Indian numbering system
The Indic numbering system is used in South Asian countries (Bangladesh, Bhutan, India , Maldives, Nepal, Pakistan , Sri Lanka) to express large numbers. The terms lakh or 1,00,000 (one hundred thousand, written as 100,000 outside the Indian subcontinent) and crore or 1,00,00,000[1] (ten million, written as 10,000,000 outside the subcontinent) are the most commonly used terms in Indic English to express large numbers in the system.
Comparison with Western system
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 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), 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 the short 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 the decimal point and the comma digit-separator, while other languages and countries using the Western numbering system use the decimal comma and the thin space or point to group digits.[2]
There are terms for numbers larger than 1 crore as well, but these are not commonly used. These include 1 arab (equal to 100 crore or 1 billion (short scale)), 1 kharab (equal to 100 arab or 100 billion (short scale)), 1 nil (sometimes 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.
Examples
- lakh: 150,000 rupees in 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 the thousand, lakh, and crore places.
Pronunciation in English
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
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.[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
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.
| Indian English | Hindustani Hindi / Urdu |
Marathi | Bengali | Odia | Tamil | Telugu | Kannada | Malayalam | Nepali | Indian notation | Power notation |
International notation[4] | Short scale Western (long scale Western) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 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) |
একশ (êkśō) |
ଶହେ (śåhe) |
நூறு (nūṟu) |
వంద/నూరు (vanda/nūru) |
ನೂರು (nūru) |
നൂറ് (nuṟ) |
सय (saya) |
100 | 102 | 100 | One hundred 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 | One thousand SI prefix: kilo- |
| Ten thousand | दस हज़ार / دس ہزار (das hazār) |
दहा हजार (dahā hajār) |
দশ হাজার (dôś hāzār) অযুত (ōjut) |
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 |
| One lakh | 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) |
দশ লাখ (dôś lākh) নিযুত (nijut) |
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 | One million SI prefix: mega- |
| One crore | 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) |
দশ কোটি (dôś kōṭi) অর্বুদ (ōrbud) |
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 / one hundred crore | अरब / ارب (arab) सौ करोड़ / سو کروڑ (sau karōṛ) |
एक अब्ज (ēk abja) |
একশ কোটি (êkśō kōṭi) মহার্বুদ (môhārbud) |
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 | One billion (one milliard) SI prefix: giga- |
| Ten / one thousand crore | दस अरब / دس ارب (das arab) एक हज़ार करोड़ / ایک ہزار کروڑ (ēk hazār karōṛ) |
एक खर्व (ek kharva) |
হাজার কোটি (hāzār kōṭi) খর্ব (khôrbō) |
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) |
एक निखर्व (ek nikharva) |
দশ হাজার কোটি (dôś hājār kōṭi) মহাখর্ব (môhākhôrbō) |
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) |
লাখ কোটি (lākh kōṭi) শঙ্খ (śôṅkhō) |
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 | One trillion (one billion) SI prefix: tera- |
| One nil / one hundred kharab / ten thousand arab / ten lakh crore | नील / نیل (nīl) |
एक महापद्म (ek mahāpadma) |
দশ লাখ কোটি (dôś lākh kōṭi) পদ্ম (pôddō) মহাশঙ্খ (môhāśôṅkhō) |
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) |
একশ লাখ কোটি (êkśō lākh kōṭi) শতকোটি লক্ষ (śôtôkōṭi lôkkō) মহাপদ্ম (môhāpôddō) |
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) |
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 | One quadrillion (one billiard) 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) |
দশ শত হাজার লাখ কোটি (doś śoto hāzār lākh kōṭi) গুলশান (gulśān) |
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 | One quintillion (one trillion) SI prefix: exa- |
Historic numbering systems
Numbering systems in Hindu epics
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 Valmiki Ramayana.[5]
| Name | Indian notation | Power notation | Indian system | Short scale Western |
|---|---|---|---|---|
| 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 | Ten million |
| शङ्कु (śaṅku) | 1,00,000 koṭi | 1012 | Ten kharab or One lakh crore | One trillion |
| महाशङ्कु (mahāśaṅku) | 1,00,000 śaṅku | 1017 | One shankh or One thousand crore crore | One hundred quadrillion |
| वृन्द (vr̥nda) | 1,00,000 mahāśaṅku | 1022 | Ten sextillion | |
| महावृन्द (mahāvr̥nda) | 1,00,000 vr̥nda | 1027 | One octillion | |
| पद्म (padma) | 1,00,000 mahāvr̥nda | 1032 | One hundred nonillion | |
| महापद्म (mahāpadma) | 1,00,000 padma | 1037 | Ten undecillion | |
| खर्व (kharva) | 1,00,000 mahāpadma | 1042 | One tredecillion | |
| महाखर्व (mahākharva) | 1,00,000 kharva | 1047 | One hundred quattuordecillion | |
| समुद्र (samudra) | 1,00,000 mahākharva | 1052 | Ten sexdecillion | |
| ओघ (ogha) | 1,00,000 samudra | 1057 | One octodecillion | |
| महौघ (mahaugha) | 1,00,000 ogha | 1062 | One hundred novemdecillion |
Other numbering systems
The denominations by which land was measured in the Kumaon Kingdom were based on arable lands and thus followed an approximate system with local variations. The most common of these was a vigesimal (base-20) numbering system with the main denomination called a bisi (see Hindustani number bīs), which corresponded to the land required to sow 20 nalis of 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
- 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 Dhivehi, a lakh is called ލައްކަ la'kha and a crore is called ކްރޯރް kroaru
- In Gujarati, a lakh is called લાખ lākh and a crore is called કરોડ karoḍ. A hundred crore is called અબજ abaj
- In Hindi, a lakh is called लाख lākh and a crore is called करोड karoḍ. A hundred crore is called अरब arab
- 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 lôkhyô and a crore is called କୋଟି koṭi.
- 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 ilaṭcam and a crore is called கோடி kōṭi.
- 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.[8]
Current usage
The usage of this system is limited to the nations of India , Pakistan , Bangladesh, and Myanmar. It is universally employed within these countries, and is preferred to the English numbering system.[9]
Sri Lanka used this system in the past but has switched to the English numbering system in recent years.
In the Maldives, the term lakh is widely used in official documents and local speech. However, the Westernised Hindu-Arabic numeral system is preferred for higher denominations (such as millions).
Most institutions and citizens in India use the Indian number system, although the Reserve Bank of India has been noted as a rare exception.[10]
See also
References
- ↑ "Knowing our Numbers". National Repository of Open Educational Resources. http://nroer.gov.in/nroer_team/file/readDoc/55b23f2881fccb054b6be25f/.
- ↑ "Decimal and Thousands Separators (International Language Environments Guide)". https://docs.oracle.com/cd/E19455-01/806-0169/overview-9/index.html.
- ↑ Emmons, John (2018-03-25). "UNICODE LOCALE DATA MARKUP LANGUAGE (LDML) PART 3: NUMBERS". https://www.unicode.org/reports/tr35/tr35-numbers.html#Special_Pattern_Characters.
- ↑ 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, Chapter (Sarga) 28,(Verses 33 – 38)". http://valmikiramayan.pcriot.com/utf8/yuddha/sarga28/yuddha_28_frame.htm.
- ↑ Traill, G.W. (1828). Batten, J.H.. ed. Statistical Sketch of Kamaon. John Murray. p. 34. https://archive.org/details/in.ernet.dli.2015.53201/page/n48/mode/1up?q=bisi.
- ↑ North Indian Notes and Queries. 1-3. Pioneer Press. 1891. p. 216. https://books.google.com/books?id=b5gsAAAAMAAJ&dq=bisi+twenty+base+counting+system+india&pg=PA216.
- ↑ Shapiro, Richard (2012-08-16). "The most distinctive counting system in English? Indian cardinal numbers". Oxford English Dictionary. https://public.oed.com/blog/the-most-distinctive-counting-system-in-english-indian-cardinal-numbers/. - 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?" (in en). https://www.npr.org/sections/krulwich/2010/10/19/130674804/counting-millionaire-india.
- ↑ Gurpur (10 August 2015). "Can we follow Indian numbering system for simplicity and good order?". https://www.moneylife.in/article/can-we-follow-indian-numbering-system-for-simplicity-and-good-order/43059.html.
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