Indian numbering system
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
There are words 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), 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 |
Five hundred thousand |
| 12,34,56,789 | 123,456,789 | Twelve crore thirty-four lakh fifty-six thousand seven hundred and eighty-nine | One hundred and twenty-three million four hundred and fifty-six thousand seven hundred and eighty-nine |
| 17,00,00,00,000 | 17,000,000,000 | Seventeen arab | Seventeen billion |
| 6,78,90,00,00,00,00,000 | 6,789,000,000,000,000 | Six padma seventy-eight nil ninety kharab | 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.
| Hindustani | Marathi | Bengali | Odia | Tamil | Telugu | Kannada | Malayalam | Nepali | Indian notation | Power notation |
International notation[3] | Short scale Western (long scale Western) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| South Asian English | ||||||||||||
| एक / ایک (ēk) |
एक (ēk) |
এক (êk) |
ଏକ (eka) |
ஒன்று (oṉṟu) |
ఒకటి (okaṭi) |
ಒಂದು (ondu) |
ഒന്ന് (onn) |
एक (ēk) |
1 | 100 | 1 | One |
| One | ||||||||||||
| दस / دس (das) |
दहा (dahā) |
দশ (dôś) |
ଦଶ (daśa) |
பத்து (pattu) |
పది (padi) |
ಹತ್ತು (hattu) |
പത്ത് (patt) |
दश (daś) |
10 | 101 | 10 | Ten SI prefix: deca- |
| Ten | ||||||||||||
| सौ / سو (sau) |
शंभर (śambhar) |
একশ' (êkśō) |
ଶହେ (śahe) |
நூறு (nūṟu) |
వంద/నూరు (vanda/nūru) |
ನೂರು (nūru) |
നൂറ് (nuṟ) |
सय (saya) |
100 | 102 | 100 | One hundred SI prefix: hecto- |
| One hundred | ||||||||||||
| सहस्र (sahasra) हज़ार / ہزار (hazār) |
एक हजार (ēk hajār) |
হাজ়ার (hāzār) |
ହଜାର (hajāra) ସହସ୍ର (sahasra) |
ஆயிரம் (āyiram) |
వెయ్యి (veyyi) |
ಸಾವಿರ (sāvira) |
ആയിരം (āyiraṁ) |
हजार (ēk hajār) |
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) |
ଦଶ ହଜାର (daśa hajāra) ଅୟୁତ (ayuta) |
பத்தாயிரம் (pattāyiram) ஆயுதம் (āyutam) |
పది వేలు (padi vēlu) |
ಹತ್ತು ಸಾವಿರ (hattu sāvira) |
പതിനായിരം (patināyiraṁ) |
दश हजार (daś hajār) |
10,000 | 104 | 10,000 | Ten thousand |
| Ten thousand | ||||||||||||
| लाख / لاکھ (lākh) |
एक लाख (ēk lākh) |
লক্ষ (lôkkhō) লাখ (lākh) |
ଲକ୍ଷ (lakṣa) |
இலட்சம் (ilaṭcam) நியுதம் (niyutam) |
లక్ష (lakṣa) |
ಲಕ್ಷ (lakṣa) |
ലക്ഷം (lakṣaṁ) |
एक लाख (ēk lākh) |
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) |
ଦଶ ଲକ୍ଷ (daśa lakṣa) ନିୟୁତ (niyuta) |
பத்து இலட்சம் (pattu ilaṭcam) |
పది లక్షలు (padi lakṣalu) |
ಹತ್ತು ಲಕ್ಷ (hattu lakṣa) |
പത്തുലക്ഷം (pattulakṣaṁ) |
दश लाख (daś lākh) |
10,00,000 | 106 | 1,000,000 | One million SI prefix: mega- |
| Ten lakh | ||||||||||||
| करोड़ / کروڑ (karōṛ) |
एक कोटी (ēk kōṭī) |
কোটি (kōṭi) |
କୋଟି (koṭi) |
கோடி (kōṭi) |
కోటి (kōṭi) |
ಕೋಟಿ (kōṭi) |
കോടി (kōṭi) |
एक करोड (ēk karoḍ) |
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) |
ଦଶ କୋଟି (daśa koṭi) ଅର୍ବୁଦ (arbuda) |
அற்புதம் (aṟputam) |
పది కోట్లు (padi kōṭlu) |
ಹತ್ತು ಕೋಟಿ (hattu kōṭi) |
പത്തുകോടി (pattukōṭi) |
दश करोड (daś karoḍ) |
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) |
ଏକ ଶହେ କୋଟି (eka śahe koṭi) ବୃନ୍ଦ (br̥nda) |
நிகற்புதம் (nikaṟputam) |
వంద కోట్లు (vanda kōṭlu) |
ನೂರು ಕೋಟಿ (nūru kōṭi) |
നൂറുകോടി (nūṟukōṭi) |
एक अर्ब (ēk arba) |
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) |
एक खर्व (ek kharva) |
হাজ়ার কোটি (hāzār kōṭi) খর্ব (khôrbō) |
ହଜାର କୋଟି (hajāra koṭi) ଖର୍ବ (kharba) |
கும்பம் (kumpam) |
వెయ్యి కోట్లు (veyyi kōṭlu) |
ಒಂದು ಸಾವಿರ ಕೋಟಿ (ondu sāvira kōṭi) |
ആയിരം കോടി (āyiraṁ kōṭi) |
दश अर्ब (daś arba) |
10,00,00,00,000 | 1010 | 10,000,000,000 | Ten billion (ten milliard) |
| Ten arab / one thousand crore | ||||||||||||
| खरब / کھرب (kharab) |
एक निखर्व (ek nikharva) |
দশ হাজ়ার কোটি (dôś hājār kōṭi) মহাখর্ব (môhākhôrbō) |
ଦଶ ହଜାର କୋଟି (daśa hajāra koṭi) ନିଖର୍ବ (nikharba) |
கணம் (kaṇam) |
పది వేల కోట్లు (padi vēla kōṭlu) |
ಹತ್ತು ಸಾವಿರ ಕೋಟಿ (hattu sāvira kōṭi) |
പതിനായിരം കോടി (patināyiraṁ kōṭi) |
एक खर्ब (ēk 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 | ||||||||||||
| दस खरब / دس کھرب (das kharab) एक लाख करोड़ / ایک لاکھ کروڑ (ēk lākh karōṛ) |
एक पद्म (ēk padma) |
লাখ কোটি (lākh kōṭi) শঙ্খ (śôṅkhō) |
ଲକ୍ଷ କୋଟି (lakṣa koṭi) ଶଙ୍ଖ (saṅkha) |
கற்பம் (kaṟpam) |
లక్ష కోట్లు (lakṣa kōṭlu) |
ಒಂದು ಲಕ್ಷ ಕೋಟಿ (ondu lakṣa kōṭi) |
ഒരു ലക്ഷം കോടി (oru lakṣaṁ kōṭi) |
दश खर्ब (daś 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 | ||||||||||||
| नील / نیل (nīl) |
एक महापद्म (ek mahāpadma) |
দশ লাখ কোটি (dôś lākh kōṭi) পদ্ম (pôddō) মহাশঙ্খ (môhāśôṅkhō) |
ଦଶ ଲକ୍ଷ କୋଟି (daśa lakṣa koṭi) ପଦ୍ମ (padma) |
நிகற்பம் (nikaṟpam) |
పది లక్షల కోట్లు (padi lakṣala kōṭlu) |
ಹತ್ತು ಲಕ್ಷ ಕೋಟಿ (hattu lakṣa kōṭi) |
പത്തുലക്ഷം കോടി (pattulakṣaṁ kōṭi) |
नील (nīl) |
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 शंखू (ēk śaṅkhū) |
একশ' লাখ কোটি (êkśō lākh kōṭi) শতকোটি লক্ষ (śôtôkōṭi lôkkō) মহাপদ্ম (môhāpôddō) |
ଶହେ ଲକ୍ଷ କୋଟି (śahe lakṣa koṭi) ସାଗର (sāgara) |
பதுமம் (patumam) |
కోటి కోట్లు (kōṭi kōṭlu) |
ಒಂದು ಕೋಟಿ ಕೋಟಿ (ondu kōṭi kōṭi) |
നൂറ് ലക്ഷം കോടി (nuṟ lakṣaṁ kōṭi) |
दश नील (daś nīl) |
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) |
एक जलधि शंखू
(eka jaladhi śaṅkhū) |
হাজ়ার লাখ কোটি (hāzār lākh kōṭi) |
ହଜାର ଲକ୍ଷ କୋଟି (hajāra lakṣa koṭi) ଅନ୍ତ୍ୟ (antya) |
சங்கம் (caṅkam) |
పది కోట్ల కోట్లు (padi kōṭla kōṭlu) |
ಹತ್ತು ಕೋಟಿ ಕೋಟಿ (hattu kōṭi kōṭi) |
ആയിരം ലക്ഷം കോടി (āyiraṁ lakṣaṁ kōṭi) |
पद्म (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 | ||||||||||||
| दस पद्म / دس پدم (das padma) |
एक अंत्य
(eka antya) |
দশ হাজ়ার লাখ কোটি (dôś hāzār lākh kōṭi) |
ଦଶ ହଜାର ଲକ୍ଷ କୋଟି (daśa hajāra lakṣa koṭi) ମଧ୍ୟ (madhya) |
வெள்ளம் (veḷḷam) சமுத்திரம் (camuttiram) |
వంద కోట్ల కోట్లు (vanda kōṭla kōṭlu) |
ನೂರು ಕೋಟಿ ಕೋಟಿ (nūru kōṭi kōṭi) |
പതിനായിരം ലക്ഷം കോടി (patināyiraṁ lakṣaṁ kōṭi) |
दश पद्म (daś 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 | ||||||||||||
| शंख / شنکھ (śaṅkh) |
एक परार्ध
(eka parārdha) |
শত হাজ়ার লাখ কোটি (śoto hāzār lākh kōṭi) |
ଶହେ ହଜାର ଲକ୍ଷ କୋଟି (śahe hajāra lakṣa koṭi) ପରାର୍ଦ୍ଧ (parārddha) |
அந்நியம் (anniyam) |
వెయ్యి కోట్ల కోట్లు (veyyi kōṭla kōṭlu) |
ಒಂದು ಸಾವಿರ ಕೋಟಿ ಕೋಟಿ (ondu sāvira kōṭi kōṭi) |
ലക്ഷം ലക്ഷം കോടി (lakṣaṁ lakṣaṁ kōṭi) |
शंख (śaṅkha) |
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) |
एक महापरार्ध
(eka mahāparārdha) |
দশ শত হাজ়ার লাখ কোটি (doś śoto hāzār lākh kōṭi) গুলশান (gulśān) |
ଦଶ ଶହେ ହଜାର ଲକ୍ଷ କୋଟି (daśa śahe hajāra lakṣa koṭi) ଦଶ ପରାର୍ଦ୍ଧ (daśa parārddha) |
அர்த்தம் (arttam) |
పది వేల కోట్ల కోట్లు (padi vēla kōṭla kōṭlu) |
ಹತ್ತು ಸಾವಿರ ಕೋಟಿ ಕೋಟಿ (hattu sāvira kōṭi kōṭi) |
പത്തുലക്ഷം ലക്ഷം കോടി (pattulakṣaṁ lakṣaṁ kōṭi) |
दश शंख (daś śaṅkha) |
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.[4]
| 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) |
10,00,000 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 |
| गौतम (gautama) | 1,00,000 mahaugha | 1067 | 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | Ten unvigintillion |
| महागौतम (mahagautama) | 1,00,000 gautama | 1072 | 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | One trevigintillion |
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 natively (tadbhava) known as লাখ lākh, though some use the ardha-tatsama লক্ষ lokkho. A crore is called কোটি kōṭi
- 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/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, 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 crore is called kuthí.
- In Sinhala, a lakh is called ලක්ෂ lakṣa and a crore is called කෝටි kōṭi.
- 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 one hundred billion/arab is called a kharab (کھرب).
- 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.[5]
Current usage
The usage of this system is limited to the nations of India, Pakistan, Bangladesh, Myanmar and Sri Lanka.[6]
Most institutions and citizens in India use Indian number system, though the Reserve Bank of India has been noted as an exception.[7]
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.
- "Valmiki Ramayana - Yuddha Kanda". www.valmikiramayan.net.
- 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."
- Krulwich, Robert; Block, Ezra (21 October 2010). "Hey! Who Can Explain What India Does With Its Commas? (Not Commies. Commas.)". NPR. Retrieved 3 August 2020.
- Gurpur (10 August 2015). "Can we follow Indian numbering system for simplicity and good order?". Moneylife News & Views. Retrieved 3 September 2020.