Indian Numbering System
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Indian Numbering System

The Indian numbering system is used in the Indian subcontinent (Bangladesh, Bhutan, India, Maldives, Nepal, and Pakistan) to express large numbers. The terms lakh (100,000) and crore (10,000,000)[1] are the most commonly used terms (even in English, such as in a local variety called Indian English) to express large numbers in the system.

System

The Indian numbering system corresponds to the Western system for the zeroth through fourth powers of ten: one (100), ten (101), one hundred (102), one thousand (103), ten thousand (104). For higher powers of ten, the names no longer correspond. In the Indian system, the next powers of ten are called one lakh, ten lakh, one crore, ten crore, one arab (or one hundred crore), and so on; there are new words for every second power of ten (105 + 2n): lakh (105), crore (107), arab (109), etc. In the Western system, the next powers of ten are called one hundred thousand, one million, ten million, one hundred million, one billion (short scale)/one thousand million (long scale), and so on; in the short scale, there are new words for every third power of ten (103n): million (106), billion (109), trillion (1012), etc.

Written numbers differ in the placement of commas, grouping digits into powers of one hundred (102) in the Indian system (except for the first thousand), and into powers of one thousand (103) in the Western system. The Indian and most English systems both use the decimal point and the comma digit-separator, while some other languages and countries using the Western numbering system use the decimal comma and the thin space or point to group digits.[2]

There are terms for numbers larger than 1 crore as well, but these are not commonly used and are unfamiliar to most.[] These include 1 arab (equal to 100 crore or 1 billion (short scale)), 1 kharab (equal to 100 arab or 100 billion (short scale)), 1 nil (sometimes incorrectly transliterated as neel; equal to 100 kharab or 10 trillion), 1 padma (equal to 100 nil or 1 quadrillion), 1 shankh (equal to 100 padma or 100 quadrillion), and 1 mahashankh (equal to 100 shankh or 10 quintillion). In common parlance, the thousand, lakh, and crore terminology (though inconsistent) repeats for larger numbers: thus 1,000,000,000,000 (one trillion) becomes 1 lakh crore, written as 10,00,00,00,00,000.

Examples

150,000 rupees in India is referred to as "1.5 lakh rupees", which is written as 1,50,000 rupees; 30,000,000 (thirty million) rupees is referred to as "3 crore rupees", which is written as 3,00,00,000 rupees with commas at the thousand, lakh, and crore places.

Use of separators

The Indian numbering system uses separators differently from the international norm. Instead of grouping digits by threes as in the international system, the Indian numbering system groups the rightmost three digits together (until the hundreds place), and thereafter groups by sets of two digits.[3] One trillion would thus be written as 10,00,00,00,00,000 or 10 kharab (or one lakh crore). This makes the number convenient to read using the system's terminology. For example:

Indian system Indian system (words) International system International system (words)
5,00,000 Five lakh
500,000 Five hundred thousand
12,34,56,789 Twelve crore thirty-four lakh fifty-six thousand seven hundred and eighty-nine 123,456,789 One hundred and twenty-three million four hundred and fifty-six thousand seven hundred and eighty-nine
17,00,00,00,000 Seventeen arab 17,000,000,000 Seventeen billion (short scale)
6,78,90,00,00,00,00,000 Six padma seventy-eight nil ninety kharab 6,789,000,000,000,000 Six quadrillion seven hundred and eighty nine trillion

This accords with the Indian numbering system, which has units for thousands, hundreds of thousands, tens of millions, etc.

Names of numbers

The table below follows the short scale usage of one billion being one thousand million. In India, Bangladesh and Pakistan, following former British usage, the long scale was used, with one billion equivalent to one million million.

Names of numbers
Hindustani Marathi Bengali Odia Tamil Telugu Kannada Malayalam Nepali Indian notation Power
notation
International notation[4] Short scale Western
(long scale Western)
South Asian English
/
(?k)

(?k)

(êk)

(eka)

(ou)
?
(oka?i)
?
(ondu)

(onn)

(?k)
1 100 1 One
One
/
(das)

(dah?)

(dô?)

(dasa)

(pattu)

(padi)

(hattu)

(patt)

(da?)
10 101 10 Ten
SI prefix: deca-
Ten
/
(sau)
?
(?ambhar)

(êk)

(sahe)
?
(nu)
/?
(vanda/n?ru)
?
(n?ru)
?
(nu?)

(saya)
100 102 100 One hundred
SI prefix: hecto-
One hundred
/ ?
(haz?r)
?
(?k haj?r)

(h?z?r)
?
(haj?ra)

(sahasra)

(?yiram)

(veyyi)

(s?vira)

(?yira?)
?
(?k haj?r)
1,000 103 1,000 One thousand
SI prefix: kilo-
One thousand
/ ?
(das haz?r)
?
(dah? haj?r)

(dô? h?z?r)
?
(?jut)
?
(dasa haj?ra)
?
(ayuta)
?
(patt?yiram)

(?yutam)
?
(padi v?lu)

(hattu s?vira)

(patin?yira?)
?
(da? haj?r)
10,000 104 10,000 Ten thousand
Ten thousand
/ ?
(l?kh)

(?k l?kh)
?
(lôkkh?)

(l?kh)
?
(lakhya)
?
(ila?cam)
?
(niyutam)
?
(lak?a)
?
(lak?a)

(lak?a?)

(?k l?kh)
1,00,000 105 100,000 One hundred thousand
One lakh (sometimes transliterated as lac)
/ ?
(das l?kh)

(dah? l?kh)

(dô? l?kh)

(nijut)
?
(da?a lakhya)

(niyuta)
?
(pattu ila?cam)

(padi lak?alu)
?
(hattu lak?a)
?
(pattulak?a?)

(da? l?kh)
10,00,000 106 1,000,000 One million
SI prefix: mega-
Ten lakh
/ ?
(kar)
?
(?k k)
?
(ki)
?
(ko?i)
?
(ki)
?
(ki)
?
(ki)
?
(ki)
?
(?k karo?)
1,00,00,000 107 10,000,000 Ten million
One crore
/ ?
(das kar)
?
(dah? k)
?
(dô? ki)

(?rbud)
?
(dasa ko?i)

(arbuda)

(a?putam)

(padi klu)
?
(hattu ki)

(pattuki)
?
(da? karo?)
10,00,00,000 108 100,000,000 One hundred million
Ten crore
/
(arab)
/ ?
(sau kar)
?
(?k abja)
?
(êk ki)

(môh?rbud)
?
(eka sahe ko?i)

(brunda)
?
(nika?putam)

(vanda klu)
? ?
(n?ru ki)

(nuki)
?
(?k arba)
1,00,00,00,000 109 1,000,000,000 One billion
(one milliard)
SI prefix: giga-
One arab / one hundred crore
/
(das arab)
/ ? ?
(?k haz?r kar)
?
(ek kharva)
?
(h?z?r ki)
?
(khôrb?)
? ?
(haj?ra ko?i)
?
(kharba)
?
(kumpam)

(veyyi klu)
? ?
(ondu s?vira ki)
?
(?yira? ki)
?
(da? arba)
10,00,00,00,000 1010 10,000,000,000 Ten billion
(ten milliard)
Ten arab / one thousand crore
/ ?
(kharab)

(ek nikharva)
?
(dô? h?j?r ki)
?
(môh?khôrb?)
? ?
(dasa haj?ra ko?i)

(nikharba)
?
(ka?am)

(padi v?la klu)
?
(hattu s?vira ki)
?
(patin?yira? ki)
?
(?k kharba)
1,00,00,00,00,000 1011 100,000,000,000 One hundred billion
(one hundred milliard)
One kharab / one hundred arab / ten thousand crore
/ ?
(das kharab)
/ ? ?
(?k l?kh kar)
?
(?k padma)
?
(l?kh ki)
?
(?ô?kh?)
? ?
(lakhya ko?i)
?
(sa?kha)

(ka?pam)
?
(lak?a klu)
? ? ?
(ondu lak?a ki)
?
(oru lak?a? ki)
?
(da? kharba)
10,00,00,00,00,000 1012 1,000,000,000,000 One trillion
(one billion)
SI prefix: tera-
Ten kharab / one thousand arab / one lakh crore
/
(n?l)
?
(ek mah?padma)
?
(dô? l?kh ki)
?
(pôdd?)
?
(môhô?kh?)
? ?
(dasa lakhya ko?i)
?
(padma)

(nika?pam)

(padi lak?ala klu)
? ?
(hattu lak?a ki)
? ?
(pattulak?a? ki)

(n?l)
1,00,00,00,00,00,000 1013 10,000,000,000,000 Ten trillion
(ten billion)
One nil / one hundred kharab / ten thousand arab / ten lakh crore
/
(das n?l)
/ ? ?
(?k kar kar)
?
(?k ?a?kh?)
?
(êk l?kh ki)
?
(?ôtôki lôkk?)
?
(môh?pôdd?)
? ?
(sahe lakhya ko?i)
?
(s?gara)

(patumam)
?
(ki klu)
? ? ?
(ondu ki ki)
? ?
(nu? lak?a? ki)

(da? n?l)
10,00,00,00,00,00,000 1014 100,000,000,000,000 One hundred trillion
(one hundred billion)
Ten nil / one crore crore
? /
(padma)
? ?
(eka jaladhi ?a?kh?)
?
(h?z?r l?kh ki)
? ? ?
(haj?ra lakhya ko?i)

(antya)

(ca?kam)

(padi kla klu)
? ?
(hattu ki ki)
?
(?yira? lak?a? ki)
?
(padma)
100,00,00,00,00,00,000 1015 1,000,000,000,000,000 One quadrillion
(one billiard)
SI prefix: peta-
One padma / one hundred nil / ten crore crore
? /
(das padma)

(eka antya)
?
(dô? h?z?r l?kh ki)
? ? ?
(dasa haj?ra lakhya ko?i)
?
(madhya)
?
(veam)
?
(camuttiram)

(vanda kla klu)
? ? ?
(n?ru ki ki)
?
(patin?yira? lak?a? ki)
?
(da? padma)
10,00,00,00,00,00,00,000 1016 10,000,000,000,000,000 Ten quadrillion
(ten billiard)
Ten padma / one hundred crore crore
/ ?
(?a?kh)

(eka par?rdha)
?
(?oto h?z?r l?kh ki)
? ? ?
(sahe haj?ra lakhya ko?i)

(par?rddha)

(anniyam)

(veyyi kla klu)
? ? ?
(ondu s?vira ki ki)
?
(lak?a? lak?a? ki)

(?a?kha)
100,00,00,00,00,00,00,000 1017 100,000,000,000,000,000 One hundred quadrillion
(one hundred billiard)
One shankh / one hundred padma / one thousand crore crore / one lakh lakh crore
/ ?
(das ?a?kh)
/ ?
(gul?an)

(eka mah?par?rdha)
?
(do? ?oto h?z?r l?kh ki)

(guln)
? ? ?
(dasa sahe haj?ra lakhya ko?i)

(da?a par?rddha)

(arttam)

(padi v?la kla klu)
? ?
(hattu s?vira ki ki)
? ?
(pattulak?a? lak?a? ki)

(da? ?a?kha)
10,00,00,00,00,00,00,00,000 1018 1,000,000,000,000,000,000 One quintillion
(one trillion)
SI prefix: exa-
Ten shankh / ten thousand crore crore

Vedic numbering systems

There are various systems of numeration found in various ancient Vedic literary works of India. The following table gives one such system used in the Valmiki Ramayana.[5]

Name Indian notation Power notation Indian system Short scale Western
(?ka) 0,00,001 100 One One
(da?a) 0,00,010 101 Ten Ten
(?ata) 0,00,100 102 One hundred One hundred
(sahasra) 0,01,000 103 One thousand One thousand
? (lak?a) 1,00,000 105 One lakh One hundred thousand
? (ki)
1,00,000 ?ata 107 One crore Ten million
(?a?ku) 1,00,000 ko?i 1012 Ten kharab or One lakh crore One trillion
(maha?ku) 1,00,000 ?a?ku 1017 One shankh or One thousand crore crore One hundred quadrillion
(vrinda) 1,00,000 maha?ku 1022 Ten sextillion (ten trilliard)
(mah?vrinda) 1,00,000 vrinda 1027 One octillion
? (padma) 1,00,000 mah?vrinda 1032 One hundred nonillion
? (mah?padma) 1,00,000 padma 1037 Ten undecillion
? (kharva) 1,00,000 mah?padma 1042 One tredecillion
? (mah?kharva) 1,00,000 kharva 1047 One hundred quattuordecillion
(samudra) 1,00,000 mah?kharva 1052 Ten sexdecillion
(ogha) 1,00,000 samudra 1057 One octodecillion
? (mahaugha) 1,00,000 ogha 1062 One hundred novemdecillion

Usage in different languages

  • In Assamese, a lakh is also called ? lokhyo, or lakh and a crore is called ? ? kouti
  • In Bengali, a lakh is natively (tadbhava) known as l?kh, though some use the ardha-tatsama ? lokkho. A crore is called ? ki
  • In Burmese, crore is called ? [dè]. Lakh is used in Burmese English.
  • In Dhivehi, a lakh is called la'kha and a crore is called kroaru
  • In Gujarati, a lakh is called l?kh and a crore is called ? karo?. A hundred crore is called abaj
  • In Kannada, a lakh is called ? lak?ha and a crore is called ? ki
  • In Khasi, a lakh is called lak and a crore is called klur or krur. A billion is called arab and hundred billion is called kharab.
  • In Malayalam, a lakh is called laksham and a crore is called ? kodi.
  • In Marathi, a lakh is called /? l?kh and a crore is called ? ko?i or ? karo?, and an arab (109) is called ? abja.
  • In Nepali, a lakh is called l?kh and a crore is called ? karo?.
  • In Odia, a lakh is called ? lakhya and a crore is called ? ko?i.
  • In Punjabi, a lakh is called lakkh (Shahmukhi: , Gurmukhi: ) and a crore is called karo? (Shahmukhi: ?, Gurmukhi: ?).
  • In Rohingya, a lakh is called lák and a crore is called kurul. A thousand crore is called kuthí.
  • In Sinhala, a lakh is called ? lak?a and a crore is called ? ki.
  • In Tamil, a lakh is called ? ila?cam and a crore is called ? ki.
  • In Telugu, a lakh is called ? lak?ha and a crore is called ? ki.
  • In Urdu, a lakh is called ? l?kh and a crore is called ? karo?. A billion is called arab (), and one hundred billion/arab is called a kharab (?).
  • Lakh has entered the Swahili language as "laki" and is in common use.

Formal written publications in English in India tend to use lakh/crore for Indian currency and International numbering for foreign currencies.[6]

Current usage

The usage of this system is limited to the nations of India, Pakistan, Bangladesh, and Myanmar. It is universally employed within these countries, and is preferred to the English numbering system.[7]

Sri Lanka used this system in the past but has switched to the English numbering system in recent years.

In the Maldives, the term lakh is widely used in official documents and local speech. However the English numbering system is preferred for higher denominations (i.e millions etc).

Most institutions and citizens in India use the Indian number system, although the Reserve Bank of India has been noted as a rare exception.[8]

References

  1. ^ "Knowing our Numbers". Department Of School Education And Literacy. National Repository of Open Educational Resources. Retrieved 2016.
  2. ^ "Decimal and Thousands Separators (International Language Environments Guide)". docs.oracle.com. Retrieved 2021.
  3. ^ Emmons, John (25 March 2018). "UNICODE LOCALE DATA MARKUP LANGUAGE (LDML) PART 3: NUMBERS". Unicode.org. Archived from the original on 25 July 2018. Retrieved 2018.
  4. ^ Use of separator in digit grouping here follows customs in most English-speaking countries. For international standards and details, see decimal mark.
  5. ^ "Valmiki Ramayana - Yuddha Kanda, Chapter (Sarga) 28,(Verses 33 - 38)". Retrieved 2021.
  6. ^ Shapiro, Richard (16 August 2012). "The most distinctive counting system in English? Indian cardinal numbers". Oxford English Dictionary. Retrieved 2020. - Shapiro is/was an OED employee. The article states: "The opinions and other information contained in the OED blog posts and comments do not necessarily reflect the opinions or positions of Oxford University Press."
  7. ^ Krulwich, Robert; Block, Ezra (21 October 2010). "Hey! Who Can Explain What India Does With Its Commas?". NPR. Retrieved 2020.
  8. ^ Gurpur (10 August 2015). "Can we follow Indian numbering system for simplicity and good order?". Moneylife News & Views. Retrieved 2020.

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