Indian numbering system
 | This articleneeds additional citations forverification.(January 2018) |
TheIndian numbering systemis used in theIndian subcontinent(Bangladesh,Bhutan,India,Maldives,Nepal,Pakistan,Sri Lanka) to express large numbers. The termslakhor 1,00,000 (one hundred thousand, written as100,000in Pakistan, and outside theIndian subcontinent) andcroreor 1,00,00,000[1](ten million, written as10,000,000outside the subcontinent) are the most commonly used terms inIndian Englishto express large numbers in the system.
Comparison with Western system
[edit]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), and ten thousand (104). For higher powers of ten, the names no longer correspond. In the ancient Indian system still in use in regional languages of India, there are words for (1062). These names respectively starting at 1000 are sahasra, 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 calledone lakh,ten lakh,one crore,ten crore,one arab(orone hundred crore), and so on; there are new words for every second power of ten (105 + 2n):lakh(105),crore(107),arab(109),kharab(1011), 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 theshort 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 thedecimal pointand the comma digit-separator, while other languages and countries using the Western numbering system use thedecimal commaand thethin spaceor point to group digits.[2]
There are terms for numbers larger than 1 crore as well, but these are not commonly used. These include 1arab(equal to 100 crore or 1 billion (short scale)), 1kharab(equal to 100 arab or 100 billion (short scale)), 1nil(sometimestransliteratedasneel;equal to 100 kharab or 10 trillion), 1padma(equal to 100 nil or 1 quadrillion), 1shankh(equal to 100 padma or 100 quadrillion), and 1mahashankh(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 (onetrillion) becomes 1lakh crore,written as 10,00,00,00,00,000.
Examples
[edit]- lakh:150,000rupeesin India is referred to as "1.5 lakh rupees", which is written as 1,50,000 rupees;
- crore: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 thethousand,lakh,andcroreplaces.
Pronunciation in English
[edit]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.
- hazar /hæˈzɔː(ɹ̠)/
- lakh /læk/
- crore /krɔː(ɹ̠)/
- arab /æˈɹ̠æb/
- kharab /kʰæˈɹ̠æb/
Use of separators
[edit]The Indian numbering system usesseparatorsdifferently 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 hazar, 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, and 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
[edit]The table below follows theshort scaleusage of one billion being one thousand million. InIndia,BangladeshandPakistan,following former British usage, thelong scalewas used, with one billion equivalent to one million million.
| Indian English | Hindustani Hindi/Urdu |
Marathi | Bengali | Odia | Tamil | Telugu | Kannada | Malayalam | Nepali | Indian notation | Power notation |
International notation[4] | Short scaleWestern (long scaleWestern) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| One | एक/ایک (ēk) |
एक (ēk) |
এক (êk) |
ଏକ (ekå) |
ஒன்று (oṉṟu) |
ఒకటి (okaṭi) |
ಒಂದು (ಬಿಡಿ) (ondu) |
ഒന്ന് (onn) |
एक (ēk) |
1 | 100 | 1 | One |
| Ten | दस/دس (das) |
दहा (dahā) |
দশ (dôś) |
ଦଶ (dåśå) |
பத்து (pattu) |
పది (padi) |
ಹತ್ತು (hattu) |
പത്ത് (patt) |
दश (daś) |
10 | 101 | 10 | Ten SI prefix:deca- |
| One hundred | सौ/سو (sau) |
शंभर (śambhar) |
শত (śato) |
ଶହେ (śåhe) |
நூறு (nūṟu) |
వంద/నూరు (vanda/nūru) |
ನೂರು (nūru) |
നൂറ് (nuṟ) |
सय (saya) |
100 | 102 | 100 | Onehundred SI prefix:hecto- |
| One thousand | हज़ार /ہزار (hazār) |
एक हजार (ēk hajār) |
হাজার (hāzār) |
ହଜାର (håjārå) ସହସ୍ର (såhåsrå) |
ஆயிரம் (āyiram) |
వెయ్యి (veyyi) |
ಸಾವಿರ (sāvira) |
ആയിരം (āyiraṁ) |
एक हजार (ēk hajār) |
1,000 | 103 | 1,000 | Onethousand SI prefix:kilo- |
| Ten thousand | दस हज़ार/دس ہزار (das hazār) |
दहा हजार (dahā hajār) |
অযুত (ōjut) দশ হাজার (dôś hāzār) |
ଦଶ ହଜାର (dåśå håjārå) ଅୟୁତ (åyutå) |
பத்தாயிரம் (pattāyiram) ஆயுதம் (āyutam) |
పది వేలు (padi vēlu) |
ಹತ್ತು ಸಾವಿರ (ಅಯುತ) (hattu sāvira) |
പതിനായിരം (patināyiraṁ) |
दश हजार (daś hajār) |
10,000 | 104 | 10,000 | Ten thousand |
| Onelakh | लाख/لاکھ (lākh) |
एक लाख (ēk lākh) |
লক্ষ (lôkkhō) লাখ (lākh) |
ଲକ୍ଷ (låkṣå) |
இலட்சம் (ilaṭcam) நியுதம் (niyutam) |
లక్ష (lakṣa) |
ಲಕ್ಷ (lakṣa) |
ലക്ഷം (lakṣaṁ) |
एक लाख (ēk lākh) |
1,00,000 | 105 | 100,000 | One hundred thousand |
| Ten lakh | दस लाख/دس لاکھ (das lākh) |
दहा लाख (dahā lākh) |
নিযুত (nijut) দশ লাখ (dôś lākh) |
ଦଶ ଲକ୍ଷ (dåśå låkṣå) ନିୟୁତ (niyutå) |
பத்து இலட்சம் (pattu ilaṭcam) |
పది లక్షలు (padi lakṣalu) |
ಹತ್ತು ಲಕ್ಷ (ನಿಯುತ) (hattu lakṣa) |
പത്തുലക്ഷം (pattulakṣaṁ) |
दश लाख (daś lākh) |
10,00,000 | 106 | 1,000,000 | Onemillion SI prefix:mega- |
| Onecrore | 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 |
| Ten crore | दस करोड़/دس کروڑ (das karōṛ) |
दहा कोटी (dahā kōṭī) |
অর্বুদ (ōrbud) দশ কোটি (dôś kōṭi) |
ଦଶ କୋଟି (dåśå koṭi) ଅର୍ବୁଦ (årbudå) |
அற்புதம் (aṟputam) |
పది కోట్లు (padi kōṭlu) |
ಹತ್ತು ಕೋಟಿ (ಅರ್ಭುಧ) (hattu kōṭi) |
പത്തുകോടി (pattukōṭi) |
दश करोड (daś karoḍ) |
10,00,00,000 | 108 | 100,000,000 | One hundred million |
| One arab/one hundred crore | अरब/ارب (arab) सौ करोड़/سو کروڑ (sau karōṛ) |
एक अब्ज (ēk abja) |
মহার্বুদ (môhārbud) একশ কোটি (êkśō kōṭi) |
ଶହେ କୋଟି (śåhe koṭi) ବୃନ୍ଦ (brundå) |
நிகற்புதம் (nikaṟputam) |
వంద కోట్లు (vanda kōṭlu) |
ನೂರು ಕೋಟಿ (ಅಭ್ಜ) (nūru kōṭi) |
നൂറുകോടി (nūṟukōṭi) |
एक अर्ब (ēk arba) |
1,00,00,00,000 | 109 | 1,000,000,000 | Onebillion (onemilliard) SI prefix:giga- |
| Ten arab /one 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) |
ହଜାର କୋଟି (håjārå koṭi) ଖର୍ବ (khårbå) |
கும்பம் (kumpam) |
వెయ్యి కోట్లు (veyyi kōṭlu) |
ಒಂದು ಸಾವಿರ ಕೋಟಿ (ಕರ್ವ) (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) |
| One kharab / one hundred arab /ten thousand crore | खरब/کھرب (kharab) |
एकनिखर्व (ek nikharva) |
মহাখর্ব (môhākhôrbō) দশ হাজার কোটি (dôś hājār kōṭi) |
ଦଶ ହଜାର କୋଟି (dåśå håjārå koṭi) ନିଖର୍ବ (nikhårbå) |
கணம் (kaṇam) |
పది వేల కోట్లు (padi vēla kōṭlu) |
ಹತ್ತು ಸಾವಿರ ಕೋಟಿ (ನಿಕರ್ವ) (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) |
| 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) |
ଲକ୍ଷ କୋଟି (låkṣå koṭi) ଶଙ୍ଖ (śåṅkhå) |
கற்பம் (kaṟpam) |
లక్ష కోట్లు (lakṣa kōṭlu) |
ಒಂದು ಲಕ್ಷ ಕೋಟಿ (ಮಹಾಪದ್ಮ) (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 | Onetrillion (one billion) SI prefix:tera- |
| One nil / one hundred kharab / ten thousand arab /ten lakh crore | नील/نیل (nīl) |
एक महापद्म (ek mahāpadma) |
মহাশঙ্খ (môhāśôṅkhō) দশ লাখ কোটি (dôś lākh kōṭi) |
ଦଶ ଲକ୍ଷ କୋଟି (dåśå låkṣå koṭi) ପଦ୍ମ (pådmå) |
நிகற்பம் (nikaṟpam) |
పది లక్షల కోట్లు (padi lakṣala kōṭlu) |
ಹತ್ತು ಲಕ್ಷ ಕೋಟಿ (ಶಂಖು) (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) |
| Ten nil /one 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)f |
ଶହେ ଲକ୍ଷ କୋଟି (śåhe låkṣå koṭi) ସାଗର (sāgårå) |
பதுமம் (patumam) |
కోటి కోట్లు (kōṭi kōṭlu) |
ಒಂದು ಕೋಟಿ ಕೋಟಿ (ಜಲಧಿ) (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) |
| One padma / one hundred nil /ten crore crore | पद्म/پدم (padma) |
एक जलधि शंखू (eka jaladhi śaṅkhū) |
মহাপদ্ম (môhāpôddō) হাজার লাখ কোটি (hāzār lākh kōṭi) |
ହଜାର ଲକ୍ଷ କୋଟି (håjārå låkṣå koṭi) ଅନ୍ତ୍ୟ (åntyå) |
சங்கம் (caṅkam) |
పది కోట్ల కోట్లు (padi kōṭla kōṭlu) |
ಹತ್ತು ಕೋಟಿ ಕೋಟಿ (ಅಂತ್ಯ) (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 | Onequadrillion (onebilliard) SI prefix:peta- |
| Ten padma /one hundred crore crore | दस पद्म/دس پدم (das padma) |
एक अंत्य (eka antya) |
দশ হাজার লাখ কোটি (dôś hāzār lākh kōṭi) |
ଦଶ ହଜାର ଲକ୍ଷ କୋଟି (dåśå håjārå låkṣå koṭi) ମଧ୍ୟ (mådhyå) |
வெள்ளம் (veḷḷam) சமுத்திரம் (camuttiram) |
వంద కోట్ల కోట్లు (vanda kōṭla kōṭlu) |
ನೂರು ಕೋಟಿ ಕೋಟಿ (ಮಧ್ಯ) (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) |
| One shankh / one hundred padma /one thousand crore crore/one lakh lakh crore | शंख/شنکھ (śaṅkh) |
एक परार्ध (eka parārdha) |
শত হাজার লাখ কোটি (śoto hāzār lākh kōṭi) |
ଶହେ ହଜାର ଲକ୍ଷ କୋଟି (śåhe håjārå låkṣå koṭi) ପରାର୍ଦ୍ଧ (pårārddhå) |
அந்நியம் (anniyam) |
వెయ్యి కోట్ల కోట్లు (veyyi kōṭla kōṭlu) |
ಒಂದು ಸಾವಿರ ಕೋಟಿ ಕೋಟಿ (ಪರಾರ್ಧ) (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) |
| Ten shankh /ten thousand crore crore | दस शंख/دس شنکھ (das śaṅkh) गुलशन/گلشن (gulśan) |
एक महापरार्ध (eka mahāparārdha) |
গুলশান (gulśān) দশ শত হাজার লাখ কোটি (doś śoto hāzār lākh kōṭi) |
ଦଶ ଶହେ ହଜାର ଲକ୍ଷ କୋଟି (dåśå śåhe håjārå låkṣå koṭi) ଦଶ ପରାର୍ଦ୍ଧ (dåśå pårārddhå) |
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 | Onequintillion (one trillion) SI prefix:exa- |
Historic numbering systems
[edit]Numbering systems in Hindu epics
[edit]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.[5]
| Name | Indian notation | Power notation | Indian system | Short scaleWestern |
|---|---|---|---|---|
| एक(ēka) | 1 | 100 | One | One |
| दश(daśa) | 10 | 101 | Ten | Ten |
| शत(śata) | 100 | 102 | One hundred | One hundred |
| सहस्र(sahasra) | 1,000 | 103 | One thousand | One thousand |
| लक्ष(lakṣa) | 1,00,000 | 105 | One lakh | One hundred thousand |
| कोटि(kōṭi) |
1,00,00,000 | 107 | One crore | Tenmillion |
| शङ्कु(śaṅku) | 1,00,000koṭi | 1012 | Ten kharab or One lakh crore | Onetrillion |
| महाशङ्कु(mahāśaṅku) | 1,00,000śaṅku | 1017 | One shankh or One thousand crore crore | One hundredquadrillion |
| वृन्द(vr̥nda) | 1,00,000mahāśaṅku | 1022 | Tensextillion | |
| महावृन्द(mahāvr̥nda) | 1,00,000vr̥nda | 1027 | Oneoctillion | |
| पद्म(padma) | 1,00,000mahāvr̥nda | 1032 | One hundrednonillion | |
| महापद्म(mahāpadma) | 1,00,000padma | 1037 | Tenundecillion | |
| खर्व(kharva) | 1,00,000mahāpadma | 1042 | Onetredecillion | |
| महाखर्व(mahākharva) | 1,00,000kharva | 1047 | One hundredquattuordecillion | |
| समुद्र(samudra) | 1,00,000mahākharva | 1052 | Tensexdecillion | |
| ओघ(ogha) | 1,00,000samudra | 1057 | Oneoctodecillion | |
| महौघ(mahaugha) | 1,00,000ogha | 1062 | One hundrednovemdecillion |
Other numbering systems
[edit]The denominations by which land was measured in theKumaon Kingdomwere 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 20nalisof seed. Consequently, its actual land measure varied based on the quality of the soil.[6]This system became the established norm in Kumaon by 1891.[7]
Usage in different languages
[edit]Below is a list of translations for the words lakh and crore in other languages spoken in the Indian subcontinent:
- InAssamese,a lakh is also calledলক্ষlokhyo,orলাখlakhand a crore is calledকৌটি বা কোটিkouti
- InBengali,a lakh is natively (tadbhava) known asলাখlākh,though some use the ardha-tatsamaলক্ষlokkho.A crore is calledকোটিkōṭi
- InBurmese,crore is calledကုဋေ[ɡədè].Lakh is used inBurmese English.
- InDhivehi,a lakh is called ލައްކަ la'kha and a crore is called ކްރޯރް kroaru
- InGujarati,a lakh is calledલાખlākhand a crore is calledકરોડkaroḍ.A hundred crore is calledઅબજabaj
- InHindi,a lakh is calledलाखlākhand a crore is calledकरोडkaroḍ.A hundred crore is calledअरबarab
- InKannada,a lakh is calledಲಕ್ಷlakṣhaand a crore is calledಕೋಟಿkōṭi
- InKhasi,a lakh is calledlakand a crore is calledklurorkrur.A billion is calledaraband hundred billion is calledkharab.
- InMalayalam,a lakh is calledലക്ഷംlakshamand a crore is calledകോടിkodi.
- InMarathi,a lakh is calledलाख/लक्षlākhand a crore is calledकोटीkoṭiorकरोडkaroḍ,and an arab (109) is calledअब्जabja.
- InNepali,a lakh is calledलाखlākhand a crore is calledकरोडkaroḍ.
- InOdia,a lakh is calledଲକ୍ଷlôkhyôand a crore is calledକୋଟିkoṭi.
- InPunjabi,a lakh is calledlakkh(Shahmukhi:لکھ,Gurmukhi:ਲੱਖ) and a crore is calledkaroṛ(Shahmukhi:کروڑ,Gurmukhi:ਕਰੋੜ).
- InRohingya,a lakh is calledlákand a crore is calledkurul.A thousand crore is calledkuthí.
- InSinhala,a lakh is calledලක්ෂlakṣaand a crore is calledකෝටිkōṭi.
- InTamil,a lakh is calledஇலட்சம்ilaṭcamand a crore is calledகோடிkōṭi.
- InTelugu,a lakh is calledలక్షlakṣhaand a crore is calledకోటిkōṭi.
- InUrdu,a lakh is calledلاکھlākhand a crore is calledکروڑkaroṛ.A billion is calledarab(ارب), and one hundred billion/arab is called akharab(کھرب).
- Lakh has entered theSwahili languageas "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.[8]
Current usage
[edit]The usage of this system is limited to the nations ofIndia,Pakistan,Bangladesh,andMyanmar.It is universally employed within these countries, and is preferred to the English numbering system.[9]
Sri Lankaused this system in the past but has switched to the English numbering system in recent years.
In theMaldives,the term lakh is widely used in official documents and local speech. However, theWesternised Hindu-Arabicnumeral systemis preferred for higher denominations (such as millions).
Most institutions and citizens in India use the Indian number system. TheReserve Bank of Indiawas noted as a rare exception in 2015,[10]whereas by 2024 the Indian system was used for amounts in rupees and the Western system for foreign currencies throughout the Reserve Bank's website.[11]
See also
[edit]References
[edit]- ^"Knowing our Numbers".Department Of School Education And Literacy.National Repository of Open Educational Resources. Archived fromthe originalon 16 February 2016.Retrieved13 February2016.
- ^"Decimal and Thousands Separators (International Language Environments Guide)".docs.oracle.Retrieved29 April2021.
- ^Emmons, John (25 March 2018)."UNICODE LOCALE DATA MARKUP LANGUAGE (LDML) PART 3: NUMBERS".Unicode.org.Archivedfrom the original on 25 July 2018.Retrieved25 March2018.
- ^Use of separator in digit grouping here follows customs in most English-speaking countries. For international standards and details, seedecimal mark.
- ^"Valmiki Ramayana - Yuddha Kanda, Chapter (Sarga) 28,(Verses 33 – 38)".Retrieved15 July2021.
- ^Traill, G.W. (1828). Batten, J.H. (ed.).Statistical Sketch of Kamaon.John Murray.p. 34.
- ^"North Indian Notes and Queries".Google Books.1–3.Pioneer Press: 216. 1891.
- ^Shapiro, Richard (16 August 2012)."The most distinctive counting system in English? Indian cardinal numbers".Oxford English Dictionary.Archivedfrom the original on 30 June 2020.Retrieved24 May2020.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 ofOxford University Press."
- ^Krulwich, Robert; Block, Ezra (21 October 2010)."Hey! Who Can Explain What India Does With Its Commas? (Not Commies. Commas.)".NPR.Retrieved3 August2020.
- ^Gurpur (10 August 2015)."Can we follow Indian numbering system for simplicity and good order?".Moneylife News & Views.Retrieved3 September2020.
- ^Reserve Bank of India,oldandnew website(known on archive.org since 5 Apr 2024). Retrieved 16 Apr 2024.