Indian numbering system
The Indian numbering system is used in the Indian subcontinent to express large numbers. The terms lakh and crore are the most commonly used terms to express large numbers in the system. For example, 150,000 rupees in India is referred to as "1.5 lakh rupees", which is written as 1,50,000 rupees; 30,000,000 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.
In the financial world, until 2018, it was customary to write lac for ₹ 1,00,000 only and for any figure above it was lakhs, like ₹ 1,40,000. Since 2018, however, lac/lacs are the norm in the financial world and lakh/lakhs for metric system.
There are words for numbers larger than 1 crore as well, but these are not commonly used and are unfamiliar to most speakers. These include 1 arab, 1 kharab, 1 nil, 1 padma, 1 shankh, and 1 mahashankh. In common parlance, the thousand, lakh, and crore terminology repeats for larger numbers: thus 1,000,000,000,000 becomes 1 lakh crore, written as 1,00,000,00,00,000.
The Indian numbering system corresponds to the Western system for the zeroth through fourth powers of ten: one, ten, one hundred, one thousand, ten thousand. 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, and so on; there are new words for every second power of ten : lakh, crore, arab, etc. In the Western system, the next powers of ten are called one hundred thousand, one million, ten million, one hundred million, one billion, and so on; there are new words for every third power of ten : million, billion, trillion, etc.
The written numbers differ only in the placement of commas, which group the digits into powers of one hundred in the Indian system, and into powers of one thousand 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.
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, and thereafter groups by sets of two digits. One trillion would thus be written as 10,00,00,00,00,000 or 10 kharab. This makes the number convenient to read using the system's terminology. Thus:| Indian system | International system | In words | In words |
| 5,00,000 | 500,000 | Five lakh | 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 | Seventeen arab | Seventeen billion |
| 67,890,00,00,00,000 | 67,890,000,000,000 | Sixty-seven lakh, eighty-nine thousand crore | Sixty-seven trillion, eight hundred and ninety billion |
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.Derh in Hindi and related languages means one and one half; this is another number unique to Indian numbering.
Vedic numbering systems
There are various systems of numeration found in various ancient Vedic literary works of India. The following table gives one such system used in the Valmiki Ramayana.| Indian notation | Power notation | Equivalent numeric representation | Short scale Western | |
| एक | 1 | 100 | 1 | One |
| दश | 10 | 101 | 10 | Ten |
| शत | 100 | 102 | 100 | One hundred |
| सहस्र | 1,000 | 103 | 1,000 | One thousand |
| अयुत | 10,000 | 104 | 10,000 | Ten thousand |
| लक्ष | 1,00,000 | 105 | 100,000 | One hundred thousand |
| नियुत | 1,00,000 daśa | 106 | 1,000,000 | One million |
| कोटि | 1,00,000 śata | 107 | 10,000,000 | Ten million |
| शङ्कु | 1,00,000 koṭi | 1012 | 1,000,000,000,000 | One trillion |
| महाशङ्कु | 1,00,000 śaṅku | 1017 | 100,000,000,000,000,000 | One hundred quadrillion |
| वृन्द | 1,00,000 mahāśaṅku | 1022 | 10,000,000,000,000,000,000,000 | Ten sextillion |
| महावृन्द | 1,00,000 vr̥nda | 1027 | 1,000,000,000,000,000,000,000,000,000 | One octillion |
| पद्म | 1,00,000 mahāvr̥nda | 1032 | 100,000,000,000,000,000,000,000,000,000,000 | One hundred nonillion |
| महापद्म | 1,00,000 padma | 1037 | 10,000,000,000,000,000,000,000,000,000,000,000,000 | Ten undecillion |
| खर्व | 1,00,000 mahāpadma | 1042 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | One tredecillion |
| महाखर्व | 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 | 1,00,000 mahākharva | 1052 | 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | Ten sexdecillion |
| ओघ | 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 | 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
- 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 also called লক্ষ lokkho, or laakh and a crore is called কোটি koti.
- In Burmese, crore is called . Lakh is used in Burmese English.
- In Gujarati, a lakh is called લાખ lākh and a crore is called કરોડ karoḍ. A hundred crore is called અબજ abaj.
- 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 / लाख/लक्ष lākh and a crore is called कोटी koṭi or करोड karoḍ, and an 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 lakhya and a crore is called କୋଟି koti.
- In Punjabi, a lakh is called lakkh and a crore is called karoṛ.
- In Rohingya, a lakh is called lák and a crore is called kurul. A thousand crores is called "kuthí ".
- In Sinhala, a lakh is called ලක්ෂ lakṣa and a crore is called කෝටි kōṭi.
- In Sylheti, a lakh is called লাখ lakh and a crore is called কোটি kuti. A billion is called "arob". And hundred billion is called "kharob".
- Lakh has entered the Swahili language as "laki" and is in common use.
- In Tamil, a lakh is called இலட்சம் ilatcham and a crore is called கோடி kodi.
- In Telugu, a lakh is called లక్ష lakṣha and a crore is called కోటి kōṭi.
- In Urdu, a lakh is called lākh and a crore is called karoṛ. A billion is called "arab". And hundred billion/ arab is called "kharab".