Orders of magnitude (numbers)

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The logarithmic scale can compactly represent the relationship among variously sized numbers. Logarithmic scale.png
The logarithmic scale can compactly represent the relationship among variously sized numbers.

This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the short scale, which is used in English-speaking countries, as well as a name in the long scale, which is used in some of the countries that do not have English as their national language.

Number mathematical object used to count, label, and measure

A number is a mathematical object used to count, measure, and also label. The original examples are the natural numbers 1, 2, 3, 4 and so forth. A notational symbol that represents a number is called a numeral. In addition to their use in counting and measuring, numerals are often used for labels, for ordering, and for codes. In common usage, number may refer to a symbol, a word, or a mathematical abstraction.

In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned. Also known as a bare, pure, scalar or a quantity of dimension one.ed and the corresponding unit of measurement in the SI is one unit and it is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Examples of quantities to which dimensions are regularly assigned are length, time, and speed, which are measured in dimensional units, such as metre, second and metre per second. This is considered to aid intuitive understanding. However, especially in mathematical physics, it is often more convenient to drop the assignment of explicit dimensions and express the quantities without dimensions, e.g., addressing the speed of light simply by the dimensionless number 1.

Probability is the measure of the likelihood that an event will occur. See glossary of probability and statistics. Probability quantifies as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2.

Contents

Smaller than 10100 (one googolth)

Monkey animal of the "higher primates" (the simians), but excluding the apes

Monkey is a common name that may refer to groups or species of mammals, in part, the simians of infraorder Simiiformes. The term is applied descriptively to groups of primates, such as families of new world monkeys and old world monkeys. Many monkey species are tree-dwelling (arboreal), although there are species that live primarily on the ground, such as baboons. Most species are also active during the day (diurnal). Monkeys are generally considered to be intelligent, especially the old world monkeys of Catarrhini.

Infinite monkey theorem Counterintuitive result in probability

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, such as the complete works of William Shakespeare. In fact, the monkey would almost surely type every possible finite text an infinite number of times. However, the probability that monkeys filling the observable universe would type a complete work such as Shakespeare's Hamlet is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low.

<i>Hamlet</i> tragedy by William Shakespeare

The Tragedy of Hamlet, Prince of Denmark, often shortened to Hamlet, is a tragedy written by William Shakespeare sometime between 1599 and 1602. Set in Denmark, the play depicts Prince Hamlet and his revenge against his uncle, Claudius, who has murdered Hamlet's father in order to seize his throne and marry Hamlet's mother.

10−100 to 10−30

Standard 52-card deck common card deck used in English-speaking countries

The standard 52-card deck of French playing cards is the most common deck of playing cards used today. It includes thirteen ranks in each of the four French suits: clubs, diamonds, hearts and spades, with reversible "court" or face cards. Each suit includes an ace, a king, queen and jack, each depicted with a symbol of its suit; and ranks two through ten, with each card depicting that many symbols (pips) of its suit. Anywhere from one to six jokers, often distinguishable with one being more colorful than the other, are added to commercial decks, as some card games require these extra cards. Modern playing cards carry index labels on opposite corners or in all four corners to facilitate identifying the cards when they overlap and so that they appear identical for players on opposite sides. The most popular standard pattern of the French deck is sometimes referred to as "English" or "Anglo-American" pattern.

In mathematics, the factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example,

10−30

(0.000000000000000000000000000001; 1000−10; short scale: one nonillionth; long scale: one quintillionth)

The long and short scales are two of several large-number naming systems for integer powers of ten that use the same words with different meanings. The long scale is based on powers of one million, whereas the short scale is based on powers of one thousand.

Contract bridge card game

Contract bridge, or simply bridge, is a trick-taking card game using a standard 52-card deck. In its basic format, it is played by four players in two competing partnerships, with partners sitting opposite each other around a table. Millions of people play bridge worldwide in clubs, tournaments, online and with friends at home, making it one of the world's most popular card games, particularly among seniors. The World Bridge Federation (WBF) is the governing body for international competitive bridge, with numerous other bodies governing bridge at the regional level.

10−27

(0.000000000000000000000000001; 1000−9; short scale: one octillionth; long scale: one quadrilliardth)

10−24

(0.000000000000000000000001; 1000−8; short scale: one septillionth; long scale: one quadrillionth)

ISO: yocto- (y)

10−21

(0.000000000000000000001; 1000−7; short scale: one sextillionth; long scale: one trilliardth)

ISO: zepto- (z)

10−18

(0.000000000000000001; 1000−6; short scale: one quintillionth; long scale: one trillionth)

ISO: atto- (a)

10−15

(0.000000000000001; 1000−5; short scale: one quadrillionth; long scale: one billiardth)

ISO: femto- (f)

10−12

(0.000000000001; 1000−4; short scale: one trillionth; long scale: one billionth)

ISO: pico- (p)

10−9

(0.000000001; 1000−3; short scale: one billionth; long scale: one milliardth)

ISO: nano- (n)

10−6

(0.000001; 1000−2; long and short scales: one millionth)

ISO: micro- (μ)

10−3

(0.001; 1000−1; one thousandth)

ISO: milli- (m)

10−2

(0.01; one hundredth)

ISO: centi- (c)

10−1

(0.1; one tenth)

ISO: deci- (d)

100

(1; one)

101

(10; ten)

ISO: deca- (da)

102

(100; hundred)

ISO: hecto- (h)

103

(1000; thousand)

ISO: kilo- (k)

104

(10000; ten thousand or a myriad)

105

(100000; one hundred thousand or a lakh).

106

(1000000; 10002; long and short scales: one million)

ISO: mega- (M)

107

(10000000; a crore; long and short scales: ten million)

108

(100000000; long and short scales: one hundred million)

109

(1000000000; 10003; short scale: one billion; long scale: one thousand million, or one milliard)

ISO: giga- (G)

1010

(10000000000; short scale: ten billion; long scale: ten thousand million, or ten milliard)

1011

(100000000000; short scale: one hundred billion; long scale: hundred thousand million, or hundred milliard)

1012

(1000000000000; 10004; short scale: one trillion; long scale: one billion)

ISO: tera- (T)

1015

(1000000000000000; 10005; short scale: one quadrillion; long scale: one thousand billion, or one billiard)

ISO: peta- (P)

1018

(1000000000000000000; 10006; short scale: one quintillion; long scale: one trillion)

ISO: exa- (E)

1021

(1000000000000000000000; 10007; short scale: one sextillion; long scale: one thousand trillion, or one trilliard)

ISO: zetta- (Z)

1024

(1000000000000000000000000; 10008; short scale: one septillion; long scale: one quadrillion)

ISO: yotta- (Y)

1027

(1000000000000000000000000000; 10009; short scale: one octillion; long scale: one thousand quadrillion, or one quadrilliard)

1030

(1000000000000000000000000000000; 100010; short scale: one nonillion; long scale: one quintillion)

1033

(1000000000000000000000000000000000; 100011; short scale: one decillion; long scale: one thousand quintillion, or one quintilliard)

1036

(1000000000000000000000000000000000000; 100012; short scale: one undecillion; long scale: one sextillion)

1039

(1000000000000000000000000000000000000000; 100013; short scale: one duodecillion; long scale: one thousand sextillion, or one sextilliard)

1042 to 10100

(1000000000000000000000000000000000000000000; 100014; short scale: one tredecillion; long scale: one septillion)

10100 (one googol) to 1010100 (one googolplex)

(10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000; 100033; short scale: ten duotrigintillion; long scale: ten thousand sexdecillion, or ten sexdecillard) [47]

Larger than 1010100

(One googolplex; 10googol; short scale: googolplex; long scale: googolplex)

See also

Related Research Articles

<span class="texhtml mvar" style="font-style:italic;">e</span> (mathematical constant) mathematical constant

The number e is a mathematical constant that is the base of the natural logarithm: the unique number whose natural logarithm is equal to one. It is approximately equal to 2.71828, and is the limit of (1 + 1/n)n as n approaches infinity, an expression that arises in the study of compound interest. It can also be calculated as the sum of the infinite series

Floating-point arithmetic computer format for representing real numbers

In computing, floating-point arithmetic (FP) is arithmetic using formulaic representation of real numbers as an approximation so as to support a trade-off between range and precision. For this reason, floating-point computation is often found in systems which include very small and very large real numbers, which require fast processing times. A number is, in general, represented approximately to a fixed number of significant digits and scaled using an exponent in some fixed base; the base for the scaling is normally two, ten, or sixteen. A number that can be represented exactly is of the following form:

Logarithm A function that maps products to sums

In mathematics, the logarithm is the inverse function to exponentiation (it is an example of a concave function). That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x. In the simplest case, the logarithm counts repeated multiplication of the same factor; e.g., since 1000 = 10 × 10 × 10 = 103, the "logarithm to base 10" of 1000 is 3. The logarithm of x to baseb is denoted as logb (x) (or, without parentheses, as logbx, or even without explicit base as log x, when no confusion is possible). More generally, exponentiation allows any positive real number to be raised to any real power, always producing a positive result, so the logarithm for any two positive real numbers b and x where b is not equal to 1, is always a unique real number y. More explicitly, the defining relation between exponentiation and logarithm is:

In poker, pot odds are the ratio of the current size of the pot to the cost of a contemplated call. Pot odds are often compared to the probability of winning a hand with a future card in order to estimate the call's expected value.

The number π is a mathematical constant. Originally defined as the ratio of a circle's circumference to its diameter, it now has various equivalent definitions and appears in many formulas in all areas of mathematics and physics. It is approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes spelled out as "pi". It is also called Archimedes' constant.

Benfords law

Benford's law, also called the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data. The law states that in many naturally occurring collections of numbers, the leading significant digit is likely to be small. For example, in sets that obey the law, the number 1 appears as the leading significant digit about 30% of the time, while 9 appears as the leading significant digit less than 5% of the time. If the digits were distributed uniformly, they would each occur about 11.1% of the time. Benford's law also makes predictions about the distribution of second digits, third digits, digit combinations, and so on.

In poker, the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands.

Rounding replacing numerical value by another approximately equal

Rounding a number means replacing it with a different number that is approximately equal to the original, but has a shorter, simpler, or more explicit representation; for example, replacing $23.4476 with $23.45, or the fraction 312/937 with 1/3, or the expression 2 with 1.414.

Odds are a numerical expression, usually expressed as a pair of numbers, used in both gambling and statistics. In statistics, the odds for or odds of some event reflect the likelihood that the event will take place, while odds against reflect the likelihood that it will not. In gambling, the odds are the ratio of payoff to stake, and do not necessarily reflect exactly the probabilities. Odds are expressed in several ways, and sometimes the term is used incorrectly to mean simply the probability of an event. Conventionally, gambling odds are expressed in the form "X to Y", where X and Y are numbers, and it is implied that the odds are odds against the event on which the gambler is considering wagering. In both gambling and statistics, the 'odds' are a numerical expression of the likelihood of some possible event.

Large numbers are numbers that are significantly larger than those ordinarily used in everyday life, for instance in simple counting or in monetary transactions. The term typically refers to large positive integers, or more generally, large positive real numbers, but it may also be used in other contexts.

Power of two two raised to an integer power

In mathematics, a power of two is a number of the form 2n where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent.

In physics and cosmology, digital physics is a collection of theoretical perspectives based on the premise that the universe is describable by information. It is a form of digital ontology about the physical reality. According to this theory, the universe can be conceived of as either the output of a deterministic or probabilistic computer program, a vast, digital computation device, or mathematically isomorphic to such a device.

An odds ratio (OR) is a statistic that quantifies the strength of the association between two events, A and B. The odds ratio is defined as the ratio of the odds of A in the presence of B and the odds of A in the absence of B, or equivalently, the ratio of the odds of B in the presence of A and the odds of B in the absence of A. Two events are independent if and only if the OR equals 1: the odds of one event are the same in either the presence or absence of the other event. If the OR is greater than 1, then A and B are associated (correlated) in the sense that, compared to the absence of B, the presence of B raises the odds of A, and symmetrically the presence of A raises the odds of B. Conversely, if the OR is less than 1, then A and B are negatively correlated, and the presence of one event reduces the odds of the other event. The OR plays an important role in the logistic model, which generalizes beyond two events.

The mathematics of gambling are a collection of probability applications encountered in games of chance and can be included in game theory. From a mathematical point of view, the games of chance are experiments generating various types of aleatory events, the probability of which can be calculated by using the properties of probability on a finite space of events.

Randomness lack of pattern or predictability in events, or, a measure of uncertainty of an outcome

Randomness is the lack of pattern or predictability in events. A random sequence of events, symbols or steps has no order and does not follow an intelligible pattern or combination. Individual random events are by definition unpredictable, but in many cases the frequency of different outcomes over a large number of events is predictable. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will occur twice as often as 4. In this view, randomness is a measure of uncertainty of an outcome, rather than haphazardness, and applies to concepts of chance, probability, and information entropy.

The hartley, also called a ban, or a dit, is a logarithmic unit which measures information or entropy, based on base 10 logarithms and powers of 10, rather than the powers of 2 and base 2 logarithms which define the bit, or shannon. One ban or hartley is the information content of an event if the probability of that event occurring is ​110. It is therefore equal to the information contained in one decimal digit, assuming a priori equiprobability of each possible value.

A mathematical constant is a special number that is "significantly interesting in some way". Constants arise in many areas of mathematics, with constants such as e and π occurring in such diverse contexts as geometry, number theory, and calculus.

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