THE INDIAN NUMERICAL SYSTEM | WHAT A SURPRISE
I´ve recently looked into an Angel Investment deal in an Indian start-up. I did not know the market firsthand; I knew I had to learn much about the ecosystem. At first, I got confused about how Indians report numbers. Once reporting millions, the legal and financial documents I went through represented numbers with apparently “misplaced commas”:
- Mr A: 3,30,000 No of Shares
- Mr B: 46,246 No of Shares
- Mr C: 248 No of Shares
The “funny” numeral system was triggered after the six-digit numbers. This was the case with the company’s shares and any financial number in the P&L and Balance sheet. So, it was not a typo, a misplaced comma, or a different way of writing numbers.
I had to dig into the rationale and tradition of such a numerical system to fully understand Indian financial statements and learn more about the history behind it. After all, the numbers we use are known for being Hindu-Arabic numbers. How hard can it be to understand them?
THE SIMPLE RULE TO UNDERSTAND THE INDIAN NUMERICAL SYSTEM
After some readings, it was “easy” to crack the code. According to the Indian numeral system, the numbers (grouped in periods) are divided according to the rule of 3:2:2. The first comma is placed after three digits starting from the right. The next commas are placed after every two digits.
For example, the number 69542189, which in most countries would be expressed with commas every three digits— 69,542,189 —in India is written as follows: 6,95,42,189.
This simple example should be enough to interpret Indian documents, such as legal contracts or financial statements.
However, if you genuinely want to understand the Indian numerical system, it can be helpful to examine another aspect: the nomenclature of different place values!
THE NOMENCLATURE OF INDIAN NUMERICAL SYSTEM
The main difference between the Indian and International numeration systems is the placement of the separators (commas) and the nomenclature of different place values. The International numeral system, used worldwide, counts in terms of ones, hundreds, thousands, ten thousand, hundred thousand, millions, and billions (as per the table below).
On the other hand, the Indian traditional numerical system can be distinguished from the other numeral systems based on not only the place value that we have already quickly covered but also the nomenclature. When we use the Indian numeral system, we count with ones, tens, hundreds, thousands, ten thousand, lakhs, ten lakhs, and crores. The following table depicts the different periods and the place values according to the number of digits in a number.
So, if you need to read and understand numbers, the place value will be enough to understand the documents. However, if you are conversing, and your partner counts numbers using Lakha and Crores, you might need to familiarize yourself with the nomenclature.
Check out this example: 1347823
- Standard International numeral system: 1,347,823
- Standard International nomenclature: One million, three hundred forty-seven thousand, eight hundred twenty-three.
- The Indian numeral system: 13,47,823
- The Indian nomenclature: Thirteen lakh, Forty-seven thousand, eight hundred twenty-three.
THE HISTORY BEHIND THE INDIAN NUMERICAL SYSTEM | THE RABBIT HOLE
If you like history like me, it is too tempting to dig a bit deeper to understand why this Indian numerical system is different. More specifically, why is a 7-digit number like 10 million written as 10,000,000 in the West and 1,00,00,0000 in India? Reference to the History of Mathematics (D.E. Smith),
“Until about 14th century, Europe didn’t have a concept called the million. There was never a need to count that many things. Then, out of nowhere, it starts appearing in a couple of works to denote 1000 1000s. Then it slowly started spreading into Italy, France, and Germany in the age of discovery when Europe suddenly found a need to count bigger numbers”.
This is fascinating because it makes me think about Marco Polo’s tales of his journey to Asia, written by Rustichello da Pisa by the end of the XIII century in Italy. While its original title was “Le Divisament du Monde,” “Livre des Merveilles du Monde,” or” De mirabilis mundi,” later on, it became known as “the Million.”
The term Million appears to be linked to Marco Polo’s nickname, Messer Marco Milioni (Mr. Marco Millions). One of the most fascinating explanations behind his nickname was that when he returned to Venice, he kept saying that Kublai Khan’s wealth was counted in millions. Others state that the Million referred to the alleged number of lies within! In fact, at the time, the stories of his travels were so incredible that few people believed him.
(Clearly, there are several other schools of thought about the origin of the term Million. Luigi Foscolo Benedetto, one of the book’s known translators, believed the nickname was the simple adaptation of the diminutive ‘Emilione’: Milion was the affective nickname – by apheresis – familiar to most Venetian Polo families. For others, ‘Milion’ was nothing other than the multiple of ‘mile’ (in Latin milium), an ancient traveling unit of measurement corresponding to a thousand steps (still in use in Anglo-Saxon countries, albeit with a different relation), since Marco Polo traveled most of his journey on foot).
Let’s zoom out from this modern Eurocentric “history,” returning to the East. Knowing that our current numerical system derives from the Arabic-Hindu system, it should not come as a surprise, digging deeper, to see that ancient epic literature of several centuries before Marco Polo’s journey (the Ramayana, which lasted from 7 BCE until 3 CE) already included references to incredibly gigantic numbers, beyond million and billions, up to 10^62 (table below).
The Indian numerical system is, therefore, older. It is still used extensively in Indian literature, religious scriptures, and mathematical works. Several commentators on online chats have also reported that most Indians can easily switch between the two systems instantly—the Indian numerical system and the international numerical system: “Even in village schools, we were taught both these systems as early as 4th standard.”
It is up to any curious mind to learn the nuances of such different numerical systems and appreciate the cultural richness behind these traditions.
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