Indian numbering system
Imagine a world where numbers like a hundred thousand and ten million have their own unique names and comma groupings — that's the fascinating reality of the Indian numbering system. Far from just a linguistic quirk, this system shapes how millions across South Asia perceive and interact with large figures every single day. Let's delve into its rhythm, history, and enduring impact. The Indian numbering system uses unique terms like 'lakh' (100,000) and 'crore' (10,000,000), which are fundamental to understanding large numbers in South Asia. Unlike the international system that groups digits by threes, the Indian system groups them initially by three, then by twos, creating a distinct visual and auditory pattern. This decimal system has deep historical roots, with ancient texts revealing an early fascination with expressing incredibly large numerical values, many of which still influence modern usage.
AI Summary
Imagine a world where numbers like a hundred thousand and ten million have their own unique names and comma groupings — that's the fascinating reality of the Indian numbering system. Far from just a linguistic quirk, this system shapes how millions across South Asia perceive and interact with large figures every single day. Let's delve into its rhythm, history, and enduring impact.
- The Indian numbering system uses unique terms like 'lakh' (100,000) and 'crore' (10,000,000), which are fundamental to understanding large numbers in South Asia.
- Unlike the international system that groups digits by threes, the Indian system groups them initially by three, then by twos, creating a distinct visual and auditory pattern.
- This decimal system has deep historical roots, with ancient texts revealing an early fascination with expressing incredibly large numerical values, many of which still influence modern usage.
The Indian Numbering System
In vast swathes of South Asia — including India, Pakistan, Bangladesh, and historically, Nepal and Sri Lanka — large numbers are expressed using a system quite different from what's used internationally. Instead of 'hundred thousand' or 'ten million,' you'll often hear 'lakh' and 'crore'—terms deeply embedded in everyday language.
A 'lakh' represents one hundred thousand (100,000), while a 'crore' signifies ten million (10,000,000). So, if someone says 'two lakh rupees,' they mean 200,000 rupees. And 'five crore people' means fifty million people. It's a fundamental part of how finances, populations, and large quantities are communicated.
Beyond lakh and crore, the system extends to even larger, though less commonly used, denominations. You might encounter 'arab' for a billion (100 crore or 10^9), and 'kharab' for a hundred billion (100 arab or 10^11). It's almost as if the numbers are building blocks, scaling up in a unique progression.
Tracing Ancient Roots
This distinct numerical rhythm isn't new; it echoes ancient Indian numbering systems. Many regional languages still use terms with incredibly deep historical roots, some capable of naming numbers up to 10^62 — a testament to an early, profound interest in mathematics and grand scales.
Terms like 'sahasra' (thousand), 'ayuta' (ten thousand), 'laksha' (hundred thousand), and 'koti' (ten million) found in ancient texts are direct ancestors of our modern 'lakh' and 'crore.' It's a living legacy, connecting today's common speech to millennia-old mathematical thought.
A Different Rhythm of Numbers
The core difference lies in how larger powers of ten are named. While both systems are decimal (base-10), the Indian system introduces new names for every second power of ten beyond ten thousand. The international system, conversely, typically introduces new names for every third power of ten.
Power of Ten Indian Name International Short Scale
10^{0} One One
10^{1} Ten Ten
10^{2} Hundred Hundred
10^{3} Thousand Thousand
10^{4} Ten Thousand Ten Thousand
10^{5} Lakh Hundred Thousand
10^{6} Ten Lakh Million
10^{7} Crore Ten Million
10^{9} Arab Billion
10^{11} Kharab Hundred Billion
10^{13} Nil Ten Trillion
10^{15} Padma Quadrillion
10^{17} Shankh Hundred Quadrillion
10^{19} Mahashankh Ten QuintillionThe Unique Comma Dance
This difference in naming conventions translates directly into how large numbers are written. The Indian system groups the first three digits to the left of the decimal point, just like the international system. But after that, it groups digits in pairs, rather than threes, to align with its lakh and crore units.
So, what in the international system would be written as 123,456,789 — one hundred twenty-three million, four hundred fifty-six thousand, seven hundred eighty-nine — becomes 12,34,56,789 in the Indian system. You'd read this as 'twelve crore, thirty-four lakh, fifty-six thousand, seven hundred eighty-nine.'
For decimal separation, however, the Indian system aligns with many English-speaking countries, using a period (.) as the decimal separator and a comma (,) for grouping digits. This avoids confusion with systems that use a comma for the decimal and a space or point for grouping.
A Multilingual Mosaic
The terms 'lakh' and 'crore' are not exclusive to Hindi; they are deeply integrated into many other languages spoken across the Indian subcontinent. From Bengali to Gujarati, Punjabi to Tamil, these words are linguistic common ground, reinforcing their cultural significance.
When speakers of these languages use English, they often naturally carry over the 'lakh' and 'crore' terms, sometimes with pronunciations reflecting their mother tongue — like /lɑkʰ/ for 'lakh' or /kɑrɔːr/ for 'crore' — a beautiful blend of linguistic traditions.
Numbers in Epics and Kingdoms
The fascination with numbering systems extends back to ancient epics. Texts like the Valmiki Ramayana, for example, reveal intricate numerical descriptions, showcasing how large quantities were conceptualized and communicated in mythological and historical narratives.
Even beyond the decimal system, unique numbering traditions existed. In the Kumaon Kingdom, for instance, land was measured using a vigesimal, or base-20, system. The primary unit, a 'bisi,' was tied to the land needed to sow 20 'nalis' of seed, demonstrating practical, localized applications of numerical systems.
Modern Relevance and Usage
Today, the Indian numbering system is still predominantly used in India, Pakistan, and Bangladesh, where it is often preferred over the international system in daily life, business, and official documents. It's a testament to its cultural entrenchment and practical utility.
While some neighboring countries like Sri Lanka and Nepal have transitioned to the international system, the term 'lakh' remains widely used in official and local contexts in the Maldives, even if higher denominations lean towards international terms like 'millions.'
Even major financial institutions within India, like the Reserve Bank of India, have fully embraced the Indian numbering system for local currency amounts, using it alongside the international system for foreign currency. This dual usage highlights its ongoing relevance and the practical necessity of being bilingual in numbers.
Article
Indian numbering system
The Indian numbering system is used in India, Pakistan, Nepal, Sri Lanka, and Bangladesh to express large numbers, which differs from the International System of Units. Commonly used quantities include lakh (one hundred thousand, 105) and crore (ten million, 107) – written as 1,00,000 and 1,00,00,000 respectively in some locales. For example: 150,000 rupees is "1.5 lakh rupees" which can be written as "1,50,000 rupees", and 30,000,000 (thirty million) rupees is referred to as "3 crore rupees" which can be written as "3,00,00,000 rupees".
There are names for numbers larger than crore, but they are less commonly used. These include arab (100 crore, 109), kharab (100 arab, 1011), nil or sometimes transliterated as neel (100 kharab, 1013), padma (100 nil, 1015), shankh (100 padma, 1017), and mahashankh (100 shankh, 1019). In common parlance (though inconsistent), the lakh and crore terminology repeats for larger numbers. Thus lakh crore is 1012.
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, the next powers of ten are one lakh, ten lakh, one crore, ten crore, one arab (or one hundred crore), and so on.
Multiples
Indian numbering system
The Indian system is decimal (base-10), same as in the International System of Units, and the first five orders of magnitude are named in a similar way: one (100), ten (101), one hundred (102), one thousand (103), and ten thousand (104). For higher powers of ten, naming diverges. The Indian system uses names for every second power of ten: lakh (105), crore (107), arab (109), kharab (1011), etc. In the long and short scales, there are names for every third power of ten. The short scale uses million (106), billion (109), trillion (1012), etc.
Decimal formatting
Indian numbering system
The Indian system groups digits of a large decimal is represented differently than the International System of Units. The Indian system does group the first three digits to the left of the decimal point, but thereafter, groups by two digits to align with the naming of quantities at multiples of 100.
<table><thead><tr><th>Indian</th><th>International</th></tr></thead><tbody><tr><td>5,00,000</td><td>500,000</td></tr><tr><td>12,34,56,789</td><td>123,456,789</td></tr><tr><td>17,00,00,00,000</td><td>17,000,000,000</td></tr><tr><td>6,78,90,00,00,00,00,000</td><td>6,789,000,000,000,000</td></tr></tbody></table>
Like English and other locales, the Indian system uses a period as the decimal separator and the comma for grouping, while others use a comma for decimal separator and a thin space or point to group digits.
Pronunciation in English
Indian numbering system
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).
• lakh /lɑːkʰ/ • crore /kɹɔːɹ/ (or /kɹoʊɹ/ in American English) • arab /ʌˈɾʌb/ • kharab /kʰʌˈɾʌb/
Names of numbers
Indian numbering system
The table below includes the spelling and pronunciation of numbers in various Indian languages along with corresponding short scale names.
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.
<table><thead><tr><th>Name</th><th>Indian decimal</th><th>Value</th><th>Short scale</th></tr></thead><tbody><tr><td>एक (ēka)</td><td>0,00,001</td><td>1</td><td>one</td></tr><tr><td>दश (daśa)</td><td>0,00,010</td><td>10</td><td>ten</td></tr><tr><td>शत (śata)</td><td>0,00,100</td><td>102</td><td>hundred</td></tr><tr><td>सहस्र (sahasra)</td><td>0,01,000</td><td>103</td><td>thousand</td></tr><tr><td>लक्ष (lakṣa)</td><td>1,00,000</td><td>105</td><td>hundred thousand</td></tr><tr><td>कोटि (kōṭi)</td><td>1,00,00,000</td><td>107</td><td>ten million</td></tr><tr><td>शङ्कु (śaṅku)</td><td>1,00,000 koṭi</td><td>1012</td><td>trillion</td></tr><tr><td>महाशङ्कु (mahāśaṅku)</td><td>1,00,000 śaṅku</td><td>1017</td><td>hundred quadrillion</td></tr><tr><td>वृन्द (vr̥nda)</td><td>1,00,000 mahāśaṅku</td><td>1022</td><td>ten sextillion</td></tr><tr><td>महावृन्द (mahāvr̥nda)</td><td>1,00,000 vr̥nda</td><td>1027</td><td>octillion</td></tr><tr><td>पद्म (padma)</td><td>1,00,000 mahāvr̥nda</td><td>1032</td><td>hundred nonillion</td></tr><tr><td>महापद्म (mahāpadma)</td><td>1,00,000 padma</td><td>1037</td><td>ten undecillion</td></tr><tr><td>खर्व (kharva)</td><td>1,00,000 mahāpadma</td><td>1042</td><td>tredecillion</td></tr><tr><td>महाखर्व (mahākharva)</td><td>1,00,000 kharva</td><td>1047</td><td>hundred quattuordecillion</td></tr><tr><td>समुद्र (samudra)</td><td>1,00,000 mahākharva</td><td>1052</td><td>ten sexdecillion</td></tr><tr><td>ओघ (ogha)</td><td>1,00,000 samudra</td><td>1057</td><td>octodecillion</td></tr><tr><td>महौघ (mahaugha)</td><td>1,00,000 ogha</td><td>1062</td><td>hundred novemdecillion</td></tr></tbody></table>
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. This system became the established norm in Kumaon by 1891.
Usage in different languages
Indian numbering system
Below is a list of translations for the words lakh and crore in other languages spoken in the Indian subcontinent:
<table><thead><tr><th>Language</th><th>Lakh</th><th>Crore</th><th>100 crores (a billion)</th><th>1000 crores (10 billion)</th><th>10,000 crores (100 billion)</th></tr></thead><tbody><tr><td>Assamese</td><td>লক্ষ lokhyo, or লাখ lakh</td><td>কৌটি kouti, or কোটি koti</td><td>—N/a</td></tr><tr><td>Bengali</td><td>লাখ lākh, or লক্ষ lokkho</td><td>কোটি kōṭi</td></tr><tr><td>Burmese</td><td>lakh</td><td>ကုဋေ [ɡədè]</td></tr><tr><td>Dhivehi</td><td>ލައްކަ la'kha</td><td>ކްރޯރް kroaru</td></tr><tr><td>Gujarati</td><td>લાખ lākh</td><td>કરોડ karoḍ</td><td>અબજ abaj</td><td>—N/a</td></tr><tr><td>Hindi</td><td>लाख lākh</td><td>करोड karoḍ</td><td>अरब arab</td></tr><tr><td>Kannada</td><td>ಲಕ್ಷ lakṣha</td><td>ಕೋಟಿ kōṭi</td><td>—N/a</td></tr><tr><td>Khasi</td><td>lak</td><td>klur or krur</td><td>arab</td><td>—N/a</td><td>kharab</td></tr><tr><td>Malayalam</td><td>ലക്ഷം laksham</td><td>കോടി kodi</td><td>—N/a</td></tr><tr><td>Marathi</td><td>लाख/लक्ष lākh</td><td>कोटी koṭi, or करोड karoḍ</td><td>अब्ज abja</td><td>—N/a</td></tr><tr><td>Nepali</td><td>लाख lākh</td><td>करोड karoḍ</td><td>—N/a</td></tr><tr><td>Odia</td><td>ଲକ୍ଷ lôkhyô</td><td>କୋଟି koṭi</td></tr><tr><td>Punjabi</td><td>lakkh (Gurmukhi: ਲੱਖ, Shahmukhi: لکھ)</td><td>karoṛ (Gurmukhi: ਕਰੋੜ, Shahmukhi: کروڑ)</td></tr><tr><td>Rohingya</td><td>lák</td><td>kurul</td><td>—N/a</td><td>kuthí</td><td>—N/a</td></tr><tr><td>Sinhala</td><td>ලක්ෂ lakṣa</td><td>කෝටි kōṭi</td><td>—N/a</td></tr><tr><td>Tamil</td><td>இலட்சம் ilaṭcam</td><td>கோடி kōṭi</td></tr><tr><td>Telugu</td><td>లక్ష lakṣha</td><td>కోటి kōṭi</td></tr><tr><td>Urdu</td><td>لاکھ lākh</td><td>کروڑ karoṛ</td><td>ارب arab</td><td>—N/a</td><td>کھرب kharab</td></tr><tr><td>Swahili</td><td>laki</td><td>—N/a</td></tr></tbody></table>
Formal written publications in English in India tend to use lakh/crore for Indian currency and International numbering for foreign currencies.
Current usage
Indian numbering system
The official usage of this system is limited to the nations of India, Pakistan and Bangladesh. It is universally employed within these countries, and is preferred to the International numbering system.
Sri Lanka and Nepal used this system in the past but has switched to the International numbering system in recent years. In the Maldives, the term lakh is widely used in official documents and local speech. However, the International System of Units is preferred for higher denominations (such as millions).
Most institutions and citizens in India use the Indian number system. The Reserve Bank of India was noted as a rare exception in 2015, whereas by 2024 the Indian system was used for amounts in rupees and the International system for foreign currencies throughout the Reserve Bank's website.