Large numbers can be fascinating and complex, often stretching our imagination and comprehension. Throughout history, people have developed various naming conventions to represent these vast quantities.
The concept of large numbers has been integral to human civilization since ancient times. Early civilizations devised their own methods for representing and calculating large quantities. In fact, the ancient Greeks had a term for extremely large numbers, known as “myriad,” which referred to 10,000. Over time, as mathematical knowledge grew, people developed more systematic ways to express larger numbers.
Different cultures have developed unique naming systems for large numbers. In the modern Western system, numbers are grouped into powers of 1,000. Each grouping is named with a Latin or Greek prefix, such as “kilo-” (thousand), “mega-” (million), “giga-” (billion), “tera-” (trillion), and so on. These prefixes make it easier to express and comprehend large numbers.
The short scale is the naming convention most commonly used in English-speaking countries and is based on powers of one thousand. In this system, each new scale is named with a Latin or Greek prefix followed by “-illion.”
The long scale is used in many non-English-speaking countries and is based on powers of one million. In this system, each new scale is named with a Latin or Greek prefix followed by “-iard” or “-liard.”
The Indian numbering system is used in South Asian countries and groups numbers in sets of two digits. It is based on powers of one hundred. Each set of two digits is named after a specific word.
I’ll be using the short scale for the examples in this post.
Examples of Big Numbers
- Thousand: 1,000 (103)
- Million: 1,000,000 (106)
- Billion: 1,000,000,000 (109)
- Trillion: 1,000,000,000,000 (1012)
- Quadrillion: 1,000,000,000,000,000 (1015)
- Quintillion: 1,000,000,000,000,000,000 (1018)
- Sextillion: 1,000,000,000,000,000,000,000 (1021)
- Septillion: 1,000,000,000,000,000,000,000,000 (1024)
- Octillion: (1027)
- Nonillion: (1030)
- Decillion: (1033)
- Undecillion: (1036)
- Duodecillion: (1039)
- Tredecillion: (1042)
- Quattuordecillion: (1045)
- Quindecillion: (1048)
- Sexdecillion: (1051)
- Septendecillion: (1054)
- Octodecillion: (1057)
- Novemdecillion: (1060)
- Vigintillion: (1063)
- Centillion: (10303)
- Ducentillion: (10603)
- Sescentillion: (101803)
- Millinillion: (103003)
A Trillion used to be a number that couldn’t be imagined when I was a child. Now the United States’ national debt is just over 19 trillion dollars. There are also about a trillion stars in the Milky Way. One trillion dollars would stretch nearly from the Earth to the sun. It would take a military jet flying at the speed of sound, reeling out a roll of dollar bills behind it, 14 years before it reeled out one trillion dollar bills. The volume of the earth is about 1.085 Sextillion cubic meters. There are about 6 sextillion cups of water in all the oceans of the world.
There are about 1 sextillion atoms in the body of a flea. The Area of the Milky Way galaxy is approximately 702 Decillion square kilometers. The mass of the sun is about 1.989 decillion grams. There are about 41.75 Quattuordecillion water molecules in all the water on the earth.
Other Big Numbers
- Googol: (10100)
- Googolplex: (1010100) or (10Googol)
- Skewes Number: (1010^10^34)
- Graham’s Number: (?) (greater than infinity)
A Googol is 1019 larger than the number of particles in the entire universe. There are not enough particles in the universe to write out a Googolplex by placing a 0 on every particle in the universe. Skewe’s number[1] is a large number in the field of number theory that is used to provide an upper bound on the first occurrence of a certain mathematical phenomenon known as the “Skewe’s number.”
The phenomenon is related to the behavior of the prime-counting function, which counts the number of prime numbers up to a given value. Graham’s number is an extremely large number that arises in the field of mathematics, specifically in the realm of Ramsey’s theory. It was first introduced by mathematician Ronald Graham[2] in a 1970 paper co-authored with other mathematicians.
Graham’s number is famously known for being one of the largest numbers ever to have a specifically defined value, though it is dwarfed by other numbers like larger “Graham-like” numbers. Graham’s number is a mind-bending huge number. This number is bigger than the age of the Universe, whether measured in years (approximately 14 billion years) or seconds (4.31017 seconds).
Footnotes
- Stanley Skewes was a British mathematician known for his contributions to number theory. In 1933, Skewes made a significant contribution to prime number theory when he proved that there must be a value of x such that the prime-counting function π(x) exceeds the logarithmic integral Li(x) for the first time. This result was groundbreaking at the time and introduced the concept of “Skewes’ number,” an upper bound for the value of x where this phenomenon occurs. Skewes’ work has had lasting implications in the study of prime numbers and the understanding of their distribution. His contributions continue to inspire research in the field of number theory. [Back]
- Ronald Graham is an influential American mathematician known for his wide-ranging contributions to various branches of mathematics and computer science. Graham’s work spans combinatorics, graph theory, optimization, and computational complexity, and he has been a pivotal figure in advancing the field of discrete mathematics. He co-authored the famous Graham-Pollak theorem, made significant contributions to Ramsey’s theory, and introduced the concept of Graham’s number, a famously large number in number theory and combinatorics. Graham’s collaborations, prolific research, and leadership roles in academia and organizations have made him a prominent figure in contemporary mathematics and computer science. [Back]
Further Reading
Sources
- “Names of large numbers” https://en.wikipedia.org/wiki/Names_of_large_numbers
- “Mathematical Quickies: 270 Stimulating Problems with Solutions (Dover Recreational Math) Paperback – October 1, 1985” https://www.amazon.com/Mathematical-Quickies-Stimulating-Solutions-Recreational/dp/0486249492
- https://googology.fandom.com/wiki/Millillion
