Indian numbering system

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The Indian numbering system is used in the Indian subcontinent (Bangladesh, India, Nepal, Maldives, Pakistan and Sri Lanka) and in Burma. The terms lakh (100,000 or 1,00,000 in the Indian system) and crore (10,000,000 or 1,00,00,000 in the Indian system)[1] are used in Indian English to express large numbers. For example, in India 150,000 rupees becomes 1.5 lakh rupees, written as 1,50,000 or INR 1,50,000, while 30,000,000 (thirty million) rupees becomes 3 crore rupees, written as 3,00,00,000 with commas at the thousand, lakh, and crore levels, and 1,000,000,000 (one billion) rupees (one hundred crore rupees or one arab अरब ) is written 1,00,00,00,000. While there are specific terms for numbers larger than 1 crore, these are not commonly used, and most practitioners are not familiar with these. In common parlance, the thousand, lakh, crore terminology repeats for larger numbers. Thus 1,000,000,000,000 (one trillion) becomes 1 lakh crore, and is written as 10,00,00,00,00,000.

The Indian numbering is equal to the western numbering system from ones then tens then hundreds then thousand then ten thousand. After ten thousand, the Indian and the western numbering diverge. According to the Indian numbering system, after ten thousand, the next power of ten is one lakh, then ten lakh, then one crore, then ten crore, and so on. According to the Western numbering system, after ten thousand, the next power of ten is referred to as one hundred thousand, then one million, then ten million, then one hundred million, and so on. The two numbering systems are not functionally different — 10,000 (Indian system) = 10,000 (Western system) — but they assign different names to the same number.

Use of separators[edit]

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 one lakh crore (or 10 kharab). This makes the number convenient to read using thousand, lakh, crore terminology. Thus:

Indian system Western system In words (Indian) In words (Western)
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 One thousand seven hundred crore Seventeen billion
6,78,90,00,00,00,000 67,890,000,000,000 Sixty-seven lakh, eighty-nine thousand crore Sixty-seven trillion, eight hundred ninety billion

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 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.

Names of numbers
Hindi / Urdu / Tamil / Telugu / Bengali / Marathi / Kannada (transliteration)
South Asian English
Indian figure Power
notation
International figure[3] Short scale Western
(long scale Western)
एक / ایک (ek) /ஒன்று/ஏகம் (Ondru/Ekam) / ఒకటి (okati) / এক (êk) / एक / ಒಂದು
one
1 100 1 One
दस / دس (das) /பத்து (Pathu) / పది (padi) / দশ (dôsh) / दहा / ಹತ್ತು
ten
10 101 10 Ten
Scientific (SI prefix): deca-
सौ / سو (sau) /நூறு (Nooru) / వంద (vandha) / একশ (êkshô) / शंभर / ನೂರು
one hundred
100 102 100 One hundred
SI prefix: hecto-
सहस्र (sahasra) / हज़ार / ہزار (hazār) / ஆயிரம் (Aayiram) / వెయ్యి (Veyyi) / হাজার (hazar) / एक हजार / ಸಾವಿರ
one thousand
1,000 103 1,000 One thousand
SI prefix: kilo-
दस हज़ार / دس ہزار (das hazār) /பத்தாயிரம்/ஆயுதம் (Pathaayiram/Ayutham) / పది వేలు (padi vēlu) /দশ হাজার (dôsh hazar) / दहा हजार / ಹತ್ತು ಸಾವಿರ
ten thousand
10,000 104 10,000 Ten thousand
लाख / لاکھ (lākh) / இலட்சம்/நியுதம் (Latcham/Niyutham) / లక్ష (Lakṣa) / লাখ (lakh) / एक लाख / ಲಕ್ಷ
one lakh (also lac)
1,00,000 105 100,000 One hundred thousand
अदन्त / ادنت (adant) / दस लाख / دس لاکھ (das lākh) / பத்து இலட்சம் (Pathu Latcham) /పది లక్షలు (padi Lakṣalu) / দশ লাখ (dôsh lakh) / दहा लाख / ಹತ್ತು ಲಕ್ಷ
ten lakh
10,00,000 106 1,000,000 One million
SI prefix: mega-
करोड़ / کروڑ (karoṛ) / கோடி (Kodi) / కోటి (Kōṭi)/ কোটি (koti) / एक कोटी / ಕೋಟಿ
one crore
1,00,00,000 107 10,000,000 Ten million
दस करोड़ / دس کروڑ (das karoṛ) / அற்புதம் (Arputham) / పది కోట్లు (Padi kōṭlu)/ দশ কোটি (dôsh koti) / दहा कोटी / ಹತ್ತು ಕೋಟಿ
ten crore
10,00,00,000 108 100,000,000 One hundred million
अरब / ارب (arab) / सौ करोड़ (sau karoṛ) /நிகற்புதம் (Nigarputham) / వంద కోట్లు (vandha kōṭlu)/ একশ কোটি (êkshô koti) / शंभर कोटी / ನೂರು ಕೋಟಿ
one arab / one hundred crore
100,00,00,000 109 1,000,000,000 One billion
(one milliard)
SI prefix: giga-
एक हजार करोड़ (ek hazār karoṛ) / دس ارب (das arab) /கும்பம் (Kumbam) / వెయ్యి కోట్లు (Veyyi kōṭlu)/ এক হাজার কোটি (êk hazar koti) / एक हजार कोटी / ಒಂದು ಸಾವಿರ ಕೋಟಿ
one thousand crore / ten arab
1,000,00,00,000 1010 10,000,000,000 Ten billion
(ten milliard)
खरब / کھرب (kharab) / கணம் (Ganam) /పది వేల కోట్లు (Padi vēla kōṭlu) / দশ হাজার কোটি (dôsh hazar koti) / दहा हजार कोटी / ಹತ್ತು ಸಾವಿರ ಕೋಟಿ
ten thousand crore / one kharab / one hundred arab
10,000,00,00,000 1011 100,000,000,000 One hundred billion
(one hundred milliard)
एक लाख करोड़ (ek lākh karoṛ) / دس کھرب (das kharab) / கற்பம் (Karpam) / లక్ష కోట్లు (Lakṣa kōṭlu) / এক লাখ কোটি (êk lakh koti) / एक लाख कोटी / ಒಂದು ಲಕ್ಷ ಕೋಟಿ
one lakh crore / ten kharab / one thousand arab
1,00,000,00,00,000 1012 1,000,000,000,000 One trillion
(one billion)
SI prefix: tera-
नील / نیل (nīl) /நிகற்பம் (Nikarpam) / పది లక్షల కోట్లు (Padi Lakṣala kōṭlu) / দশ লাখ কোটি (dôsh lakh koti) / दहा लाख कोटी / ಹತ್ತು ಲಕ್ಷ ಕೋಟಿ
ten lakh crore / one neel / one hundred kharab / ten thousand arab
10,00,000,00,00,000 1013 10,000,000,000,000 Ten trillion
(ten billion)
एक करोड़ करोड़ (ek karod karod) / دس نیل (das nīl) / பதுமம் (Padhumam) /కోటి కోట్లు (Kōṭi kōṭlu)/ শত লাখ কোটি (shôtô lakh koti) / ಒಂದು ಕೋಟಿ ಕೋಟಿ
one crore crore / ten neel
1,00,00,000,00,00,000 1014 100,000,000,000,000 One hundred trillion
(one hundred billion)
पद्म / پدم (padma) / சங்கம் (Sangam) /పది కోటి కోట్లు (Padi Kōṭi kōṭlu) / হাজার লাখ কোটি (hajar lakh koti) / ಹತ್ತು ಕೋಟಿ ಕೋಟಿ
one padma / one hundred neel / ten crore crore
10,00,00,000,00,00,000 1015 1,000,000,000,000,000 One quadrillion
(one billiard)
SI prefix: peta-
दस पद्म / دس پدم (das padm) /வெள்ளம்/சமுத்திரம் (Vellam/Samuthiram) / వంద కోటి కోట్లు (Vandha Kōṭi kōṭlu) / দশ হাজার লাখ কোটি (dôsh hajar lakh koti) / ನೂರು ಕೋಟಿ ಕೋಟಿ
ten padma / one hundred crore crore
100,00,00,000,00,00,000 1016 10,000,000,000,000,000 Ten quadrillion
(ten billiard)
शङ्ख (शंख) / شنکھ (śaṅkh) / அந்நியம் (Anniyam) / వెయ్యి కోటి కోట్లు (Veyyi Kōṭi kōṭlu) / শত হাজার লাখ কোটি (shôtô hajar lakh koti) / ಒಂದು ಸಾವಿರ ಕೋಟಿ ಕೋಟಿ
one shankh / one hundred padma / one thousand crore crore / one lakh lakh crore
1,000,00,00,000,00,00,000 1017 100,000,000,000,000,000 One hundred quadrillion
(one hundred billiard)
गुलशन / گلشن (Gulshan) / அர்த்தம் (Artham) / పది వేల కోటి కోట్లు (Padi vēla Kōṭi kōṭlu) / দশ শত হাজার লাখ কোটি (dôsh shôtô hajar lakh koti) / ಹತ್ತು ಸಾವಿರ ಕೋಟಿ ಕೋಟಿ
(ten shankh / ten thousand crore crore)
10,000,00,00,000,00,00,000 1018 1,000,000,000,000,000,000 One quintillion
(one trillion)
SI prefix: exa-

Vedic numbering systems[edit]

There are various systems of numeration found in various ancient Vedic literatures of India. The following table gives one such system used in the Tamil ancient numbering system.

Indian figure Power
notation
Equivalent numeric representation Short scale Western
एक (eka) 0,00,001 100 1 One
दश (daśa) 0,00,010 101 10 Ten
शत (śata) 0,00,100 102 100 One hundred
सहस्र (sahasra) 0,01,000 103 1,000 One thousand
अयुत (ayuta) 0,10,000 104 10,000 Ten thousand
लक्ष (lakṣa) 1,00,000 105 1,00,000 One hundred thousand
नियुत (niyuta) 1,00,000 daśa 106 10,00,000 One million
कोटि (koṭi)
1,00,000 śata 107 1,00,00,000 Ten million
शङ्कु (śaṅku) 1,00,000 koṭi 1012 1,00000,00,00,000 One trillion
महाशङ्कु (mahā-śaṅku) 1,00,000 śaṅku 1017 1,00000,00000,00,00,000 One hundred quadrillion
वृन्द (vṛnda) 1,00,000 mahā-śaṅku 1022 1,00000,00000,00000,00,00,000 Ten sextillion (ten trilliard)
महावृन्द (mahā-vṛnda) 1,00,000 vṛnda 1027 1,00000,00000,00000,00000,00,00,000 One octillion
पद्म (padma) 1,00,000 mahā-vṛnda 1032 1,00000,00000,00000,00000,00000,00,00,000 One hundred nonillion
महापद्म (mahā-padma) 1,00,000 padma 1037 1,00000,00000,00000,00000,00000,00000,00,00,000 Ten undecillion
खर्व (kharva) 1,00,000 mahā-padma 1042 1,00000,00000,00000,00000,00000,00000,00000,00,00,000 One tredecillion
महाखर्व (mahā-kharva) 1,00,000 kharva 1047 1,00000,00000,00000,00000,00000,00000,00000,00000,00,00,000 One hundred quattuordecillion
समुद्र (samudra) 1,00,000 mahā-kharva 1052 1,00000,00000,00000,00000,00000,00000,00000,00000,00000,00,00,000 Ten sexdecillion
ओघ (ogha) 1,00,000 samudra 1057 1,00000,00000,00000,00000,00000,00000,00000,00000,00000,00000,00,00,000 One octodecillion
महौघ (mahaugha) 1,00,000 ogha 1062 1,00000,00000,00000,00000,00000,00000,00000,00000,00000,00000,00000,00,00,000 One hundred novemdecillion

Usage in different languages[edit]

  • In Punjabi, a lakh is called lakkh (Shahmukhi: لکھ, Gurmukhi: ਲੱਖ) and a crore is called karoṛ (Shahmukhi: کروڑ, Gurmukhi: ਕਰੋੜ).
  • In Bengali, a lakh is also called লক্ষ lokkho (ardha-tatsama), or laakh (tadbhava) and a crore is called কোটি koti.
  • In Gujarati, a lakh is called લાખ lākh and a crore is called કરોડ karoḍ. A hundred crore is called અબજ abaj.
  • In Sylheti, a lakh is called লাখ lakh (lax) and a crore is called কোটি kuti.
  • In Kannada, a lakh is called ಲಕ್ಷ lakṣha and a crore is called ಕೋಟಿ kōṭi.
  • In Malayalam, a lakh is called ലക്ഷം laksham and a crore is called കോടി kodi.
  • In Marathi, a lakh is called लाख 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 Sinhalese, a lakh is called ලක්ෂ lakṣa and a crore is called කෝටි kōṭi.
  • In Tamil, a lakh is called நூறாயிரம் nooRaayiram as well as இலட்சம் 'ilatcham and a crore is called கோடி kodi.
  • In Telugu, a lakh is called లక్ష lakṣa 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).
  • Lakh has entered the Swahili language as "laki" and is in common use.
  • In Burmese, crore is called ကုဋေ [ɡədè]. Lakh is used in Burmese English.

References[edit]

  1. ^ "Knowing our Numbers". Department Of School Education And Literacy. National Repository of Open Educational Resources. Retrieved 13 February 2016.
  2. ^ Emmons, John (2018-03-25). "UNICODE LOCALE DATA MARKUP LANGUAGE (LDML) PART 3: NUMBERS". Unicode.org. Archived from the original on 2018-07-25. Retrieved 2018-03-25.
  3. ^ Use of separator in digit grouping is following customs in most English speaking countries. For international standard and details cf. Decimal mark