Indian numbering system
The Indian numbering system is used in the Indian subcontinent 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. For example, 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.
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.
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.[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 |
| 67,890,00,00,00,000 | 67,890,000,000,000 | Sixty-seven lakh, eighty-nine thousand crore | 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
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.
| 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) |
হাজার (hājār) |
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 হাজার (dôś hājār) 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 |
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) |
100,00,00,000 | 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) |
হাজার কোটি (hājār kōṭi) খর্ব (khôrbō) |
கும்பம் (kumpam) |
వెయ్యి కోట్లు (veyyi kōṭlu) |
ಒಂದು ಸಾವಿರ ಕೋಟಿ (ondu sāvira kōṭi) |
ആയിരം കോടി (āyiraṁ kōṭi) |
1,000,00,00,000 | 1010 | 10,000,000,000 | Ten billion (ten milliard) |
| Ten arab / one thousand crore | ||||||||||
| खरब / کھرب (kharab) |
शंभर अब्ज (śambhar abja) |
দশ হাজার কোটি (dôś hājār kōṭi) মহাখর্ব (môhākhôrbō) |
கணம் (kaṇam) |
పది వేల కోట్లు (padi vēla kōṭlu) |
ಹತ್ತು ಸಾವಿರ ಕೋಟಿ (hattu sāvira kōṭi) |
പതിനായിരം കോടി (patināyiraṁ kōṭi) |
10,000,00,00,000 | 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) |
1,00,000,00,00,000 | 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) |
10,00,000,00,00,000 | 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) |
1,00,00,000,00,00,000 | 1014 | 100,000,000,000,000 | One hundred trillion (one hundred billion) |
| Ten nil / one crore crore | ||||||||||
| पद्म / پدم (padma) |
হাজার লাখ কোটি (hājār lākh kōṭi) |
சங்கம் (caṅkam) |
పది కోట్ల కోట్లు (padi kōṭla kōṭlu) |
ಹತ್ತು ಕೋಟಿ ಕೋಟಿ (hattu kōṭi kōṭi) |
ആയിരം ലക്ഷം കോടി (āyiraṁ lakṣaṁ kōṭi) |
10,00,00,000,00,00,000 | 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 হাজার লাখ কোটি (dôś hājār lākh kōṭi) |
வெள்ளம் (veḷḷam) சமுத்திரம் (camuttiram) |
వంద కోట్ల కోట్లు (vanda kōṭla kōṭlu) |
ನೂರು ಕೋಟಿ ಕೋಟಿ (nūru kōṭi kōṭi) |
പതിനായിരം ലക്ഷം കോടി (patināyiraṁ lakṣaṁ kōṭi) |
100,00,00,000,00,00,000 | 1016 | 10,000,000,000,000,000 | Ten quadrillion (ten billiard) | |
| Ten padma / one hundred crore crore | ||||||||||
| शंख / شنکھ (śaṅkh) |
শত হাজার লাখ কোটি (śata hājār lākh kōṭi) |
அந்நியம் (anniyam) |
వెయ్యి కోట్ల కోట్లు (veyyi kōṭla kōṭlu) |
ಒಂದು ಸಾವಿರ ಕೋಟಿ ಕೋಟಿ (ondu sāvira kōṭi kōṭi) |
ലക്ഷം ലക്ഷം കോടി (lakṣaṁ lakṣaṁ kōṭi) |
1,000,00,00,000,00,00,000 | 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 হাজার লাখ কোটি (daś śata hājār lākh kōṭi) |
அர்த்தம் (arttam) |
పది వేల కోట్ల కోట్లు (padi vēla kōṭla kōṭlu) |
ಹತ್ತು ಸಾವಿರ ಕೋಟಿ ಕೋಟಿ (hattu sāvira kōṭi kōṭi) |
പത്തുലക്ഷം ലക്ഷം കോടി (pattulakṣaṁ lakṣaṁ kōṭi) |
10,000,00,00,000,00,00,000 | 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' repectively; these are numbers unique to Indian numbering.[4]
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]
| Indian notation | Power notation | Equivalent numeric representation | Short scale Western | |
|---|---|---|---|---|
| एक (ēka) | 1 | 100 | 1 | One |
| दश (daśa) | 10 | 101 | 10 | Ten |
| शत (śata) | 100 | 102 | 100 | One hundred |
| सहस्र (sahasra) | 1,000 | 103 | 1,000 | One thousand |
| अयुत (ayuta) | 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
- 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.
- In Sylheti, a lakh is called লাখ lakh (lax) and a crore is called কোটি kuti. A billion is called "arob". And hundred billion is called "kharob".
- 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]
Criticisms
There are problems arising from the usage of the Indian numbering system in the modern context.[7] These problems include:
- The usage of this system is limited to the nations of India, Pakistan, Bangladesh, Myanmar and Sri Lanka. For example, the movie Slumdog Millionaire was titled Slumdog Crorepati on posters in Mumbai.[8]
- Apart from lakh and crore, other terms are rarely used. This has led to what one news article from ThePrint describes as "mental gymnastics". For example, 1 kharab is called "1 thousand crore", 1 padma is called "10 crore crore", etc.
- Computer programs are automatically set to add a thousands separator after every 3 digits. This is challenging for people who use this system to understand what has been typed.
- Also, those who will be either travelling to India, or learning the language, etc. will find it difficult to understand the system, due to the increase in the number of terms used.
There are advantages mentioned of converting to the international numeral system from this system.[7] These advantages include:
- Increased linkage with the global economy.
- Countries that use the Indian numbering system currently teach both this system and the international system. Using only one would decrease overall teaching time and would be easier to understand.
- People will not need to context switch between the international system as well as this system anymore.
References
- "Knowing our Numbers". Department Of School Education And Literacy. National Repository of Open Educational Resources. Retrieved 13 February 2016.
- 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.
- Use of separator in digit grouping here follows customs in most English-speaking countries. For international standards and details, see decimal mark.
- Miller, Sam (20 July 2010). Delhi: Adventures in a Megacity. St. Martin's Publishing Group. p. 31. ISBN 9781429963855.
- Valmiki Ramayana Yuddha Kanda
- 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."
- Ninan, T. N. (9 December 2017). "It's time India switches to millions and billions instead of lakhs and crores". ThePrint. Retrieved 3 August 2020.
- "Hey! Who Can Explain What India Does With Its Commas? (Not Commies. Commas.)". NPR.org. Retrieved 3 August 2020.