Numbers are the mathematical figures or values that are involved in mathematical operations like addition, subtraction, multiplication, and division. These values are also known as numerals and are generally used for determining time, measurement, labeling of products, sales, trading, etc in our daily life.
Numbers are the mathematical values used for the purpose of counting, measuring, and other arithmetic calculations. Some examples of numbers are integers, whole numbers, natural numbers, rational and irrational numbers, etc.
The number system is a way of representing these mathematical figures in different forms. The numerals in the number system are categorized into different types of numbers for example prime numbers, odd numbers, even numbers, rational numbers, whole numbers, etc. The system determines whether the numbers will be expressed in the form of figures or words accordingly.
A Number system is defined as a way of standard representation to express numbers. It is the unique way of representation in which numbers are represented in arithmetic and algebraic structure.
Types of Number System
As we studied that number systems are the standardized systems to express mathematical figures either in the form of figures or words. On the basis of the way of expression, number systems are categorized into four common types.
- Decimal Number System: The decimal number system represents numbers in expressions of units, tens, hundreds, thousands as it moves ahead from the decimal point. For example, 35 is a value where 5 is at units and 3 is at tens position.
- Binary Number System: The number system which involves only two digits is 0 and 1 is called a binary number system. For example,10011011 is a binary number.
- Octal Number System: It is the number system most applicable in computer applications that uses numbers from 0 to 7 for the representation of values. For example 1535
- Hexadecimal System: This system includes the method of representing numbers with figures as well as alphabets. In a hexadecimal binary system, the numbers are first expressed in terms of the decimal system and then with alphabets from A to F.
Types Of Numbers
Numerals are the mathematical figures which represent certain values in mathematical operations. There are different types of numbers categorized into sets by the number system.
- Natural numbers: Natural numbers are the set of numbers counting from 1 to infinity. The set of natural numbers is represented by ‘N’. It is the numbers we generally use for counting. The set of natural numbers by is given N=1,2,.3,4,5,6,7,……………
- Whole numbers: Whole numbers are the set of natural numbers including zero, which counts from 0 to infinity. Whole numbers do not include fractions or decimals. The set of whole numbers is represented by ‘W’. The set of whole numbers is given by W=0,1,2,3,4,5,………………
- Integers: Integers are the set of numbers including all the positive natural numbers, zero as well as all negative counting numbers which count from negative infinity to positive infinity. The set doesn’t include fractions and decimals. The set of integers is denoted by ‘Z. The set of integers is given by Z=………..,-5.-4,-3,-2,-1,0,1,2,3,4,,5,………….
- Decimal numbers: Any numeral value that consists of a decimal point is a decimal number. It can be expressed as 2.5,0.567, etc.
- Real number: Real numbers are the set numbers that do not include any imaginary value. It includes all the positive integers, negative integers, fractions, and decimal values. It is generally denoted by ‘R”.
- Complex number: Complex numbers are a set of numbers that include imaginary numbers. It can be expressed as a+bi where “a” and “b” are real numbers. It is denoted by ‘C’.
- Rational numbers: Rational numbers are the numbers that can be expressed as the ratio of two integers. It includes all the integers and can be expressed in terms of fractions or decimals. It is denoted by ‘Q’.
- Irrational numbers: Irrational numbers are numbers that cannot be expressed in fractions or ratios of integers. it can be written in decimals and have endless non-repeating digits after the decimal point. It is denoted by ‘P’.
What is the largest number in the world?
A Googolplex is considered to be the biggest number in the world. It is written as 10googol. The number 10googol can also be expressed in the exponential format that will equal 1010^100. While writing the number googol in normal number writing format the probability of losing count is very high. Hence, it is more convenient to express it in the form of exponent and powers.
The number googolplex is so ridiculously large that it is unimaginable to be written down in number writing format. The number hence remains a concept as it is of no use in mathematics for basic calculations.
Sample Questions
Question 1. Which number in the world holds a Guinness world record?
Answer:
Graham’s number holds the Guinness World Record for the biggest specific integer used in a published mathematical proof.
Question 2. Who attempted to write down the number googolplex?
Answer:
A mathematician Wolfgang H Nitsche attempted to write down the number googolplex and started releasing editions of a book of it.
Question 3. What is a sextillion?
Answer:
A sextillion is a number counting one million million million million million million, in the exponential form it is written as 1036 for the long scale countries. The number is symbolically represented by SX.
Question 4. How many billions equal to one quadrillion?
Answer:
1000000 billions equal to one quadrillion.
Question 5. Does a set of counting numbers ever end?
Answer:
No, the numbers in the universe have no end.
Question 6. Is infinity a real number?
Answer:
Infinity isn’t a number as it is not mathematically represented in figures. Infinity is more of a concept rather than being a definite real number.
Googol. It is a large number, unimaginably large. It is easy to write in exponential format: 10100, an extremely compact method, to easily represent the largest numbers (and also the smallest numbers).
Which is the largest number in the world?
A googolplex was then defined to equal a one followed by a googol zeros. Writing out a googolplex in the usual base ten notation would take up a lot of paper! = 10000. equals 10↑(googol) = 10↑(10↑(10↑2)).
What is the highest number known to man?
The biggest number referred to regularly is a googolplex (10googol), which works out as 1010^100.
Is the largest number infinity?
There is no biggest, last number … except infinity. Except infinity isn’t a number. But some infinities are literally bigger than others.
A googol is a 1 with a hundred zeroes behind it. We can write a googol using exponents by saying a googol is 10^100. The biggest named number that we know is googolplex, ten to the googol power, or (10)^(10^100).
What is the smallest number in the world?
1 : The smallest natural number(i.e. positive integer) is 1. 2 : The smallest whole number is 0.
What is the number 1000000000000000000000000?
Some Very Big, and Very Small Numbers
Name | The Number | Symbol |
---|---|---|
quintillion | 1,000,000,000,000,000,000 | E |
quadrillion | 1,000,000,000,000,000 | P |
Very Small ! | ||
quadrillionth | 0.000 000 000 000 001 | f |
How many zeros are in a bajillion?
“Oh, a bajillion has 42 zeroes, then I mean a bajillion and 1, that must be bigger!”
What is g64 number?
g64 is Graham’s number. First, here are some examples of up-arrows: is 3x3x3 which equals 27. An arrow between two numbers just means the first number multiplied by itself the second number of times.
Is Googolplex bigger than infinity?
Almost inevitably, at this point someone proffers an even bigger number, “googolplex.” It is true that the word “googolplex” was coined to mean a one followed by a googol zeros. It’s way bigger than a measly googol! … True enough, but there is nothing as large as infinity either: infinity is not a number.
What is higher than Graham’s number?
See YouTube or wikipedia for the defination of Graham’s number. A Googol is defined as 10100. A Googolplex is defined as 10Googol. A Googolplexian is defined as 10Googolplex.
Do numbers end?
The sequence of natural numbers never ends, and is infinite. There’s no reason why the 3s should ever stop: they repeat infinitely. So, when we see a number like “0.999…” (i.e. a decimal number with an infinite series of 9s), there is no end to the number of 9s.
What number is after 999 billion?
Here is s look into the future. After 999 billion we have 1 trillion. After 999 trillion we have a quad trillion, then we progress onto quintillion, sex tillion (I like that number) and into the Latin derivative for our numbering scheme. Measuring water uses a different scale.
Is Google a number Yes or no?
A googol equals 1 followed by 100 zeros. Googol is a mathematical term to describe a huge quantity. … Googol, a quantity that surpasses even the number of hydrogen atoms in the observable universe, is a number dating back to the mid-1900s and is still used by mathematicians today.
What’s the first number?
Zero (0) is used as a number and also as the numerical digit. Zero gives the additive identity of the integers, real numbers, and many algebraic structures. It is used as a placeholder for writing numbers. Natural numbers start from 1, then 2 and so on.
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-English-speaking areas, including continental Europe and Spanish-speaking countries in Latin America. These naming procedures are based on taking the number n occurring in 103n+3 (short scale) or 106n (long scale) and concatenating Latin roots for its units, tens, and hundreds place, together with the suffix -illion.
Names of numbers above a trillion are rarely used in practice; such large numbers have practical usage primarily in the scientific domain, where powers of ten are expressed as 10 with a numeric superscript.
Indian English does not use millions, but has its own system of large numbers including lakhs and crores.[1] English also has many words, such as «zillion», used informally to mean large but unspecified amounts; see indefinite and fictitious numbers.
Standard dictionary numbers
x | Name (SS/LS, LS) |
SS (103x+3) |
LS (106x, 106x+3) |
Authorities | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
AHD4[2] | CED[3] | COD[4] | OED2[5] | OEDweb[6] | RHD2[7] | SOED3[8] | W3[9] | HM[10] | ||||
1 | Million | 106 | 106 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
Milliard | 109 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |||||
2 | Billion | 109 | 1012 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
3 | Trillion | 1012 | 1018 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
4 | Quadrillion | 1015 | 1024 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
5 | Quintillion | 1018 | 1030 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |
6 | Sextillion | 1021 | 1036 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |
7 | Septillion | 1024 | 1042 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |
8 | Octillion | 1027 | 1048 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |
9 | Nonillion | 1030 | 1054 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |
10 | Decillion | 1033 | 1060 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |
11 | Undecillion | 1036 | 1066 | ✓ | ✓ | ✓ | ✓ | ✓ | ||||
12 | Duodecillion | 1039 | 1072 | ✓ | ✓ | ✓ | ✓ | ✓ | ||||
13 | Tredecillion | 1042 | 1078 | ✓ | ✓ | ✓ | ✓ | ✓ | ||||
14 | Quattuordecillion | 1045 | 1084 | ✓ | ✓ | ✓ | ✓ | ✓ | ||||
15 | Quindecillion | 1048 | 1090 | ✓ | ✓ | ✓ | ✓ | ✓ | ||||
16 | Sexdecillion | 1051 | 1096 | ✓ | ✓ | ✓ | ✓ | ✓ | ||||
17 | Septendecillion | 1054 | 10102 | ✓ | ✓ | ✓ | ✓ | ✓ | ||||
18 | Octodecillion | 1057 | 10108 | ✓ | ✓ | ✓ | ✓ | ✓ | ||||
19 | Novemdecillion | 1060 | 10114 | ✓ | ✓ | ✓ | ✓ | ✓ | ||||
20 | Vigintillion | 1063 | 10120 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |
100 | Centillion | 10303 | 10600 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
Usage:
- Short scale: US, English Canada, modern British, Australia, and Eastern Europe
- Long scale: French Canada, older British, Western & Central Europe
Apart from million, the words in this list ending with —illion are all derived by adding prefixes (bi-, tri-, etc., derived from Latin) to the stem —illion.[11] Centillion[12] appears to be the highest name ending in -«illion» that is included in these dictionaries. Trigintillion, often cited as a word in discussions of names of large numbers, is not included in any of them, nor are any of the names that can easily be created by extending the naming pattern (unvigintillion, duovigintillion, duoquinquagintillion, etc.).
Name | Value | Authorities | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
AHD4 | CED | COD | OED2 | OEDnew | RHD2 | SOED3 | W3 | UM | ||
Googol | 10100 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
Googolplex | 10googol (1010100) | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
All of the dictionaries included googol and googolplex, generally crediting it to the Kasner and Newman book and to Kasner’s nephew (see below). None include any higher names in the googol family (googolduplex, etc.). The Oxford English Dictionary comments that googol and googolplex are «not in formal mathematical use».
Usage of names of large numbers
Some names of large numbers, such as million, billion, and trillion, have real referents in human experience, and are encountered in many contexts. At times, the names of large numbers have been forced into common usage as a result of hyperinflation. The highest numerical value banknote ever printed was a note for 1 sextillion pengő (1021 or 1 milliard bilpengő as printed) printed in Hungary in 1946. In 2009, Zimbabwe printed a 100 trillion (1014) Zimbabwean dollar note, which at the time of printing was worth about US$30.[13]
Names of larger numbers, however, have a tenuous, artificial existence, rarely found outside definitions, lists, and discussions of how large numbers are named. Even well-established names like sextillion are rarely used, since in the context of science, including astronomy, where such large numbers often occur, they are nearly always written using scientific notation. In this notation, powers of ten are expressed as 10 with a numeric superscript, e.g. «The X-ray emission of the radio galaxy is 1.3×1045 joules.» When a number such as 1045 needs to be referred to in words, it is simply read out as «ten to the forty-fifth». This is easier to say and less ambiguous than «quattuordecillion», which means something different in the long scale and the short scale.
When a number represents a quantity rather than a count, SI prefixes can be used—thus «femtosecond», not «one quadrillionth of a second»—although often powers of ten are used instead of some of the very high and very low prefixes. In some cases, specialized units are used, such as the astronomer’s parsec and light year or the particle physicist’s barn.
Nevertheless, large numbers have an intellectual fascination and are of mathematical interest, and giving them names is one way people try to conceptualize and understand them.
One of the earliest examples of this is The Sand Reckoner, in which Archimedes gave a system for naming large numbers. To do this, he called the numbers up to a myriad myriad (108) «first numbers» and called 108 itself the «unit of the second numbers». Multiples of this unit then became the second numbers, up to this unit taken a myriad myriad times, 108·108=1016. This became the «unit of the third numbers», whose multiples were the third numbers, and so on. Archimedes continued naming numbers in this way up to a myriad myriad times the unit of the 108-th numbers, i.e. and embedded this construction within another copy of itself to produce names for numbers up to Archimedes then estimated the number of grains of sand that would be required to fill the known universe, and found that it was no more than «one thousand myriad of the eighth numbers» (1063).
Since then, many others have engaged in the pursuit of conceptualizing and naming numbers that have no existence outside the imagination. One motivation for such a pursuit is that attributed to the inventor of the word googol, who was certain that any finite number «had to have a name». Another possible motivation is competition between students in computer programming courses, where a common exercise is that of writing a program to output numbers in the form of English words.[citation needed]
Most names proposed for large numbers belong to systematic schemes which are extensible. Thus, many names for large numbers are simply the result of following a naming system to its logical conclusion—or extending it further.[citation needed]
Origins of the «standard dictionary numbers»
The words bymillion and trimillion were first recorded in 1475 in a manuscript of Jehan Adam. Subsequently, Nicolas Chuquet wrote a book Triparty en la science des nombres which was not published during Chuquet’s lifetime. However, most of it was copied by Estienne de La Roche for a portion of his 1520 book, L’arismetique. Chuquet’s book contains a passage in which he shows a large number marked off into groups of six digits, with the comment:
Ou qui veult le premier point peult signiffier million Le second point byllion Le tiers point tryllion Le quart quadrillion Le cinqe quyllion Le sixe sixlion Le sept.e septyllion Le huyte ottyllion Le neufe nonyllion et ainsi des ault’s se plus oultre on vouloit preceder
(Or if you prefer the first mark can signify million, the second mark byllion, the third mark tryllion, the fourth quadrillion, the fifth quyillion, the sixth sixlion, the seventh septyllion, the eighth ottyllion, the ninth nonyllion and so on with others as far as you wish to go).
Adam and Chuquet used the long scale of powers of a million; that is, Adam’s bymillion (Chuquet’s byllion) denoted 1012, and Adam’s trimillion (Chuquet’s tryllion) denoted 1018.
The googol family
The names googol and googolplex were invented by Edward Kasner’s nephew Milton Sirotta and introduced in Kasner and Newman’s 1940 book Mathematics and the Imagination[14] in the following passage:
The name «googol» was invented by a child (Dr. Kasner’s nine-year-old nephew) who was asked to think up a name for a very big number, namely 1 with one hundred zeroes after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. At the same time that he suggested «googol» he gave a name for a still larger number: «googolplex.» A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out. It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired. This is a description of what would happen if one tried to write a googolplex, but different people get tired at different times and it would never do to have Carnera a better mathematician than Dr. Einstein, simply because he had more endurance. The googolplex is, then, a specific finite number, equal to 1 with a googol zeros after it.
Value | Name | Authority |
---|---|---|
10100 | Googol | Kasner and Newman, dictionaries (see above) |
10googol = 1010100 | Googolplex | Kasner and Newman, dictionaries (see above) |
John Horton Conway and Richard K. Guy[15] have suggested that N-plex be used as a name for 10N. This gives rise to the name googolplexplex for 10googolplex = 101010100. Conway and Guy[15] have proposed that N-minex be used as a name for 10−N, giving rise to the name googolminex for the reciprocal of a googolplex, which is written as 10-(10100). None of these names are in wide use.
The names googol and googolplex inspired the name of the Internet company Google and its corporate headquarters, the Googleplex, respectively.
Extensions of the standard dictionary numbers
This section illustrates several systems for naming large numbers, and shows how they can be extended past vigintillion.
Traditional British usage assigned new names for each power of one million (the long scale): 1,000,000 = 1 million; 1,000,0002 = 1 billion; 1,000,0003 = 1 trillion; and so on. It was adapted from French usage, and is similar to the system that was documented or invented by Chuquet.
Traditional American usage (which was also adapted from French usage but at a later date), Canadian, and modern British usage assign new names for each power of one thousand (the short scale.) Thus, a billion is 1000 × 10002 = 109; a trillion is 1000 × 10003 = 1012; and so forth. Due to its dominance in the financial world (and by the US dollar), this was adopted for official United Nations documents.
Traditional French usage has varied; in 1948, France, which had originally popularized the short scale worldwide, reverted to the long scale.
The term milliard is unambiguous and always means 109. It is seldom seen in American usage and rarely in British usage, but frequently in continental European usage. The term is sometimes attributed to French mathematician Jacques Peletier du Mans circa 1550 (for this reason, the long scale is also known as the Chuquet-Peletier system), but the Oxford English Dictionary states that the term derives from post-Classical Latin term milliartum, which became milliare and then milliart and finally our modern term.
Concerning names ending in -illiard for numbers 106n+3, milliard is certainly in widespread use in languages other than English, but the degree of actual use of the larger terms is questionable. The terms «Milliarde» in German, «miljard» in Dutch, «milyar» in Turkish, and «миллиард,» milliard (transliterated) in Russian, are standard usage when discussing financial topics.
For additional details, see billion and long and short scale.
The naming procedure for large numbers is based on taking the number n occurring in 103n+3 (short scale) or 106n (long scale) and concatenating Latin roots for its units, tens, and hundreds place, together with the suffix -illion. In this way, numbers up to 103·999+3 = 103000 (short scale) or 106·999 = 105994 (long scale) may be named. The choice of roots and the concatenation procedure is that of the standard dictionary numbers if n is 9 or smaller. For larger n (between 10 and 999), prefixes can be constructed based on a system described by Conway and Guy.[15] Today, sexdecillion and novemdecillion are standard dictionary numbers and, using the same reasoning as Conway and Guy did for the numbers up to nonillion, could probably be used to form acceptable prefixes. The Conway–Guy system for forming prefixes:
Units | Tens | Hundreds | |
---|---|---|---|
1 | Un | N Deci | NX Centi |
2 | Duo | MS Viginti | N Ducenti |
3 | Tre (*) | NS Triginta | NS Trecenti |
4 | Quattuor | NS Quadraginta | NS Quadringenti |
5 | Quinqua | NS Quinquaginta | NS Quingenti |
6 | Se (*) | N Sexaginta | N Sescenti |
7 | Septe (*) | N Septuaginta | N Septingenti |
8 | Octo | MX Octoginta | MX Octingenti |
9 | Nove (*) | Nonaginta | Nongenti |
- (*) ^ When preceding a component marked S or X, «tre» changes to «tres» and «se» to «ses» or «sex»; similarly, when preceding a component marked M or N, «septe» and «nove» change to «septem» and «novem» or «septen» and «noven».
Since the system of using Latin prefixes will become ambiguous for numbers with exponents of a size which the Romans rarely counted to, like 106,000,258, Conway and Guy co-devised with Allan Wechsler the following set of consistent conventions that permit, in principle, the extension of this system indefinitely to provide English short-scale names for any integer whatsoever.[15] The name of a number 103n+3, where n is greater than or equal to 1000, is formed by concatenating the names of the numbers of the form 103m+3, where m represents each group of comma-separated digits of n, with each but the last «-illion» trimmed to «-illi-«, or, in the case of m = 0, either «-nilli-» or «-nillion».[15] For example, 103,000,012, the 1,000,003rd «-illion» number, equals one «millinillitrillion»; 1033,002,010,111, the 11,000,670,036th «-illion» number, equals one «undecillinilliseptuagintasescentillisestrigintillion»; and 1029,629,629,633, the 9,876,543,210th «-illion» number, equals one «nonilliseseptuagintaoctingentillitresquadragintaquingentillideciducentillion».[15]
The following table shows number names generated by the system described by Conway and Guy for the short and long scales.[16]
Base -illion (short scale) |
Base -illion (long scale) |
Value | US, Canada and modern British (short scale) |
Traditional British (long scale) |
Traditional European (Peletier) (long scale) |
SI Symbol |
SI Prefix |
---|---|---|---|---|---|---|---|
1 | 1 | 106 | Million | Million | Million | M | Mega- |
2 | 1 | 109 | Billion | Thousand million | Milliard | G | Giga- |
3 | 2 | 1012 | Trillion | Billion | Billion | T | Tera- |
4 | 2 | 1015 | Quadrillion | Thousand billion | Billiard | P | Peta- |
5 | 3 | 1018 | Quintillion | Trillion | Trillion | E | Exa- |
6 | 3 | 1021 | Sextillion | Thousand trillion | Trilliard | Z | Zetta- |
7 | 4 | 1024 | Septillion | Quadrillion | Quadrillion | Y | Yotta- |
8 | 4 | 1027 | Octillion | Thousand quadrillion | Quadrilliard | R | Ronna- |
9 | 5 | 1030 | Nonillion | Quintillion | Quintillion | Q | Quetta- |
10 | 5 | 1033 | Decillion | Thousand quintillion | Quintilliard | ||
11 | 6 | 1036 | Undecillion | Sextillion | Sextillion | ||
12 | 6 | 1039 | Duodecillion | Thousand sextillion | Sextilliard | ||
13 | 7 | 1042 | Tredecillion | Septillion | Septillion | ||
14 | 7 | 1045 | Quattuordecillion | Thousand septillion | Septilliard | ||
15 | 8 | 1048 | Quindecillion | Octillion | Octillion | ||
16 | 8 | 1051 | Sedecillion | Thousand octillion | Octilliard | ||
17 | 9 | 1054 | Septendecillion | Nonillion | Nonillion | ||
18 | 9 | 1057 | Octodecillion | Thousand nonillion | Nonilliard | ||
19 | 10 | 1060 | Novendecillion | Decillion | Decillion | ||
20 | 10 | 1063 | Vigintillion | Thousand decillion | Decilliard | ||
21 | 11 | 1066 | Unvigintillion | Undecillion | Undecillion | ||
22 | 11 | 1069 | Duovigintillion | Thousand undecillion | Undecilliard | ||
23 | 12 | 1072 | Tresvigintillion | Duodecillion | Duodecillion | ||
24 | 12 | 1075 | Quattuorvigintillion | Thousand duodecillion | Duodecilliard | ||
25 | 13 | 1078 | Quinvigintillion | Tredecillion | Tredecillion | ||
26 | 13 | 1081 | Sesvigintillion | Thousand tredecillion | Tredecilliard | ||
27 | 14 | 1084 | Septemvigintillion | Quattuordecillion | Quattuordecillion | ||
28 | 14 | 1087 | Octovigintillion | Thousand quattuordecillion | Quattuordecilliard | ||
29 | 15 | 1090 | Novemvigintillion | Quindecillion | Quindecillion | ||
30 | 15 | 1093 | Trigintillion | Thousand quindecillion | Quindecilliard | ||
31 | 16 | 1096 | Untrigintillion | Sedecillion | Sedecillion | ||
32 | 16 | 1099 | Duotrigintillion | Thousand sedecillion | Sedecilliard | ||
33 | 17 | 10102 | Trestrigintillion | Septendecillion | Septendecillion | ||
34 | 17 | 10105 | Quattuortrigintillion | Thousand septendecillion | Septendecilliard | ||
35 | 18 | 10108 | Quintrigintillion | Octodecillion | Octodecillion | ||
36 | 18 | 10111 | Sestrigintillion | Thousand octodecillion | Octodecilliard | ||
37 | 19 | 10114 | Septentrigintillion | Novendecillion | Novendecillion | ||
38 | 19 | 10117 | Octotrigintillion | Thousand novendecillion | Novendecilliard | ||
39 | 20 | 10120 | Noventrigintillion | Vigintillion | Vigintillion | ||
40 | 20 | 10123 | Quadragintillion | Thousand vigintillion | Vigintilliard | ||
50 | 25 | 10153 | Quinquagintillion | Thousand quinvigintillion | Quinvigintilliard | ||
60 | 30 | 10183 | Sexagintillion | Thousand trigintillion | Trigintilliard | ||
70 | 35 | 10213 | Septuagintillion | Thousand quintrigintillion | Quintrigintilliard | ||
80 | 40 | 10243 | Octogintillion | Thousand quadragintillion | Quadragintilliard | ||
90 | 45 | 10273 | Nonagintillion | Thousand quinquadragintillion | Quinquadragintilliard | ||
100 | 50 | 10303 | Centillion | Thousand quinquagintillion | Quinquagintilliard | ||
101 | 51 | 10306 | Uncentillion | Unquinquagintillion | Unquinquagintillion | ||
110 | 55 | 10333 | Decicentillion | Thousand quinquinquagintillion | Quinquinquagintilliard | ||
111 | 56 | 10336 | Undecicentillion | Sesquinquagintillion | Sesquinquagintillion | ||
120 | 60 | 10363 | Viginticentillion | Thousand sexagintillion | Sexagintilliard | ||
121 | 61 | 10366 | Unviginticentillion | Unsexagintillion | Unsexagintillion | ||
130 | 65 | 10393 | Trigintacentillion | Thousand quinsexagintillion | Quinsexagintilliard | ||
140 | 70 | 10423 | Quadragintacentillion | Thousand septuagintillion | Septuagintilliard | ||
150 | 75 | 10453 | Quinquagintacentillion | Thousand quinseptuagintillion | Quinseptuagintilliard | ||
160 | 80 | 10483 | Sexagintacentillion | Thousand octogintillion | Octogintilliard | ||
170 | 85 | 10513 | Septuagintacentillion | Thousand quinoctogintillion | Quinoctogintilliard | ||
180 | 90 | 10543 | Octogintacentillion | Thousand nonagintillion | Nonagintilliard | ||
190 | 95 | 10573 | Nonagintacentillion | Thousand quinnonagintillion | Quinnonagintilliard | ||
200 | 100 | 10603 | Ducentillion | Thousand centillion | Centilliard | ||
300 | 150 | 10903 | Trecentillion | Thousand quinquagintacentillion | Quinquagintacentilliard | ||
400 | 200 | 101203 | Quadringentillion | Thousand ducentillion | Ducentilliard | ||
500 | 250 | 101503 | Quingentillion | Thousand quinquagintaducentillion | Quinquagintaducentilliard | ||
600 | 300 | 101803 | Sescentillion | Thousand trecentillion | Trecentilliard | ||
700 | 350 | 102103 | Septingentillion | Thousand quinquagintatrecentillion | Quinquagintatrecentilliard | ||
800 | 400 | 102403 | Octingentillion | Thousand quadringentillion | Quadringentilliard | ||
900 | 450 | 102703 | Nongentillion | Thousand quinquagintaquadringentillion | Quinquagintaquadringentilliard | ||
1000 | 500 | 103003 | Millillion (alt. millinillion)[17] | Thousand quingentillion | Quingentilliard |
Value | Name | Equivalent | ||
---|---|---|---|---|
US, Canadian and modern British (short scale) |
Traditional British (long scale) |
Traditional European (Peletier) (long scale) |
||
10100 | Googol | Ten duotrigintillion | Ten thousand sedecillion | Ten sedecilliard |
1010100 | Googolplex | [1] Ten trillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentillitrestrigintatrecentilliduotrigintatrecentillion | [2] Ten thousand millisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillion | [2] Ten millisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentillisesexagintasescentilliard |
- ^[1] Googolplex’s short scale name is derived from it equal to ten of the 3,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,332nd «-illion»s (This is the value of n when 10 X 10(3n + 3) = 1010100)
- ^[2] Googolplex’s long scale name (both traditional British and traditional European) is derived from it being equal to ten thousand of the 1,666,666,666,666,666,666,666,666,666,666,666,666,666,666,666,666,666,666,666,666,666,666,666,666,666,666,666,666,666,666,666,666,666th «-illion»s (This is the value of n when 10,000 X 106n = 1010100).
Binary prefixes
The International System of Quantities (ISQ) defines a series of prefixes denoting integer powers of 1024 between 10241 and 10248.[18]
Power | Value | ISQ symbol |
ISQ prefix |
---|---|---|---|
1 | 10241 | Ki | Kibi- |
2 | 10242 | Mi | Mebi- |
3 | 10243 | Gi | Gibi- |
4 | 10244 | Ti | Tebi- |
5 | 10245 | Pi | Pebi- |
6 | 10246 | Ei | Exbi- |
7 | 10247 | Zi | Zebi- |
8 | 10248 | Yi | Yobi- |
Other large numbers used in mathematics, physics and chemistry
- Avogadro number
- Graham’s number
- Skewes’ number
- Steinhaus–Moser notation
- TREE(3)
- Rayo’s number
See also
- -yllion
- Asaṃkhyeya
- Chinese numerals
- History of large numbers
- Indefinite and fictitious numbers
- Indian numbering system
- Knuth’s up-arrow notation
- Law of large numbers
- List of numbers
- Long and short scale
- Metric prefix
- Names of small numbers
- Number names
- Number prefix
- Orders of magnitude
- Orders of magnitude (data)
- Orders of magnitude (numbers)
- Power of 10
References
- ^
Bellos, Alex (2011). Alex’s Adventures in Numberland. A&C Black. p. 114. ISBN 978-1-4088-0959-4. - ^
The American Heritage Dictionary of the English Language (4th ed.). Houghton Mifflin. 2000. ISBN 0-395-82517-2. - ^
«Collins English Dictionary». HarperCollins. - ^
«Cambridge Dictionaries Online». Cambridge University Press. - ^
The Oxford English Dictionary (2nd ed.). Clarendon Press. 1991. ISBN 0-19-861186-2. - ^
«Oxford English Dictionary». Oxford University Press. - ^
The Random House Dictionary of the English Language (2nd ed.). Random House. 1987. - ^
Brown, Lesley; Little, William (1993). The New Shorter Oxford English Dictionary. Oxford University Press. ISBN 0198612710. - ^
Webster, Noah (1981). Webster’s Third New International Dictionary of the English Language, Unabridged. Merriam-Webster. ISBN 0877792011. - ^
Rowlett, Russ. «How Many? A Dictionary of Units of Measures». Russ Rowlett and the University of North Carolina at Chapel Hill. Archived from the original on 1 March 2000. Retrieved 25 September 2022. - ^
Emerson, Oliver Farrar (1894). The History of the English Language. Macmillan and Co. p. 316. - ^
«Entry for centillion in dictionary.com». dictionary.com. Retrieved 25 September 2022. - ^
«Zimbabwe rolls out Z$100tr note». BBC News. 16 January 2009. Retrieved 25 September 2022. - ^
Kasner, Edward; Newman, James (1940). Mathematics and the Imagination. Simon and Schuster. ISBN 0-486-41703-4. - ^ a b c d e f
Conway, J. H.; Guy, R. K. (1998). The Book of Numbers. Springer Science & Business Media. pp. 15–16. ISBN 0-387-97993-X. - ^ Fish. «Conway’s illion converter». Retrieved 1 March 2023.
- ^
Stewart, Ian (2017). Infinity: A Very Short Introduction. Oxford University Press. p. 20. ISBN 978-0-19-875523-4. - ^
«IEC 80000-13:2008». International Organization for Standardization. Retrieved 25 September 2022.
Last Updated: April 20, 2022 | Author: howto-Trust
Contents
- 1 What is this number 1000000000000000000000000?
- 2 Is Googolplex bigger than infinity?
- 3 Is zillion a number?
- 4 Do numbers go on forever?
- 5 What is Vigintillion?
- 6 Is Google a number?
- 7 What’s after Octillion?
- 8 How much is a bazillion?
- 9 How long is a googol seconds?
- 10 Will Pi ever end?
- 11 What is 1×10 100 called?
- 12 How long is a Google?
- 13 How long would it take to count to a trillion out loud?
- 14 How long would it take to count to 1million?
- 15 Is there a last number?
- 16 How many millions are in a quadrillion?
- 17 Why is 100 a special number?
- 18 How much is infinite?
- 19 What is after infinity?
- 20 What’s the number before infinity?
- 21 Who invented 0?
What is this number 1000000000000000000000000?
Some Very Big, and Very Small Numbers
Name | The Number | Symbol |
---|---|---|
septillion | 1,000,000,000,000,000,000,000,000 | Y |
sextillion | 1,000,000,000,000,000,000,000 | Z |
quintillion | 1,000,000,000,000,000,000 | E |
quadrillion | 1,000,000,000,000,000 | P |
Is Googolplex bigger than infinity?
Almost inevitably, at this point someone proffers an even bigger number, “googolplex.” It is true that the word “googolplex” was coined to mean a one followed by a googol zeros. … True enough, but there is nothing as large as infinity either: infinity is not a number. It denotes endlessness.
Is zillion a number?
A zillion is a huge but nonspecific number. … Zillion sounds like an actual number because of its similarity to billion, million, and trillion, and it is modeled on these real numerical values. However, like its cousin jillion, zillion is an informal way to talk about a number that’s enormous but indefinite.
Do numbers go on forever?
The sequence of natural numbers never ends, and is infinite. … So, when we see a number like “0.999…” (i.e. a decimal number with an infinite series of 9s), there is no end to the number of 9s. You cannot say “but what happens if it ends in an 8?”, because it simply does not end.
What is Vigintillion?
Definition of vigintillion
US : a number equal to 1 followed by 63 zeros — see Table of Numbers also, British : a number equal to 1 followed by 120 zeros — see Table of Numbers.
Is Google a number?
Google is the word that is more common to us now, and so it is sometimes mistakenly used as a noun to refer to the number 10100. That number is a googol, so named by Milton Sirotta, the nephew of the American mathematician Edward Kasner, who was working with large numbers like 10100.
What’s after Octillion?
There’s quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion and more. Each is a thousand of the previous one.
How much is a bazillion?
(slang) A very large, indefinite number. (slang, hyperbolic) An unspecified large number (of).
How long is a googol seconds?
A googol seconds is about a sexvigintillion (1081) times the estimated age of the universe. A googol angstroms is approximately 100 trevigintillion light-years. It takes approximately 317 novemvigintillion years to count to a googol one integer at a time.
Will Pi ever end?
Technically no, though no one has ever been able to find a true end to the number. It’s actually considered an “irrational” number, because it keeps going in a way that we can’t quite calculate. Pi dates back to 250 BCE by a Greek mathematician Archimedes, who used polygons to determine the circumference.
What is 1×10 100 called?
The scientific notation for a googol is 1 x 10100.
“Googol” got its name in 1938, when nine-year-old Milton Sirotta came up with the name and suggested it to his uncle, mathematician Edward Kasner.
How long is a Google?
A googol is a 1 followed by 100 zeros (or 10100 ). It was given its whimsical name in 1937 by mathematician Edward Kasner’s young nephew, and became famous when an internet search engine, wanting to suggest that it could process a huge amount of data, named itself Google.
How long would it take to count to a trillion out loud?
To find how long it would take to count to a trillion dollars divide 1 trillion by 31,536,000. That is 1,000,000,000,000/31,536,000 = 31,709.79 years.
How long would it take to count to 1million?
– 1 Million: To count to 1 million will take you about 11 days.
Is there a last number?
There is no biggest, last number … except infinity. Except infinity isn’t a number.
How many millions are in a quadrillion?
A thousand million millions. We could also think of it as a thousand trillion or a million billion.
Why is 100 a special number?
100 is a perfect square number and its square root is 10. 100 is the basis of percentages (“per cent” meaning “per hundred” in Latin), with 100 percent being a full amount. There are 100 pennies in one dollar.
How much is infinite?
infinity, the concept of something that is unlimited, endless, without bound. The common symbol for infinity, ∞, was invented by the English mathematician John Wallis in 1655. Three main types of infinity may be distinguished: the mathematical, the physical, and the metaphysical.
What is after infinity?
With this definition, there is nothing (meaning: no real numbers) larger than infinity. There is another way to look at this question. It come from an idea of Georg Cantor who lived from 1845 to 1918. … Cantor’s idea seems really clear at first but it gives some surprising results when you apply it to infinite sets.
What’s the number before infinity?
There is no last number before infinity, because simply put, infinity isn’t a number. The most common definition of (positive) infinity is x such that x>n for all real n. Assume s is a real number and is in fact the largest real number. Consider s+1.
Who invented 0?
mathematician Brahmagupta
The first modern equivalent of numeral zero comes from a Hindu astronomer and mathematician Brahmagupta in 628. His symbol to depict the numeral was a dot underneath a number.
infinity
When it comes to large numbers, we’ve got lots to discuss. You might say there’s an infinity of ways to talk about numbers so large they are written in scientific notation or exist only in the imagination.
While terms like million and infinity have been in use for hundreds of years, newer terms such as gargantuul debuted more recently. With this in mind, we thought we’d take a look at some of the vocabulary, definitions, and linguistic trivia surrounding large numbers. Who knows? You might be inspired to invent your own … or at least find math a little more interesting.
Speaking of infinity … in mathematics, infinity refers to “an indefinitely great amount or number” or “a number that is larger than all other numbers.”
The word is derived from the late 14c. Old French infinité, itself derived from the Latin infinitatem meaning “boundlessness” or “endlessness.” Infinity is often represented by the symbol (∞).
John Wallis (1616–1703) is credited with introducing the infinity symbol in 1655. It has been conjectured that Wallis chose the symbol as a variant of a Roman numeral 1,000 (CIƆ, also CƆ).
Philosophers and mathematicians, from Zeno of Elea (c.495–430 BC) to Isaac Newton (1642–1727) and beyond, have studied the nature and concept of infinity. One example of the questions posed by infinity is Zeno’s dichotomy paradox.
The paradox imagines that Homer (legendary author of the Iliad and the Odyssey) wishes to walk to the end of a short path. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there and so on. To get to the end of the path, Zeno argues, would require Homer to complete an infinite number of tasks (i.e., crossing progressively shorter and shorter distances). The fact that Homer can do so is, therefore, a paradox and quite an achievement.
If you’ve made it to the end of this slide without being confused, that’s quite an achievement, too … on to the next!