Indian Number System

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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?

Indian Number System
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

Numerals - Sanskrit
Numerals - Sanskrit

India has a very ancient history dating back to thousands of years[1]. In those days Samskrit was commonly used.

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 (104). In India there were eighteen specific denominations (1018 ).[2]

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[3] .

Decimal Place Value System

Decimal Place Value System
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

5 6 7
Hundreds Tens Units

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.[4]

Name Indian Notation Power

Notation

Indian System
एक (eka) 1 100 One
दश (daśa) 10 101 Ten
शत (śata) 100 102 One hundred
सहस्र (sahasra) 1,000 103 One thousand
लक्ष (lakṣa) 1,00,000 105 One lakh
कोटि (koṭi) 1,00,000 śata 107 One crore
शङ्कु (śaṅku) 1,00,000 koṭi 1012 One lakh crore
महाशङ्कु (mahāśaṅku) 1,00,000 śaṅku 1017 One thousand crore crore
वृन्द (vr̥nda) 1,00,000 mahāśaṅku 1022
महावृन्द (mahāvr̥nda) 1,00,000 vr̥nda 1027
पद्म (padma) 1,00,000 mahāvr̥nda 1032
महापद्म (mahāpadma) 1,00,000 padma 1037
खर्व (kharva) 1,00,000 mahāpadma 1042
महाखर्व (mahākharva) 1,00,000 kharva 1047
समुद्र (samudra) 1,00,000 mahākharva 1052
ओघ (ogha) 1,00,000 samudra 1057
महौघ (mahaugha) 1,00,000 ogha 1062

See Also

भारतीय संख्या प्रणाली

External Links

References

  1. A Primer to Bhāratīya Gaṇitam , Bhāratīya-Gaṇita-Praveśa- Part-1. Samskrit Promotion Foundation. 2021. ISBN 978-81-951757-2-7.
  2. JAWAHARLAL NEHRU , The Discovery of India. New Delhi: Oxford University Press. p. 116.
  3. Datta, Bibhutibhusan; Narayan Singh, Avadhesh (1962). History of Hindu Mathematics. Mumbai: Asia Publishing House.
  4. "Valmiki Ramayana - Yuddha Kanda, Chapter (Sarga) 28,(Verses 33 – 38)".