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TheIndian numbering system is used inIndia,Pakistan,Nepal,Sri Lanka, andBangladesh to express large numbers, which differs from theInternational System of Units. Commonly used quantities includelakh (one hundred thousand, 105) andcrore (ten million, 107) – written as 1,00,000 and 1,00,00,000 respectively in somelocales.[1] For example: 150,000rupees is "1.5lakh rupees" which can be written as "1,50,000 rupees", and 30,000,000 (thirty million) rupees is referred to as "3crore rupees" which can be written as "3,00,00,000 rupees".
There are names for numbers larger thancrore, but they are less commonly used. These includearab (100crore, 109),kharab (100arab, 1011),nil or sometimestransliterated asneel (100 kharab, 1013),padma (100 nil, 1015),shankh (100 padma, 1017), andmahashankh (100 shankh, 1019). In common parlance (though inconsistent), thelakh andcrore terminology repeats for larger numbers. Thuslakh crore is 1012.
In the ancient Indian system, still in use in regional languages of India, there are words for[clarification needed] (1062). These names respectively starting at 1000 aresahasra,ayuta,laksha,niyuta,koti,arbhudha,abhja,karva,nikarva,mahapadma,shanmkhu,jaladhi,amtya,madhya,paraardha. In the Indian system, now prevalent in the northern parts,[clarification needed] the next powers of ten are onelakh, tenlakh, onecrore, tencrore, onearab (or one hundredcrore), and so on.
The Indian system isdecimal (base-10), same as in theInternational System of Units, and the first fiveorders of magnitude are named in a similar way: one (100), ten (101), one hundred (102), one thousand (103), and ten thousand (104). For higher powers of ten, naming diverges. The Indian system uses names for everysecond power of ten:lakh (105),crore (107),arab (109),kharab (1011), etc. In thelong and short scales, there are names for everythird power of ten. The short scale uses million (106), billion (109), trillion (1012), etc.
The Indian system groups digits of a large decimal is represented differently than theInternational System of Units. The Indian system does group the first three digits to the left of the decimal point, but thereafter, groups by two digits to align with the naming of quantities at multiples of 100.[2]
| Indian | English |
|---|---|
| 5,00,000 | 500,000 |
| 12,34,56,789 | 123,456,789 |
| 17,00,00,00,000 | 17,000,000,000 |
| 6,78,90,00,00,00,00,000 | 6,789,000,000,000,000 |
Like English and other locales, the Indian system uses aperiod as thedecimal separator and thecomma for grouping, while others use a comma for decimal separator and athin space or point to group digits.[3]
When speakers of indigenous Indian languages are speaking English, the pronunciations may be closer to their mother tongue; e.g. "lakh" and "crore" might be pronounced /lɑkʰ/, /kɑrɔːr/, respectively.
The table below includes the spelling and pronunciation of numbers in various Indian languages along with corresponding short scale names.
| Value | Numerals | Short scale | Indian English | Hindustani Hindi /Urdu | Marathi | Bengali | Nepali | Tamil | Telugu | |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | one | one | एक /ایک (ēk) | एक (ēk) | এক (êk) | एक (ēk) | ஒன்று (oṉṟu) | ఒకటి (okaṭi) | |
| 10 | 10 | ten | ten | दस /دس (das) | दहा (dahā) | দশ (dôś) | दश (daś) | பத்து (pattu) | పది (padi) | |
| 102 | 100 | hundred | hundred | सौ /سو (sau) | शंभर (śambhar) | শত (śato) | सय (saya) | நூறு (nūṟu) | వంద/నూరు (vanda/nūru) | |
| 103 | 1,000 | thousand | thousand | हज़ार /ہزار (hazār) | एक हजार (ēk hajār) | হাজার (hāzār) | एक हजार (ēk hajār) | ஆயிரம் (āyiram) | వెయ్యి (veyyi) | |
| 104 | 10,000 | ten thousand | ten thousand | दस हज़ार /دس ہزار (das hazār) | दहा हजार (dahā hajār) | অযুত (ōjut) | দশ হাজার (dôś hāzār) | दश हजार (daś hajār) | பத்தாயிரம் (pattāyiram) ஆயுதம் (āyutam) | పది వేలు (padi vēlu) |
| 105 | 1,00,000 | hundred thousand | lakh | लाख /لاکھ (lākh) | एक लाख (ēk lākh) | লক্ষ (lôkkhō) | লাখ (lākh) | एक लाख (ēk lākh) | இலட்சம் (ilaṭcam) நியுதம் (niyutam) | లక్ష (lakṣa) |
| 106 | 10,00,000 | million | ten lakh | दस लाख /دس لاکھ (das lākh) | दहा लाख (dahā lākh) | নিযুত (nijut) | দশ লাখ (dôś lākh) | दश लाख (daś lākh) | பத்து இலட்சம் (pattu ilaṭcam) | పది లక్షలు (padi lakṣalu) |
| 107 | 1,00,00,000 | ten million | crore | करोड़ /کروڑ (karōṛ) | एक कोटी (ēk kōṭī) | কোটি (kōṭi) | एक करोड (ēk karoḍ) | கோடி (kōṭi) | కోటి (kōṭi) | |
| 108 | 10,00,00,000 | hundred million | ten crore | दस करोड़ /دس کروڑ (das karōṛ) | दहा कोटी (dahā kōṭī) | অর্বুদ (ōrbud) | দশ কোটি (dôś kōṭi) | दश करोड (daś karoḍ) | அற்புதம் (aṟputam) | పది కోట్లు (padi kōṭlu) |
| 109 | 1,00,00,00,000 | billion | arab / hundred crore | अरब /ارب (arab) सौ करोड़ /سو کروڑ (sau karōṛ) | एक अब्ज (ēk abja) | মহার্বুদ (môhārbud) | একশ কোটি (êkśō kōṭi) | एक अर्ब (ēk arba) | நிகற்புதம் (nikaṟputam) | వంద కోట్లు (vanda kōṭlu) |
| 1010 | 10,00,00,00,000 | ten billion | ten arab / thousand crore | दस अरब /دس ارب (das arab) एक हज़ार करोड़ /ایک ہزار کروڑ (ēk hazār karōṛ) | एक खर्व (ek kharva) | খর্ব (khôrbō) | হাজার কোটি (hāzār kōṭi) | दश अर्ब (daś arba) | கும்பம் (kumpam) | వెయ్యి కోట్లు (veyyi kōṭlu) |
| 1011 | 1,00,00,00,00,000 | hundred billion | kharab / hundred arab / ten thousand crore | खरब /کھرب (kharab) | एकनिखर्व (ek nikharva) | মহাখর্ব (môhākhôrbō) দশ হাজার কোটি (dôś hājār kōṭi) | एक खर्ब (ēk kharba) | கணம் (kaṇam) | పది వేల కోట్లు (padi vēla kōṭlu) | |
| 1012 | 10,00,00,00,00,000 | trillion | ten kharab / one thousand arab /one lakh crore | दस खरब /دس کھرب (das kharab) एक लाख करोड़ /ایک لاکھ کروڑ (ēk lākh karōṛ) | एक पद्म (ēk padma) | শঙ্খ (śôṅkhō) লাখ কোটি (lākh kōṭi) | दश खर्ब (daś kharba) | கற்பம் (kaṟpam) | లక్ష కోట్లు (lakṣa kōṭlu) | |
| 1013 | 1,00,00,00,00,00,000 | ten trillion | nil / hundred kharab / ten thousand arab / ten lakh crore | नील /نیل (nīl) | एक महापद्म (ek mahāpadma) | মহাশঙ্খ (môhāśôṅkhō) দশ লাখ কোটি (dôś lākh kōṭi) | नील (nīl) | நிகற்பம் (nikaṟpam) | పది లక్షల కోట్లు (padi lakṣala kōṭlu) | |
| 1014 | 10,00,00,00,00,00,000 | hundred trillion | ten nil /crore crore | दस नील /دس نیل (das nīl) एक करोड़ करोड़ /ایک کروڑ کروڑ (ēk karōṛ karōṛ) | एक शंखू (ēk śaṅkhū) | পদ্ম (pôddō) একশ লাখ কোটি (êkśō lākh kōṭi) শতলক্ষ কোটি (śôtôkōṭi lôkkō) | दश नील (daś nīl) | பதுமம் (patumam) | కోటి కోట్లు (kōṭi kōṭlu) | |
| 1015 | 1,00,00,00,00,00,00,000 | quadrillion | padma / hundred nil / ten crore crore | पद्म /پدم (padma) | एक जलधि शंखू (eka jaladhi śaṅkhū) | মহাপদ্ম (môhāpôddō) হাজার লাখ কোটি (hāzār lākh kōṭi) | पद्म (padma) | சங்கம் (caṅkam) | పది కోట్ల కోట్లు (padi kōṭla kōṭlu) | |
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 ValmikiRamayana.[4]
| Name | Indian decimal | Value | Short scale |
|---|---|---|---|
| एक (ēka) | 1 | 1 | one |
| दश (daśa) | 10 | 10 | ten |
| शत (śata) | 100 | 102 | hundred |
| सहस्र (sahasra) | 1,000 | 103 | thousand |
| लक्ष (lakṣa) | 1,00,000 | 105 | hundred thousand |
| कोटि (kōṭi) | 1,00,00,000 | 107 | ten million |
| शङ्कु (śaṅku) | 1,00,000koṭi | 1012 | trillion |
| महाशङ्कु (mahāśaṅku) | 1,00,000śaṅku | 1017 | hundred quadrillion |
| वृन्द (vr̥nda) | 1,00,000mahāśaṅku | 1022 | ten sextillion |
| महावृन्द (mahāvr̥nda) | 1,00,000vr̥nda | 1027 | octillion |
| पद्म (padma) | 1,00,000mahāvr̥nda | 1032 | hundred nonillion |
| महापद्म (mahāpadma) | 1,00,000padma | 1037 | ten undecillion |
| खर्व (kharva) | 1,00,000mahāpadma | 1042 | tredecillion |
| महाखर्व (mahākharva) | 1,00,000kharva | 1047 | hundred quattuordecillion |
| समुद्र (samudra) | 1,00,000mahākharva | 1052 | ten sexdecillion |
| ओघ (ogha) | 1,00,000samudra | 1057 | octodecillion |
| महौघ (mahaugha) | 1,00,000ogha | 1062 | hundred novemdecillion |
The denominations by which land was measured in theKumaon Kingdom were based on arable lands and thus followed an approximate system with local variations. The most common of these was avigesimal (base-20) numbering system with the main denomination called abisi (seeHindustani numberbīs), which corresponded to the land required to sow 20nalis of seed. Consequently, its actual land measure varied based on the quality of the soil.[5] This system became the established norm in Kumaon by 1891.[6]
Below is a list of translations for the words lakh and crore in other languages spoken in the Indian subcontinent:
| Language | Lakh | Crore | 100 crores (a billion) | 1000 crores (10 billion) | 10,000 crores (100 billion) |
|---|---|---|---|---|---|
| Assamese | লক্ষlokhyo, orলাখlakh | কৌটিkouti, orকোটিkoti | — | ||
| Bengali | লাখlākh[a], orলক্ষlokkho[b] | কোটিkōṭi | |||
| Burmese | lakh[c] | ကုဋေ[ɡədè] | |||
| Dhivehi | ލައްކަla'kha | ކްރޯރްkroaru | |||
| Gujarati | લાખlākh | કરોડkaroḍ | અબજabaj | — | |
| Hindi | लाखlākh | करोडkaroḍ | अरबarab | ||
| Kannada | ಲಕ್ಷlakṣha | ಕೋಟಿkōṭi | — | ||
| Khasi | lak | klur orkrur | arab | — | kharab |
| Malayalam | ലക്ഷംlaksham | കോടിkodi | — | ||
| Marathi | लाख/लक्षlākh | कोटीkoṭi, orकरोडkaroḍ | अब्जabja | — | |
| Nepali | लाखlākh | करोडkaroḍ | — | ||
| Odia | ଲକ୍ଷlôkhyô | କୋଟିkoṭi | |||
| Punjabi | lakkh (Gurmukhi:ਲੱਖ,Shahmukhi:لکھ) | karoṛ (Gurmukhi:ਕਰੋੜ,Shahmukhi:کروڑ) | |||
| Rohingya | lák | kurul | — | kuthí | — |
| Sinhala | ලක්ෂlakṣa | කෝටිkōṭi | — | ||
| Tamil | இலட்சம்ilaṭcam | கோடிkōṭi | |||
| Telugu | లక్షlakṣha | కోటిkōṭi | |||
| Urdu | لاکھlākh | کروڑkaroṛ | اربarab | — | کھربkharab |
| Swahili | laki | — | |||
Formal written publications in English in India tend to use lakh/crore for Indian currency and International numbering for foreign currencies.[7]
The official usage of this system is limited to the nations ofIndia,Pakistan andBangladesh. It is universally employed within these countries, and is preferred to the International numbering system.[8]
Sri Lanka andNepal used this system in the past but has switched to the International numbering system in recent years. In theMaldives, the term lakh is widely used in official documents and local speech. However, theInternational System of Units is preferred for higher denominations (such as millions).[citation needed]
Most institutions and citizens in India use the Indian number system. TheReserve Bank of India was noted as a rare exception in 2015,[9] whereas by 2024 the Indian system was used for amounts in rupees and the International system for foreign currencies throughout the Reserve Bank's website.[10]