South Asian numbering system
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The South Asian numbering system is used throughout the Indian subcontinent (India, Pakistan, Bangladesh, Nepal, and Sri Lanka). It is based on the Vedic numbering system in which numbers over 9,999 are written in two-digit groups rather than the three-digit groups used in most other parts of the world.
The terms lakh (100,000) and crore (10,000,000) are used in Indian English and Pakistani 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; 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) is written 1,00,00,00,000.
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Use of separators [edit]
The Indian numbering system uses separators differently from the Arabic system; besides the three least significant digits of the integer part, a comma divides every two rather than every three digits, thus:
| Indian System | Arabic System |
|---|---|
| 5,05,000 | 505,000 |
| 12,12,12,123 | 121,212,123 |
| 7,00,00,00,000 | 7,000,000,000 |
This accords with the Indian numbering system, which has units for thousand, hundred thousand, ten million, etc.
Names of numbers [edit]
The table below follows the short scale usage of billion being a thousand million. In India, following former British usage, the long scale was used, with one billion equivalent to one million million.
| Hindi/Urdu (transliteration) South Asian English |
Indian figure | Power notation |
Arabic figure | Short scale Arabic (long scale Arabic) |
|---|---|---|---|---|
| एक / ایک (ek) one |
1 | 100 | 1 | one |
| दस / دس (das) ten |
10 | 101 | 10 | ten Scientific (SI prefix): deca- |
| सौ / سو (sau) one hundred |
100 | 102 | 100 | one hundred SI prefix: hecto- |
| सहस्र (sahasra) Hindi / हज़ार/ہزار (hazār) Hindustani one thousand |
1,000 | 103 | 1,000 | one thousand SI prefix: kilo- |
| दस हज़ार / دس ہزار (das hazār) ten thousand |
10,000 | 104 | 10,000 | ten thousand |
| लाख / لاکھ (lākh) one lakh |
1,00,000 | 105 | 100,000 | one hundred thousand |
| अदन्त / ادنت (adant) / दस लाख/دس لاکھ (das lākh) ten lakh |
10,00,000 | 106 | 1,000,000 | one million SI prefix: mega- |
| करोड़ / کروڑ (karoṛ) one crore |
1,00,00,000 | 107 | 10,000,000 | ten million |
| दस करोड़ / دس کروڑ (das karoṛ) ten crore |
10,00,00,000 | 108 | 100,000,000 | one hundred million |
| अरब / ارب (arab) one arab / one hundred crore |
1,00,00,00,000 | 109 | 1,000,000,000 | one billion (one milliard) SI prefix: giga- |
| एक हज़ार करोड़ (ek hazār karoṛ) / دس ارب (das arab) ten arab / one thousand crore |
10,00,00,00,000 | 1010 | 10,000,000,000 | ten billion (ten milliard) |
| खरब / کھرب (kharab) one kharab / one hundred arab / ten thousand crore |
1,00,00,00,00,000 | 1011 | 100,000,000,000 | one hundred billion (one hundred milliard) |
| एक लाख करोड़ (ek lākh karoṛ) / دس کھرب (das kharab) ten kharab / one thousand arab / one lakh crore |
10,00,00,00,00,000 | 1012 | 1,000,000,000,000 | one trillion (one billion) SI prefix: tera- |
| नील / نیل (neel / nīl) one neel / one hundred kharab / ten thousand arab / ten lakh crore |
1,00,00,00,00,00,000 | 1013 | 10,000,000,000,000 | ten trillion (ten billion) |
| एक करोड़ करोड़ (ek karoṛ karoṛ) / دس نیل (das nīl) ten neel / one crore crore |
10,00,00,00,00,00,000 | 1014 | 100,000,000,000,000 | one hundred trillion (one hundred billion) |
| पद्म / پدم (padm) one padm / one hundred neel / ten crore crore |
1,00,00,00,00,00,00,000 | 1015 | 1,000,000,000,000,000 | one quadrillion (one billiard) SI prefix: peta- |
| दस पद्म / دس پدم (das padm) ten padm / one hundred crore crore |
10,00,00,00,00,00,00,000 | 1016 | 10,000,000,000,000,000 | ten quadrillion (ten billiard) |
| शङ्ख / شنکھ (shankh / śaṅkh) one shankh / one hundred padm / one thousand crore crore / one lakh lakh crore |
1,00,00,00,00,00,00,00,000 | 1017 | 100,000,000,000,000,000 | one hundred quadrillion (one hundred billiard) |
Larger numbers [edit]
The following hidden table shows names of larger numbers which are very rarely used or never used in South Asia. However the names of some large numbers may be disputed.
| More numbers (table is hidden) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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- The term crore (کرور [korur] in Persian) was also used in Iran until recent decades, but with the meaning of one half million (500,000), instead of ten million (10,000,000) in India.
- Instead of saying the higher numbers, it is more common to use lakh and crore repeatedly or in combination, e.g. saying 1 lakh crore for 1012 or one trillion.
- The terms neel, padm and shankh are more commonly found in old sections of Indian Mathematics.
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 Valmiki Ramayana.[1]
| Sanskrit (transliteration) | Indian figure | Power notation |
Arabic figure | Short scale Arabic |
|---|---|---|---|---|
| एक (eka) | 1 | 100 | 1 | one |
| दश (dasha) | 10 | 101 | 10 | ten |
| शत (shata) | 100 | 102 | 100 | hundred |
| सहस्र (sahasra) | 1,000 | 103 | 1,000 | one thousand |
| अयुत (ayuta) | 10,000 | 104 | 10,000 | ten thousand |
| लक्ष (lakṣa) one lakh | 1,00,000 | 105 | 100,000 | one hundred thousand |
| कोटि (koṭi) one crore | 1,00,000 śata | 107 | 10,000,000 | ten million |
| शङ्कु (śaṅku) | 1,00,000 koṭi | 1012 | 1,000,000,000,000 | one trillion |
| महाशङ्कु (mahā-śaṅku) | 1,00,000 śaṅku | 1017 | 100,000,000,000,000,000 | one hundred quadrillion |
| वृन्द (vṛnda) | 1,00,000 mahā-śaṅku | 1022 | 10,000,000,000,000,000,000,000 | ten sextillion |
| महावृन्द (mahā-vṛnda) | 1,00,000 vṛnda | 1027 | 1,000,000,000,000,000,000,000,000,000 | one octillion |
| पद्म (padma) | 1,00,000 mahā-vṛnda | 1032 | 100,000,000,000,000,000,000,000,000,000,000 | one hundred nonillion |
| महापद्म (mahā-padma) | 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 mahā-padma | 1042 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | one tredecillion |
| महाखर्व (mahā-kharva) | 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 mahā-kharva | 1052 | 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ten sexdecillion |
| ओघ (ogha) | 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/mahā-ogha) | 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 |
Usage in different languages [edit]
- In Bengali, a lakh is called লক্ষ lokkho and a crore is called কোটি koti.
- In Gujarati, a lakh is called લાખ lākh and a crore is called કરોડ karod. A hundred crore is called અબજ abaj.
- In Kannada, a lakh is called ಲಕ್ಷ laksha and a crore is called ಕೋಟಿ koti.
- 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 koti, and an Arab (109) is called अब्ज abja.
- In Oriya, a lakh is called ଲକ୍ଷ lakhya and a crore is called କୋଟି koti.
- In Sinhalese, a lakh is called ලක්ෂ laksha and a crore is called කෝටි koti.
- In Tamil, a lakh is called இலட்சம் latcham and a crore is called கோடி kodi.
- In Telugu, a lakh is called లక్ష laksha and a crore is called కోటి koti.
- In Urdu, a lakh is called لاکھ lākh and a crore is called کروڑ karod.
- In Mandarin, lakh (洛叉; luòchā) and crore (倶胝; jùzhī) are used.
- 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.
