A googol is the

large number Large numbers are numbers significantly larger than those typically used in everyday life (for instance in simple counting or in monetary transactions), appearing frequently in fields such as mathematics, cosmology, cryptography, and statistical m ...

10¹⁰⁰. In decimal notation, it is written as the digit 1 followed by one hundred zeroes: 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.

Etymology

The term was coined in 1920 by 9-year-old Milton Sirotta (1911–1981), nephew of U.S.

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

Edward Kasner Edward Kasner (April 2, 1878 – January 7, 1955) was an American mathematician who was appointed Tutor on Mathematics in the Columbia University Mathematics Department. Kasner was the first Jewish person appointed to a faculty position in t ...

. He may have been inspired by the contemporary comic strip character

Barney Google ''Barney Google and Snuffy Smith'', originally ''Take Barney Google, F'rinstance'', is an American comic strip created by cartoonist Billy DeBeck. Since its debut on June 17, 1919, the strip has gained a large international readership, appearin ...

. Kasner popularized the concept in his 1940 book ''

Mathematics and the Imagination ''Mathematics and the Imagination'' is a book published in New York by Simon & Schuster in 1940. The authors are Edward Kasner and James R. Newman. The illustrator Rufus Isaacs provided 169 figures. It rapidly became a best-seller and received s ...

''. Other

names A name is a term used for identification by an external observer. They can identify a class or category of things, or a single thing, either uniquely, or within a given context. The entity identified by a name is called its referent. A persona ...

for this quantity include ''ten duotrigintillion'' on the

short scale The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes. For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the t ...

, ''ten thousand sexdecillion'' on the

long scale The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes. For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the ...

, or ''ten sexdecilliard'' on the Peletier long scale.

Size

A googol has no special significance in mathematics. However, it is useful when comparing with other very large quantities such as the number of

subatomic particles In physical sciences, a subatomic particle is a particle that composes an atom. According to the Standard Model of particle physics, a subatomic particle can be either a composite particle, which is composed of other particles (for example, a pro ...

in the visible universe or the number of hypothetical possibilities in a

chess Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to disti ...

game. Kasner used it to illustrate the difference between an unimaginably large number and

infinity Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol . Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions amo ...

, and in this role it is sometimes used in teaching mathematics. To give a sense of how big a googol really is, the mass of an electron, just under , can be compared to the mass of the visible universe, estimated at between and . It is a ratio in the order of about 10⁸⁰ to 10⁹⁰, or at most one ten-billionth of a googol (0.00000001% of a googol). Another way of illustrating the immense size of a googol is to picture the Frontier

supercomputer A supercomputer is a computer with a high level of performance as compared to a general-purpose computer. The performance of a supercomputer is commonly measured in floating-point operations per second ( FLOPS) instead of million instructions ...

, which as of 2022 is the most powerful supercomputer in the world and measures 680 m² (7,300 sq ft), almost exactly the same size of a

basketball court In basketball, the basketball court is the playing surface, consisting of a rectangular floor, with baskets at each end. Indoor basketball courts are almost always made of polished wood, usually maple, with -high rims on each basket. Outdoor sur ...

with run-offs and sidelines. The Frontier is capable of making 1,102,000

TFLOPs In computing, floating point operations per second (FLOPS, flops or flop/s) is a measure of computer performance, useful in fields of scientific computations that require floating-point calculations. For such cases, it is a more accurate mea ...

(1.1 quintillion calculations per second). Imagine if the supercomputer, which cost approximately US$600 million to build, was shrunk down to the size of an atom (for reference, a typical grain of sand might have 37 quintillion atoms). If every atom in the observable universe (~ atoms total) was as powerful as a Frontier supercomputer, it would take approximately 100 seconds of

parallel computing Parallel computing is a type of computation in which many calculations or processes are carried out simultaneously. Large problems can often be divided into smaller ones, which can then be solved at the same time. There are several different fo ...

to manually add up all the digits like an

adding machine An adding machine is a class of mechanical calculator, usually specialized for bookkeeping calculations. In the United States, the earliest adding machines were usually built to read in dollars and cents. Adding machines were ubiquitous off ...

(instead of using shorthand calculations).

Carl Sagan Carl Edward Sagan (; ; November 9, 1934December 20, 1996) was an American astronomer, planetary scientist, cosmologist, astrophysicist, astrobiologist, author, and science communicator. His best known scientific contribution is research on ext ...

pointed out that the total number of elementary particles in the universe is around 10⁸⁰ (the

Eddington number In astrophysics, the Eddington number, , is the number of protons in the observable universe. Eddington originally calculated it as about ; current estimates make it approximately . The term is named for British astrophysicist Arthur Eddington, ...

) and that if the whole universe were packed with neutrons so that there would be no empty space anywhere, there would be around 10¹²⁸. He also noted the similarity of the second calculation to that of

Archimedes Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists ...

in ''

The Sand Reckoner ''The Sand Reckoner'' ( el, Ψαμμίτης, ''Psammites'') is a work by Archimedes, an Ancient Greek mathematician of the 3rd century BC, in which he set out to determine an upper bound for the number of grains of sand that fit into the unive ...

''. By Archimedes's calculation, the universe of Aristarchus (roughly 2 light years in diameter), if fully packed with sand, would contain 10⁶³ grains. If the much larger observable universe of today were filled with sand, it would still only equal 10⁹⁵ grains. Another 100,000 observable universes filled with sand would be necessary to make a googol. The decay time for a supermassive

black hole A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...

of roughly 1 galaxy-mass (10¹¹

solar mass The solar mass () is a standard unit of mass in astronomy, equal to approximately . It is often used to indicate the masses of other stars, as well as stellar clusters, nebulae, galaxies and black holes. It is approximately equal to the mass ...

es) due to

Hawking radiation Hawking radiation is theoretical black body radiation that is theorized to be released outside a black hole's event horizon because of relativistic quantum effects. It is named after the physicist Stephen Hawking, who developed a theoretical a ...

is on the order of 10¹⁰⁰ years. See in particular equation (27). Therefore, the

heat death Heat death may refer to: *Heat death of the universe, a proposed cosmological event ** Heat death paradox, a philosophical examination of the cosmological event *Hyperthermia, injury up to and including death, from excessive heat *Thermal shock ...

of an

expanding universe The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion whereby the scale of space itself changes. The universe does not exp ...

is lower-bounded to occur at least one googol years in the future. A googol is considerably smaller than a

centillion Two naming scales for large numbers have been used in English and other European languages since the early modern era: the long and short scales. Most English variants use the short scale today, but the long scale remains dominant in many non-Eng ...

Properties

A googol is approximately ''70!'' (

factorial In mathematics, the factorial of a non-negative denoted is the product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times (n-1) \times (n-2) \t ...

of 70). Using an

integral In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented i ...

binary numeral system A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" ( one). The base-2 numeral system is a positional notatio ...

, one would need 333 bits to represent a googol, i.e., 1 googol =

2^

≈ 2^332.19280949. However, a googol is well within the maximum bounds of an

IEEE 754 The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard addressed many problems found i ...

double-precision

floating point In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be ...

type, but without full precision in the mantissa. Using

modular arithmetic In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book ...

, the series of residues (mod ''n'') of one googol, starting with mod 1, is as follows: :0, 0, 1, 0, 0, 4, 4, 0, 1, 0, 1, 4, 3, 4, 10, 0, 4, 10, 9, 0, 4, 12, 13, 16, 0, 16, 10, 4, 16, 10, 5, 0, 1, 4, 25, 28, 10, 28, 16, 0, 1, 4, 31, 12, 10, 36, 27, 16, 11, 0, ... This sequence is the same as that of the residues (mod n) of a googolplex up until the 17th position.

Cultural impact

Widespread sounding of the word occurs through the name of the company

Google Google LLC () is an American multinational technology company focusing on search engine technology, online advertising, cloud computing, computer software, quantum computing, e-commerce, artificial intelligence, and consumer electronics. ...

, with the name "Google" being an accidental misspelling of "googol" by the company's founders, which was picked to signify that the search engine was intended to provide large quantities of information. In 2004, family members of Kasner, who had inherited the right to his book, were considering suing Google for their use of the term "googol"; however, no suit was ever filed. Since October 2009, Google has been assigning domain names to its servers under the domain "1e100.net", the scientific notation for 1 googol, in order to provide a single domain to identify servers across the Google network. The word is notable for being the subject of the £1 million question in a 2001 episode of the British quiz show ''

Who Wants to Be a Millionaire? ''Who Wants to Be a Millionaire?'' (often informally called ''Millionaire'') is an international television game show franchise of British origin, created by David Briggs, Mike Whitehill and Steven Knight. In its format, currently owned and ...

'', when contestant

Charles Ingram Charles William Ingram (born 6 August 1963) is an English novelist and former British Army major who gained notoriety for his appearance on the ITV television game show ''Who Wants to Be a Millionaire?''. In episodes recorded in September 200 ...

cheated his way through the show with the help of a confederate in the studio audience..

Notes

References

External links

* * * {{Large numbers Large integers Integers Units of amount 1920s neologisms