Big numbers
Big numbers table. Examples of big numbers used to describe objects in the world.
Big numbers
(long scale)
(short scale) |
Prefix (Symbol) | Decimal | Power of ten |
---|---|---|---|
million
million |
mega- (M) | 1,000,000 | 10^{6} |
milliard
billion |
giga- (G) | 1,000,000,000 | 10^{9} |
billion
trillion |
tera- (T) | 1,000,000,000,000 | 10^{12} |
billiard
quadrillion |
peta- (P) | 1,000,000,000,000,000 | 10^{15} |
trillion
quintillion |
exa- (E) | 1,000,000,000,000,000,000 | 10^{18} |
trilliard
sextillion |
zetta- (Z) | 1,000,000,000,000,000,000,000 | 10^{21} |
quadrillion
septillion |
yotta- (Y) | 1,000,000,000,000,000,000,000,000 | 10^{24} |
Big/large numbers
Numbers that are much larger than those commonly used in everyday life, for example in simple calculations or payments, appear frequently in fields such as mathematics, cosmology, cryptography, and mathematical machines. The term usually refers to large positive deposit numbers, or more commonly, real positive positive numbers, but may also be used in some cases. The study of nomenclature and structures of large numbers is sometimes referred to as googology.
People sometimes refer to large numbers as "astronomical;" however, it is easier to interpret numbers in terms much higher than those used in astronomy.
In the everyday world
Scientific inventions were created to manage the variety of values that occur in scientific research. 1.0 × 10^{9}, for example, means one billion, 1 followed by nine zeros: 1,000 000 000 000, and 1.0 × 10−9 means half a billion, or 0.000 000 literacy effort 001009. to calculate a long series of zeros to see how big a number is.
Examples of large numbers describing everyday objects in the real world include:
- Number of cells in the human body (approximately 3.72 × 10^{13})
- Number of bits on computer hard disk (from 2021, usually about 10^{13}, 1–2 TB)
- Number of neuronal connections in the human brain (estimated 10^{14})
- Avogadro constant number of “basic businesses” (usually atoms or molecules) in a single mole; total number of atoms in 12 grams of carbon-12 - about 6.022 × 10^{23}.
- The total number of DNA-based pairs among all the biomass on Earth, as a possible estimate of the world's biodiversity, is estimated at (5.3 ± 3.6) × 10^{37}
- Earth's mass contains approximately 4x10^{51} nucleons
- Limited number of atoms in the physical universe (10^{80v)}
- The lower limit of the chess tree complex, also known as the "Shannon number" (estimated at about 10^{120})
Astronomy
Some of the largest numbers, in terms of length and time, are found in astronomy and cosmology. For example, the current Big Bang model suggests that the universe is 13.8 billion years (4.355 × 10^{17} seconds), and that the observable universe is 93 billion light-years (8.8 × 10^{26} meters), and contains 125 billion galaxies (1.25 × 10^{11}), according to the Hubble Space Telescope. There are about 1080 atoms in the visible universe, in the wrong proportions.
According to Don Page, a physicist at the University of Alberta, Canada, the longest time limit has been clearly defined by any natural scientist.
Equal to Poincaré's average time-of-term quantum measurement of a speculative box containing a black hole with an estimated universal weight, visible or not, assuming that a certain inflation model with inflaton is 10−6. Plack Crowds. This time it takes a mathematical model under Poincaré multiplication. The simplified way of thinking at this time is in the model where the history of the universe automatically repeats itself many times due to the mathematical properties of the mathematicians; this is a measure of the time at which it will begin to resemble in some way (with the correct choice of "similar") and its current state again.
Blending processes quickly produce even larger numbers. The factorial function, which defines the number of permissions in a set of fixed objects, grows very rapidly with the number of objects. Stirling's formula provides an accurate description of this growth rate.
Blending processes produce very large numbers in mathematical mechanics. These numbers are so large that they are usually only called using their logarithms.
Gödel's numbers, as well as similar numbers used to represent bit-strings in algorithmic information theory, are enormous, even in mathematical terms. However, some pathological numbers are much larger than Gödel's numbers for standard mathematical suggestions.
Logician Harvey Friedman has done work related to very large numbers, such as the Kruskal tree theory and Robertson – Seymour theorem.
"Billions and billions"
To help Cosmos viewers distinguish between "millions" and "billions", astronomer Carl Sagan emphasized "b". Sagan did not, however, say "billions and billions". The public association of this name with Sagan came from the Tonight Show skit. Laughing at Sagan's touch, Johnny Carson joked "billions and billions".
Examples of big/large numbers
Numbers expressible in decimal notation:
2^{2} = 2^2 = 42^2^2 = 2 ↑↑ 3 = 16
10^{6} = 1,000,000 = 1 million
8^{8} = 16,777,216
9^{9} = 387,420,489
10^{9} = 1,000,000,000 = 1 billion
10^{10} = 10,000,000,000
10^{12} = 1,000,000,000,000 = 1 trillion
3^3^3 = 3 ↑↑ 3 = 7,625,597,484,987 ≈ 7.63 × 1012
10^{15} = 1,000,000,000,000,000 = 1 million billion = 1 quadrillion
Approximate number of atoms in the observable universe = 10^{80} = 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
googol = 10^{100} = 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
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