Names of large numbers

Large numbers help us talk about huge amounts without writing long strings of digits. For example, instead of writing 10,000,000, we can say "ten million." Different places and languages have their own ways of naming these big numbers, which can sometimes cause confusion.

Two main systems are used in the world: the short scale and the long scale. In the short scale, used in most English-speaking countries, each new name for a large number adds a thousand times more than the last. The long scale, used in many parts of Europe and South America, adds a million times more. This means that the same name, like "billion," can mean different amounts depending on which system is used.

Some large numbers, like "lakh" and "crore," are special to certain regions. In the Indian numbering system, a lakh is 100,000, and a crore is 10,000,000. These names make talking about big amounts easier in everyday life.

Even though we often use scientific notation in science, knowing the names of large numbers can be fun and useful. It helps us understand statements like "There are about seven octillion atoms in the human body," even if we don’t use such big numbers every day.

Informal words like "zillion" are sometimes used to mean any very large amount, even if it isn’t a real number. These fun terms add color to how we talk about huge quantities.

Standard dictionary numbers

Different places use different systems to name very large numbers. For example, US, English Canada, modern British, Australia, and Eastern Europe use what is called the short scale. On the other hand, French Canada, older British, Western Europe, and Central Europe use the long scale.

Most of these large numbers end in -illion, like million. Words like centillion are among the highest names ending in -illion found in dictionaries. Some people talk about even bigger numbers like trigintillion, but these are not usually listed in standard dictionaries. Two special numbers, googol and googolplex, are included in dictionaries. They were first mentioned in a book by Kasner and Newman. However, these are not used in formal math.

Usage of names of large numbers

Some large numbers, like million, billion, and trillion, are used often in everyday life, especially in topics like money and economics. For example, during times of hyperinflation, countries have needed to use very large numbers to describe their money.

However, very large numbers like sextillion are rarely used outside of special lists or discussions. In science, these huge numbers are usually written using scientific notation, like "10⁴⁵", instead of their name. One early example of naming large numbers is found in The Sand Reckoner by Archimedes, where he created a system to name extremely large numbers and even estimated how many grains of sand it would take to fill the entire universe.

Origins of the "standard dictionary numbers"

The words bymillion and trimillion were first recorded in 1475 in a manuscript by Jehan Adam. Later, Nicolas Chuquet wrote a book called Triparty en la science des nombres, which was not published during his lifetime but was partly copied by Estienne de La Roche in his 1520 book L'arismetique.

Chuquet described large numbers in groups of six digits. He used names like byllion for 10¹² and tryllion for 10¹⁸. These early writers used what is called the long scale to name very large numbers.

Googol family

The words googol and googolplex were created by a young boy, the nephew of mathematician Edward Kasner. They appeared in the 1940 book Mathematics and the Imagination. A googol is the number 1 followed by one hundred zeros, and a googolplex is an even larger number — 1 followed by a googol zeros.

These fun names inspired the big tech company Google and its headquarters, called the Googleplex. Some mathematicians have suggested other names for huge numbers, like googolplexplex for a number that's 10 raised to the power of a googolplex, but these aren't used very often.

Extensions of the standard dictionary numbers

Further information: billion and Long and short scales

Different cultures and languages have their own ways of naming very large numbers. In traditional British usage, each new name was given for every power of one million. For example, 1,000,000 is called one million, and 1,000,000 squared (1,000,000²) is called one billion.

In traditional American, Canadian, and modern British usage, new names are given for each power of one thousand. Here, a billion means 1000 × 1000², which equals 10⁹. This system is widely used in finance and international documents, like those from the United Nations.

The way these names are created involves using Latin roots and adding the suffix "-illion". For example, by combining roots for numbers, we can name numbers as large as 10³⁰⁰⁰ or even bigger!

Unit prefixes

Main articles: Metric prefix and Binary prefix

Unit prefixes are special names used to describe very large or very small numbers. They help us talk about quantities like a thousand or a million in a shorter way. For example, instead of saying "one billion bytes," we can say "one gigabyte." These prefixes are used with two common systems: one for powers of 1000 and another for powers of 1024.

Other named large numbers used in mathematics, physics and chemistry

Some very large numbers have special names used in science and math. For example, the Avogadro number tells us how many tiny particles are in one mole, a unit used in chemistry. Other big numbers like the Eddington number, which estimates the number of protons in the whole universe, or Graham's number, which comes from a complex math problem, help scientists talk about incredibly large amounts in a shorter way than using all the digits.