Indian numbering system

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The Indian numbering system is used in the Indian subcontinent (Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan and Sri Lanka) 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[edit]

There are words for numbers larger than 1 crore as well, but these are not commonly used and are unfamiliar to most speakers. These include 1 arab (equal to 100 crore or 1 billion), 1 kharab (equal to 100 arab or 100 billion), 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.

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, and so on; there are new words for every third power of ten (103n): million (106), billion (109), trillion (1012), etc.

The written numbers differ only in the placement of commas, which group the digits into powers of one hundred in the Indian system (except for the first thousand), and into powers of one thousand 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.

Examples[edit]

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[edit]

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.[2] 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. Thus:

Indian system International system In words (Indian) In words (International)
5,00,000 500,000 Five lakh(s)
Five hundred thousand
12,12,12,123 121,212,123 Twelve crore, twelve lakh, twelve thousand, one hundred and twenty-three One hundred and twenty-one million, two hundred and twelve thousand, one hundred and twenty-three
17,00,00,00,000 17,000,000,000 Seventeen arab Seventeen billion
6,78,90,00,00,00,000 67,890,000,000,000 Six nil, seventy eight kharab, ninety arab Sixty-seven trillion, eight hundred and ninety billion

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

Names of numbers[edit]

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
Hindi/Urdu Marathi Bengali Tamil Telugu Kannada Malayalam Indian notation Power
notation
International notation[3] Short scale Western
(long scale Western)
South Asian English
एक / ایک
(ēk)
एक
(ēk)
এক
(êk)
ஒன்று
(oṉṟu)
ఒకటి
(okaṭi)
ಒಂದು
(ondu)
ഒന്ന്
(onn)
1 100 1 One
One
दस / دس
(das)
दहा
(dahā)
দশ
(dôś)
பத்து
(pattu)
పది
(padi)
ಹತ್ತು
(hattu)
പത്ത്
(patt)
10 101 10 Ten
SI prefix: deca-
Ten
सौ / سو
(sau)
शंभर
(śambhar)
একশ'
(êkśō)
நூறு
(nūṟu)
వంద/నూరు
(vanda/nūru)
ನೂರು
(nūru)
നൂറ്
(nuṟ)
100 102 100 One hundred
SI prefix: hecto-
One hundred
सहस्र
(sahasra)
हज़ार / ہزار
(hazār)
एक हजार
(ēk hajār)
হাজ়ার
(hāzār)
ஆயிரம்
(āyiram)
వెయ్యి
(veyyi)
ಸಾವಿರ
(sāvira)
ആയിരം
(āyiraṁ)
1,000 103 1,000 One thousand
SI prefix: kilo-
One thousand
दस हज़ार / دس ہزار
(das hazār)
दहा हजार
(dahā hajār)
দশ হাজ়ার
(dôś hāzār)
অযুত
(ōjut)
பத்தாயிரம்
(pattāyiram)
ஆயுதம்
(āyutam)
పది వేలు
(padi vēlu)
ಹತ್ತು ಸಾವಿರ
(hattu sāvira)
പതിനായിരം
(patināyiraṁ)
10,000 104 10,000 Ten thousand
Ten thousand
लाख / لاکھ
(lākh)
एक लाख
(ēk lākh)
লক্ষ(lôkkhō)

লাখ
(lākh)

இலட்சம்
(ilaṭcam)
நியுதம்
(niyutam)
లక్ష
(lakṣa)
ಲಕ್ಷ
(lakṣa)
ലക്ഷം
(lakṣaṁ)
1,00,000 105 100,000 One hundred thousand
One lakh (sometimes incorrectly transliterated as lac)
दस लाख / دس لاکھ
(das lākh)
अदन्त / ادنت
(adanta)
दहा लाख
(dahā lākh)
দশ লাখ
(dôś lākh)
নিযুত
(nijut)
பத்து இலட்சம்
(pattu ilaṭcam)
పది లక్షలు
(padi lakṣalu)
ಹತ್ತು ಲಕ್ಷ
(hattu lakṣa)
പത്തുലക്ഷം
(pattulakṣaṁ)
10,00,000 106 1,000,000 One million
SI prefix: mega-
Ten lakh
करोड़ / کروڑ
(karōṛ)
एक कोटी
(ēk kōṭī)
কোটি
(kōṭi)
கோடி
(kōṭi)
కోటి
(kōṭi)
ಕೋಟಿ
(kōṭi)
കോടി
(kōṭi)
1,00,00,000 107 10,000,000 Ten million
One crore
दस करोड़ / دس کروڑ
(das karōṛ)
दहा कोटी
(dahā kōṭī)
দশ কোটি
(dôś kōṭi)
অর্বুদ
(ōrbud)
அற்புதம்
(aṟputam)
పది కోట్లు
(padi kōṭlu)
ಹತ್ತು ಕೋಟಿ
(hattu kōṭi)
പത്തുകോടി
(pattukōṭi)
10,00,00,000 108 100,000,000 One hundred million
Ten crore
अरब / ارب
(arab)
सौ करोड़ / سو کروڑ
(sau karōṛ)
एक अब्ज
(ēk abja)
একশ' কোটি
(êkśō kōṭi)

মহার্বুদ

(môhārbud)

நிகற்புதம்
(nikaṟputam)
వంద కోట్లు
(vanda kōṭlu)
ನೂರು ಕೋಟಿ
(nūru kōṭi)
നൂറുകോടി
(nūṟukōṭi)
1,00,00,00,000 109 1,000,000,000 One billion
(one milliard)
SI prefix: giga-
One arab / one hundred crore
दस अरब / دس ارب
(das arab)
एक हज़ार करोड़ / ایک ہزار کروڑ
(ēk hazār karōṛ)
दहा अब्ज
(dahā abja)
হাজ়ার কোটি
(hāzār kōṭi)
খর্ব
(khôrbō)
கும்பம்
(kumpam)
వెయ్యి కోట్లు
(veyyi kōṭlu)
ಒಂದು ಸಾವಿರ ಕೋಟಿ
(ondu sāvira kōṭi)
ആയിരം കോടി
(āyiraṁ kōṭi)
10,00,00,00,000 1010 10,000,000,000 Ten billion
(ten milliard)
Ten arab / one thousand crore
खरब / کھرب
(kharab)
शंभर अब्ज
(śambhar abja)
দশ হাজ়ার কোটি
(dôś hājār kōṭi)

মহাখর্ব

(môhākhôrbō)

கணம்
(kaṇam)
పది వేల కోట్లు
(padi vēla kōṭlu)
ಹತ್ತು ಸಾವಿರ ಕೋಟಿ
(hattu sāvira kōṭi)
പതിനായിരം കോടി
(patināyiraṁ kōṭi)
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
दस खरब / دس کھرب
(das kharab)
एक लाख करोड़ / ایک لاکھ کروڑ
(ēk lākh karōṛ)
एक हजार अब्ज
(ēk hajār abja)
লাখ কোটি
(lākh kōṭi)

শঙ্খ

(śôṅkhō)

கற்பம்
(kaṟpam)
లక్ష కోట్లు
(lakṣa kōṭlu)
ಒಂದು ಲಕ್ಷ ಕೋಟಿ
(ondu lakṣa kōṭi)
ഒരു ലക്ഷം കോടി
(oru lakṣaṁ kōṭi)
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
नील / نیل
(nīl)
दहा हजार अब्ज
(dahā hajār abja)
দশ লাখ কোটি
(dôś lākh kōṭi)

পদ্ম

(pôddō)

মহাশঙ্খ

(môhāśôṅkhō)

நிகற்பம்
(nikaṟpam)
పది లక్షల కోట్లు
(padi lakṣala kōṭlu)
ಹತ್ತು ಲಕ್ಷ ಕೋಟಿ
(hattu lakṣa kōṭi)
പത്തുലക്ഷം കോടി
(pattulakṣaṁ kōṭi)
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
दस नील / دس نیل
(das nīl)
एक करोड़ करोड़ / ایک کروڑ کروڑ
(ēk karōṛ karōṛ)
एक लाख अब्ज
(ēk lākh abja)
একশ' লাখ কোটি
(êkśō lākh kōṭi)

শতকোটি লক্ষ

(śôtôkōṭi lôkkō)

মহাপদ্ম

(môhāpôddō)

பதுமம்
(patumam)
కోటి కోట్లు
(kōṭi kōṭlu)
ಒಂದು ಕೋಟಿ ಕೋಟಿ
(ondu kōṭi kōṭi)
നൂറ് ലക്ഷം കോടി
(nuṟ lakṣaṁ kōṭi)
10,00,00,00,00,00,000 1014 100,000,000,000,000 One hundred trillion
(one hundred billion)
Ten nil / one crore crore
पद्म / پدم
(padma)
হাজ়ার লাখ কোটি
(hāzār lākh kōṭi)
சங்கம்
(caṅkam)
పది కోట్ల కోట్లు
(padi kōṭla kōṭlu)
ಹತ್ತು ಕೋಟಿ ಕೋಟಿ
(hattu kōṭi kōṭi)
ആയിരം ലക്ഷം കോടി
(āyiraṁ lakṣaṁ kōṭi)
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
दस पद्म / دس پدم
(das padma)
দশ হাজ়ার লাখ কোটি
(dôś hāzār lākh kōṭi)
வெள்ளம்
(veḷḷam)
சமுத்திரம்
(camuttiram)
వంద కోట్ల కోట్లు
(vanda kōṭla kōṭlu)
ನೂರು ಕೋಟಿ ಕೋಟಿ
(nūru kōṭi kōṭi)
പതിനായിരം ലക്ഷം കോടി
(patināyiraṁ lakṣaṁ kōṭi)
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
शंख / شنکھ
(śaṅkh)
শত হাজ়ার লাখ কোটি
(śoto hāzār lākh kōṭi)
அந்நியம்
(anniyam)
వెయ్యి కోట్ల కోట్లు
(veyyi kōṭla kōṭlu)
ಒಂದು ಸಾವಿರ ಕೋಟಿ ಕೋಟಿ
(ondu sāvira kōṭi kōṭi)
ലക്ഷം ലക്ഷം കോടി
(lakṣaṁ lakṣaṁ kōṭi)
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
दस शंख / دس شنکھ
(das śaṅkh)
गुलशन / گلشن
(gulśan)
দশ শত হাজ়ার লাখ কোটি
(doś śoto hāzār lākh kōṭi)

গুলশান

(gulśān)

அர்த்தம்
(arttam)
పది వేల కోట్ల కోట్లు
(padi vēla kōṭla kōṭlu)
ಹತ್ತು ಸಾವಿರ ಕೋಟಿ ಕೋಟಿ
(hattu sāvira kōṭi kōṭi)
പത്തുലക്ഷം ലക്ഷം കോടി
(pattulakṣaṁ lakṣaṁ kōṭi)
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

Derh and Dhai in Hindi and related languages means 'one and half' and 'two and half' respectively; these are numbers unique to Indian numbering.[4]

Vedic numbering systems[edit]

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]

Indian notation Power notation Equivalent numeric representation Short scale Western
एक (ēka) 0,00,001 100 1 One
दश (daśa) 0,00,010 101 10 Ten
शत (śata) 0,00,100 102 100 One hundred
सहस्र (sahasra) 0,01,000 103 1,000 One thousand
अयुत (ayuta) 0,10,000 104 10,000 Ten thousand
लक्ष (lakṣa) 1,00,000 105 100,000 One hundred thousand
नियुत (niyuta) 1,00,000 daśa 106 1,000,000 One million
कोटि (kōṭi)
1,00,000 śata 107 10,000,000 Ten million
शङ्कु (śaṅku) 1,00,000 koṭi 1012 1,000,000,000,000 One trillion
महाशङ्कु (mahāśaṅku) 1,00,000 śaṅku 1017 100,000,000,000,000,000 One hundred quadrillion
वृन्द (vr̥nda) 1,00,000 mahāśaṅku 1022 10,000,000,000,000,000,000,000 Ten sextillion (ten trilliard)
महावृन्द (mahāvr̥nda) 1,00,000 vr̥nda 1027 1,000,000,000,000,000,000,000,000,000 One octillion
पद्म (padma) 1,00,000 mahāvr̥nda 1032 100,000,000,000,000,000,000,000,000,000,000 One hundred nonillion
महापद्म (mahāpadma) 1,00,000 padma 1037 10,000,000,000,000,000,000,000,000,000,000,000,000 Ten undecillion
खर्व (kharva) 1,00,000 mahāpadma 1042 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000 One tredecillion
महाखर्व (mahākharva) 1,00,000 kharva 1047 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 One hundred quattuordecillion
समुद्र (samudra) 1,00,000 mahākharva 1052 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 Ten sexdecillion
ओघ (ōgha) 1,00,000 samudra 1057 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 One octodecillion
महौघ (mahaugha) 1,00,000 ogha 1062 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 One hundred novemdecillion

Usage in different languages[edit]

  • In Assamese, a lakh is also called লক্ষ lokhyo, or লাখ lakh and a crore is called কৌটি বা কোটি kouti
  • In Bengali, a lakh is also called লক্ষ lokkho (ardha-tatsama), or laakh (tadbhava) and a crore is called কোটি koti
  • In Burmese, crore is called ကုဋေ [ɡədè]. Lakh is used in Burmese English.
  • In Gujarati, a lakh is called લાખ lākh and a crore is called કરોડ karoḍ. A hundred crore is called અબજ abaj
  • In Kannada, a lakh is called ಲಕ್ಷ lakṣha and a crore is called ಕೋಟಿ kōṭi
  • 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 ലക്ഷം laksham and a crore is called കോടി kodi.
  • In Marathi, a lakh is called लाख / लाख/लक्ष lākh and a crore is called कोटी koṭi or करोड karoḍ, and an arab (109) is called अब्ज abja.
  • In Nepali, a lakh is called लाख lākh and a crore is called करोड karoḍ.
  • In Odia (Oriya), a lakh is called ଲକ୍ଷ lakhya and a crore is called କୋଟି koti.
  • In Punjabi, a lakh is called lakkh (Shahmukhi: لکھ, Gurmukhi: ਲੱਖ) and a crore is called karoṛ (Shahmukhi: کروڑ, Gurmukhi: ਕਰੋੜ).
  • In Rohingya, a lakh is called lák and a crore is called kurul. A thousand crores is called "kuthí ".
  • In Sinhala, a lakh is called ලක්ෂ lakṣa and a crore is called කෝටි kōṭi.
  • Lakh has entered the Swahili language as "laki" and is in common use.
  • In Tamil, a lakh is called இலட்சம் ilatcham and a crore is called கோடி kodi.
  • In Telugu, a lakh is called లక్ష lakṣha and a crore is called కోటి kōṭi.
  • In Urdu, a lakh is called لاکھ lākh and a crore is called کروڑ karoṛ. A billion is called "arab"ارب . And hundred billion/ arab (ارب) is called "kharab"( کھرب).

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

Criticism[edit]

The usage of this system is limited to the nations of India, Pakistan, Bangladesh, Myanmar and Sri Lanka.[7]

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

T. N. Ninan, in an article published by ThePrint and elsewhere,[9] examined reasons why India should consider switching away from using the terminology of lakhs and crores. This would include harmonization with the international numeral system.[9] Issues can occur with computer software with some applications configured to insert a thousands separator after every 3 digits.[9] Ninan notes the rare usage of identities other than lakh and crore are rarely used, leading to "mental gymnastics",[9] and with a Government post of spending "20 lakh crore" (2 nil) being claimed to have gone viral on social media discussing the number of zeros involved.[10]

References[edit]

  1. ^ "Knowing our Numbers". Department Of School Education And Literacy. National Repository of Open Educational Resources. Retrieved 13 February 2016.
  2. ^ 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 25 March 2018.
  3. ^ Use of separator in digit grouping here follows customs in most English-speaking countries. For international standards and details, see decimal mark.
  4. ^ Miller, Sam (20 July 2010). Delhi: Adventures in a Megacity. St. Martin's Publishing Group. p. 31. ISBN 9781429963855.
  5. ^ "Valmiki Ramayana - Yuddha Kanda". www.valmikiramayan.net.
  6. ^ Shapiro, Richard (16 August 2012). "The most distinctive counting system in English? Indian cardinal numbers". Oxford English Dictionary. Retrieved 24 May 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."
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