template:IPA ञै Template:IPA ञो Template:IPA ञौ Template:IPA Five retroflex plosives Template:IAST - ट 11 ट Template:IAST टि Template:IAST टु Template:IAST टृ Template:IAST टॢ Template:IAST टे Template:IAST टै Template:IAST टो Template:IAST टौ Template:IAST Template:IAST - ठ 12 ठ Template:IAST ठि Template:IAST ठु Template:IAST ठृ Template:IAST ठॢ Template:IAST ठे Template:IAST ठै Template:IAST ठो Template:IAST ठौ Template:IAST Template:IAST - ड 13 ड Template:IAST डि Template:IAST डु Template:IAST डृ Template:IAST डॢ Template:IAST डे Template:IAST डै Template:IAST डो Template:IAST डौ Template:IAST Template:IAST - ढ 14 ढ Template:IAST ढि Template:IAST ढु Template:IAST ढृ Template:IAST ढॢ Template:IAST ढे Template:IAST ढै Template:IAST ढो Template:IAST ढौ Template:IAST Template:IAST - ण 15 ण Template:IAST णि Template:IAST णु Template:IAST णृ Template:IAST णॢ Template:IAST णे Template:IAST णै Template:IAST णो Template:IAST णौ Template:IAST Five dental plosives Template:IPA - त 16 त Template:IPA ति Template:IPA तु Template:IPA तृ Template:IAST तॢ Template:IAST ते Template:IPA तै Template:IPA तो Template:IPA तौ Template:IPA Template:IPA - थ 17 थ Template:IPA थि Template:IPA थु Template:IPA थृ Template:IAST थॢ Template:IAST थे Template:IPA थै Template:IPA थो Template:IPA थौ Template:IPA Template:IPA - द 18 द Template:IPA दि Template:IPA दु Template:IPA दृ Template:IAST दॢ Template:IAST दे Template:IPA दै Template:IPA दो Template:IPA दौ Template:IPA Template:IPA - ध 19 ध Template:IPA धि Template:IPA धु Template:IPA धृ Template:IAST धॢ Template:IAST धे Template:IPA धै Template:IPA धो Template:IPA धौ Template:IPA Template:IPA - न 20 न Template:IPA नि Template:IPA नु Template:IPA नृ Template:IAST नॢ Template:IAST ने Template:IPA नै Template:IPA नो Template:IPA नौ Template:IPA Five labial plosives Template:IPA - प 21 प Template:IPA पि Template:IPA पु Template:IPA पृ Template:IAST पॢ Template:IAST पे Template:IPA पै Template:IPA पो Template:IPA पौ Template:IPA Template:IPA - फ 22 फ Template:IPA फि Template:IPA फु Template:IPA फृ Template:IAST फॢ Template:IAST फे Template:IPA फै Template:IPA फो Template:IPA फौ Template:IPA Template:IPA - ब 23 ब Template:IPA बि Template:IPA बु Template:IPA बृ Template:IAST बॢ Template:IAST बे Template:IPA बै Template:IPA बो Template:IPA बौ Template:IPA Template:IPA - भ 24 भ Template:IPA भि Template:IPA भु Template:IPA भृ Template:IAST भॢ Template:IAST भे Template:IPA भै Template:IPA भो Template:IPA भौ Template:IPA Template:IPA - म 25 म Template:IPA मि Template:IPA मु Template:IPA मृ Template:IAST मॢ Template:IAST मे Template:IPA मै Template:IPA मो Template:IPA मौ Template:IPA Four approximants or trill Template:IPA - य 30 य Template:IPA यि Template:IPA यु Template:IPA यृ Template:IAST यॢ Template:IAST ये Template:IPA यै Template:IPA यो Template:IPA यौ Template:IPA Template:IPA - र 40 र Template:IPA रि Template:IPA रु Template:IPA रृ Template:IAST रॢ Template:IAST रे Template:IPA रै Template:IPA रो Template:IPA रौ Template:IPA Template:IPA - ल 50 ल Template:IPA लि Template:IPA लु Template:IPA लृ Template:IAST लॢ Template:IAST ले Template:IPA लै Template:IPA लो Template:IPA लौ Template:IPA Template:IPA - व 60 व Template:IPA वि Template:IPA वु Template:IPA वृ Template:IAST वॢ Template:IAST वे Template:IPA वै Template:IPA वो Template:IPA वौ Template:IPA Three coronal fricatives Template:IPA - श 70 श Template:IPA शि Template:IPA शु Template:IPA शृ Template:IAST शॢ Template:IAST शे Template:IPA शै Template:IPA शो Template:IPA शौ Template:IPA Template:IAST - ष 80 ष Template:IAST षि Template:IAST षु Template:IAST षृ Template:IAST षॢ Template:IAST षे Template:IAST षै Template:IAST षो Template:IAST षौ Template:IAST Template:IPA - स 90 स Template:IPA सि Template:IPA सु Template:IPA सृ Template:IAST सॢ Template:IAST से Template:IPA सै Template:IPA सो Template:IPA सौ Template:IPA One glottal fricative Template:IPA - ह 100 ह Template:IPA हि Template:IPA हु Template:IPA हृ Template:IAST हॢ Template:IAST हे Template:IPA है Template:IPA हो Template:IPA हौ Template:IPA

## See also

• Bhutasamkhya system
• Katapayadi system

## References

• Kurt Elfering: Die Mathematik des Aryabhata I. Text, Übersetzung aus dem Sanskrit und Kommentar. Wilhelm Fink Verlag, München, 1975, ISBN 3-7705-1326-6
• Georges Ifrah: The Universal History of Numbers. From Prehistory to the Invention of the Computer. John Wiley & Sons, New York, 2000, ISBN 0-471-39340-1.
• B. L. van der Waerden: Erwachende Wissenschaft. Ägyptische, babylonische und griechische Mathematik. Birkhäuser-Verlag, Basel Stuttgart, 1966, ISBN 3-764-30399-9
• Template:Cite journal
• Template:Cite jstor

de:Aryabhata-Code hi:आर्यभट्ट की संख्यापद्धति nds:Aryabhata-Tallen pt:Numeração Āryabhaṭa

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