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Indian numbering system
The Indian numbering system is commonly used in Indian English and across the Indian subcontinent to represent large numbers. Key terms include "lakh," which stands for one hundred thousand, and "crore," which means ten million, and these are written as 1,00,000 for a lakh and 1,00,00,000 for a crore.[1] For instance, 150,000 rupees is expressed as "1.5 lakh rupees" or written as "150,000 rupees." Similarly, 30,000,000 rupees is referred to as "3 crore rupees" and can be written as "3,00,00,000 rupees".
There are specific terms for numbers larger than a crore. These terms include "arab,"[lower-alpha 1] which represents 100 crores or 1 billion; "kharab,"[lower-alpha 2] meaning 100 arab or 100 billion; "nil" (sometimes written as "neel"),[lower-alpha 3] equivalent to 100 kharab or 10 trillion; "padma,"[lower-alpha 4] which stands for 100 nil or 1 quadrillion; "shankh,"[lower-alpha 5] representing 100 padma or 100 quadrillion; and "mahashankh,"[lower-alpha 6] which equals 100 shankh or 10 quintillion. In everyday language, the terms lakh and crore are often repeated for larger figures, so "lakh crore" refers to 1 trillion.
System[edit | edit source]
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), ten thousand (104). For higher powers of ten, the names no longer correspond. In the Indian system, 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), 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 some 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 and are unfamiliar to most.[citation needed] 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 incorrectly 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[edit | edit source]
150,000 rupees in India is referred to as "1.5 lakh rupees", which is written as 1,50,000 rupees; 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.
Use of separators[edit | edit source]
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 thousand 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 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 | edit source]
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 | Hindi / Urdu | Marathi | Bengali | Nepali | Tamil | Telugu | |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | one | one | एक / ایک | एक | এক | एक | ஒன்று | ఒకటి | |
| 10 | 10 | ten | ten | दस / دس | दहा | দশ | दश | பத்து | పది | |
| 102 | 100 | hundred | hundred | सौ / سو | शम्भर | শত | सय | நூறு | వంద/నూరు | |
| 103 | 1,000 | thousand | thousand | हजार / ہزار | एक हजार | হাজার | एक हजार | ஆயிரம் | వెయ్యి | |
| 104 | 10,000 | ten thousand | ten thousand | दस हजार / دس ہزار | दहा हजार | অযুত | দশ হাজার | दश हजार | பத்தாயிரம் or ஆயுதம் |
పది వేలు |
| 105 | 1,00,000 | hundred thousand | lakh | लाख / لاکھ | एक लाख | লক্ষ | লাখ | एक लाख | இலட்சம் or நியுதம் |
లక్ష |
| 106 | 10,00,000 | million | ten lakh | दस लाख / دس لاکھ | दहा लाख | নিযুত | দশ লাখ | दश लाख | பத்து இலட்சம் | పది లక్షలు |
| 107 | 1,00,00,000 | ten million | crore | करोड़ / کروڑ | एक कोटी | কোটি | एक करोड | கோடி | కోటి | |
| 108 | 10,00,00,000 | hundred million | ten crore | दस करोड़ / دس کروڑ | दहा कोटी | অর্বুদ | দশ কোটি | दश करोड | அற்புதம் | పది కోట్లు |
| 109 | 1,00,00,00,000 | billion | arab / hundred crore | अरब / ارب सौ करोड़ / سو کروڑ |
एक अब्ज | মহার্বুদ | একশ কোটি | एक अर्ब | நிகற்புதம் | వంద కోట్లు |
| 1010 | 10,00,00,00,000 | ten billion | ten arab / thousand crore | दस अरब / دس ارب एक हजार करोड़ / ایک ہزار کروڑ |
एक खर्व | খর্ব | হাজার কোটি | दश अर्ब | கும்பம் | వెయ్యి కోట్లు |
| 1011 | 1,00,00,00,00,000 | hundred billion | kharab / hundred arab / ten thousand crore | खरब / کھرب | एक निखर्व | মহাখর্ব or দশ হাজার কোটি |
एक खर्ब | கணம் | పది వేల కోట్లు | |
| 1012 | 10,00,00,00,00,000 | trillion | ten kharab / one thousand arab / one lakh crore | दस खरब / دس کھرب एक लाख करोड़ / ایک لاکھ کروڑ |
एक पद्म | শঙ্খ (śôṅkhō) লাখ কোটি |
दश खर्ब | கற்பம் | లక్ష కోట్లు | |
| 1013 | 1,00,00,00,00,00,000 | ten trillion | nil / hundred kharab / ten thousand arab / ten lakh crore | नील / نیل | एक महापद्म | মহাশঙ্খ দশ লাখ কোটি |
नील | நிகற்பம் | పది లక్షల కోట్లు | |
| 1014 | 10,00,00,00,00,00,000 | hundred trillion | ten nil / crore crore | दस नील / دس نیل एक करोड़ करोड़ / ایک کروڑ کروڑ |
एक शङ्खू | পদ্ম একশ লাখ কোটি শতলক্ষ কোটি |
दश नील | பதுமம் | కోటి కోట్లు | |
| 1015 | 1,00,00,00,00,00,00,000 | quadrillion | padma / hundred nil / ten crore crore | पद्म / پدم | एक जलधि शङ्खू | মহাপদ্ম হাজার লাখ কোটি |
पद्म | சங்கம் | పది కోట్ల కోట్లు | |
| 1016 | 10,00,00,00,00,00,00,000 | Ten quadrillion | Ten Padma | दस पद्म / دس پدم | ||||||
| 1017 | 1,00,00,00,00,00,00,00,000 | Hundred quadrillion | Shankha | शङ्ख | ||||||
| 1018 | 10,00,00,00,00,00,00,00,000 | Quintillion | Ten Shankha | दस शङ्ख | ||||||
Numbering systems in Hindu epics[edit | edit source]
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.[4]
| Name | Indian decimal | Value | Short scale |
|---|---|---|---|
| (
ēka (IAST: ēka) ) |
1 | 1 | one |
| (
daśa (IAST: daśa) ) |
10 | 10 | ten |
| (
śata (IAST: śata) ) |
100 | 102 | hundred |
| (
sahasra (IAST: sahasra) ) |
1,000 | 103 | thousand |
| (
lakṣa (IAST: lakṣa) ) |
1,00,000 | 105 | hundred thousand |
| (
kōṭi (IAST: kōṭi) ) |
1,00,00,000 | 107 | ten million |
| (
śaṅku (IAST: śaṅku) ) |
1,00,000
koṭi (IAST: koṭi) |
1012 | trillion |
| (
mahāśaṅku (IAST: mahāśaṅku) ) |
1,00,000
śaṅku (IAST: śaṅku) |
1017 | hundred quadrillion |
| (
vr̥nda (IAST: vr̥nda) ) |
1,00,000
mahāśaṅku (IAST: mahāśaṅku) |
1022 | ten sextillion |
| (
mahāvr̥nda (IAST: mahāvr̥nda) ) |
1,00,000
vr̥nda (IAST: vr̥nda) |
1027 | octillion |
| (
padma (IAST: padma) ) |
1,00,000
mahāvr̥nda (IAST: mahāvr̥nda) |
1032 | hundred nonillion |
| (
mahāpadma (IAST: mahāpadma) ) |
1,00,000
padma (IAST: padma) |
1037 | ten undecillion |
| (
kharva (IAST: kharva) ) |
1,00,000
mahāpadma (IAST: mahāpadma) |
1042 | tredecillion |
| (
mahākharva (IAST: mahākharva) ) |
1,00,000
kharva (IAST: kharva) |
1047 | hundred quattuordecillion |
| (
samudra (IAST: samudra) ) |
1,00,000
mahākharva (IAST: mahākharva) |
1052 | ten sexdecillion |
| (
ogha (IAST: ogha) ) |
1,00,000
samudra (IAST: samudra) |
1057 | octodecillion |
| (
mahaugha (IAST: mahaugha) ) |
1,00,000
ogha (IAST: ogha) |
1062 | hundred novemdecillion |
Other numbering systems[edit | edit source]
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.[5] This system became the established norm in Kumaon by 1891.[6]
Usage in different languages[edit | edit source]
- In Assamese, a lakh is also called lokhyo, or lakh and a crore is called kouti
- In Bengali, a lakh is natively (tadbhava) known as lākh, though some use the ardha-tatsama lokkho. A crore is called kōṭi
- In Burmese, crore is called [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 lākh and a crore is called karoḍ. A hundred crore is called abaj
- In Kannada, a lakh is called lakṣha and a crore is called 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 laksham and a crore is called kodi.
- In Marathi, a lakh is called lākh and a crore is called koṭi or karoḍ, and an arab (109) is called abja.
- In Nepali, a lakh is called lākh and a crore is called karoḍ.
- In Odia, a lakh is called lakhya and a crore is called koṭi.
- In Punjabi, a lakh is called lakkh (Shahmukhi: , Gurmukhi: ) and a crore is called karoṛ (Shahmukhi: , Gurmukhi: ).
- 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
lakṣa (IAST: lakṣa)
and a crore is called
kōṭi (IAST: kōṭi)
.
- In Tamil, a lakh is called ilaṭcam and a crore is called kōṭi.
- In Telugu, a lakh is called lakṣha and a crore is called kōṭi.
- In Urdu, a lakh is called lākh and a crore is called karoṛ. A billion is called arab (), and one hundred billion/arab is called a kharab ().
- Lakh has entered the Swahili language as "" 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.[7]
Current usage[edit | edit source]
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.[8]
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 English numbering system is preferred for higher denominations (i.e millions etc).
Most institutions and citizens in India use the Indian number system, although the Reserve Bank of India has been noted as a rare exception.[9]
References[edit | edit source]
- ↑ "Knowing our Numbers". Department Of School Education And Literacy. National Repository of Open Educational Resources. Archived from the original on 16 February 2016. Retrieved 13 February 2016.
- ↑ "Decimal and Thousands Separators (International Language Environments Guide)". docs.oracle.com. Retrieved 29 April 2021.
- ↑ 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.
- ↑ "Valmiki Ramayana - Yuddha Kanda, Chapter (Sarga) 28,(Verses 33 – 38)". Retrieved 2021-07-15.
- ↑ Traill, G.W. (1828). Batten, J.H. (ed.). Statistical Sketch of Kamaon. John Murray. p. 34.
- ↑ "North Indian Notes and Queries". Google Books. Pioneer Press. 1–3: 216. 1891.
- ↑ Shapiro, Richard (2012-08-16). "The most distinctive counting system in English? Indian cardinal numbers". Oxford English Dictionary. Retrieved 2020-05-24. - 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?". NPR. Retrieved 2020-08-03.
- ↑ Gurpur (10 August 2015). "Can we follow Indian numbering system for simplicity and good order?". Moneylife News & Views. Retrieved 3 September 2020.