Mathematics and numbers

Mathematics is not only about formulas and calculations. It requires logical thinking and reasoning, and once a method is clear, we can work out the result and obtain answer as a number. That result may be a small number or a very large one.

How big numbers and the "illion" suffix work

Depending on the country and the context, we normally do not use numbers beyond tens of thousands. This is because in our daily life we usually use numbers to count money and things. But in science and astronomy, we often encounter very large numbers, and there are cases when we need to use especially big numbers. For example, the distance to the nearest star, our Sun, is 150 million kilometers (this is a so-called parsec). In such cases, people prefer to say something like "150 with 6 zeros". But what if count the number of atoms in a pinch of salt. It is much more intriguing to say that it is 100 sextillions. Then a question from your friends will appear - what is a sextillion?

First of all, let's answer a different question: where does the "llion" suffix come from? It comes from the Italian word "milione," which means a "big thousand." Literally, that is right: we need a million to count many thousands. The suffix became part of the number system when Marco Polo, who spoke Italian, traveled to China. He was impressed by the wealth of the Chinese emperors and wanted to estimate it, so he started counting it in ever-larger thousands. Later, the word was adopted by French and English speakers. Over time, humans started counting even bigger numbers, and we arrived at billions, trillions, and so on. It is simple: every time you hear the word "illion", it means a very large number.

Marco Polo was not the inventor of the word million, but he was the one who helped popularize the idea of counting very large numbers using the already existing word "milione."

Big numbers in the modern mathematics

The modern number system is not the same everywhere. There are many languages and cultures in the world, and the way large numbers are written and grouped can vary quite a lot. For example, in Korea, the number 1,000,000 is written as 100만 (baekman), which literally means "hundred ten-thousands." This reminds us that number names are shaped by culture and language, not just by mathematics alone.

For now, let's focus on English and similar languages, because that is the system behind the names we use most often in science, finance, and everyday discussion of large numbers. English language somehow is considered the international language of science and finance, so it is important to know how to read and write big numbers in English.

The most common names for big numbers

Here are the most common large-number names in English, with their values and the number of zeros they contain.

This is the system people use when they talk about million, billion, trillion, and beyond:

• Million - 1,000,000 (6 zeros)
• Billion - 1,000,000,000 (9 zeros)
• Trillion - 1,000,000,000,000 (12 zeros)
• Quadrillion =10¹⁵ = 1,000,000,000,000,000 (15 zeros)
• Quintillion = 10¹⁸ = 1,000,000,000,000,000,000 (18 zeros)
• Sextillion = 10²¹ = 1,000,000,000,000,000,000,000 (21 zeros)
• Septillion = 10²⁴ (24 zeros)
• Octillion = 10²⁷ (27 zeros)
• Nonillion = 10³⁰ (30 zero)
• Decillion = 10³³ (33 zeros)
• Vigintillion = 10⁶³ (63 zeros)
• Centillion = 10³⁰³ (303... many many zeros)

Beyond the "illion" suffix

Accidentally it was done or not, or on purpose but there are some big numbers that don't have the "illion" suffix.

Googol is a number that is 10¹⁰⁰, which is a 1 followed by 100 zeros, it is not that big compared to the numbers given above.

Googolplex is a number that is 10^googol . The reader would like to know how many zeros it is. Sorry, we cannot write it down, because it is a number that is 1 followed by googol zeros. Try to raise 10 to the 100th and then raise 10 to that number.

But when written in words it is "Ten to the power of ten to the power of one hundred":

Wait a second—the reader may ask: is the name Google derived from the googol number?

Yes, it is. We cannot omit the fact that founders of Google were inspired by the word googol when they were thinking about a name for their company. It is a big number of something, and Google is extremely good at processing massive amounts of data.

The words Googol and Googolplex were invented by a 9 year old boy named Milton, long before Google was founded. His uncle, Edward Kasner, was a mathematician, and he asked his nephew to invent a name for a very big number.

Interesting facts about huge numbers

1. Currently, the world population is over 8 billion people (today is the 2026 year).
2. World GDP, the total value of all goods and services produced in a year, was roughly $100 trillion in 2022. That is an enormous amount of money. Again, a trillion is a 1 with 12 twelve zeros, it 12,000,000,000,000. Maybe this is the reason why majority of people still don't think in numbers greater than a trillion. Humanity just doesn't have that amount of money in total.
3. The number of days since the dinosaurs went extinct (~66 million years ago): 66,000,000 years × 365.25 days/year ≈ 24.1 billion days (24,106,500,000).