How Many Names of Large Numbers How Many

How Many? Names of Large Numbers How Many?

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Thousands of Thousands. One calls them Millions. Please watch a movie clip from http: //www. math. harvard. edu/~knill/mathmovies /swf/onceuponatime_millions. html This clip is from the 1968 spaghetti Western “Once Upon A Time in the West”, produced by Sergio Leone and starring Henry Fonda and Charles Bronson. How Many? 3

Million • Milionis an Old French word thought to derive from Old Italian milionean , intensification of mille a , thousand. That is, a million a big thousand is. How Many? 4

Billion, Trillion, … Traditional American usage and modern British usage, assigns new names for each power of one thousand. Thus, a billion 1000 × 10002 = 109; a is trillionis 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. How Many? 5

Usage of names of large numbers • Some names of large numbers, such as millionbillionand 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 excessive inflation. The highest numerical value banknote ever printed was a note for 1 sextillion pengő (1021) printed in Hungary in 1946. In 2009, Zimbabwe printed a 100 trillion (1014) Zimbabwean dollar note, which in January 2009 was only worth about 30 US dollars. How Many? 6

Usage of names of large numbers Names of larger numbers have a tenuous, artificial existence, rarely found outside definitions, lists, and discussions of the ways in which large numbers are named. Even well-established names like sextillion are rarely used, since in the contexts of science, astronomy, and engineering, where large numbers often occur, numbers are usually 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 x 1045 ergs. " When a number such as 1045 needs to be referred to in words, it is simply read out: "ten to the forty-fifth. " This is just as easy to say, easier to understand, and less ambiguous than “quattuordecillion”. How Many? 7

Base-illion Value 1 106 2 109 3 1012 4 1015 5 1018 6 1021 7 1024 8 1027 9 1030 10 1033 USA and modern British Million Billion Trillion Quadrillion Quintillion Sextillion Septillion Octillion Nonillion Decillion How Many? 8

Base-illion Value 11 1036 12 1039 13 1042 14 1045 15 1048 16 1051 17 1054 18 1057 19 1060 20 1063 USA and modern British Undecillion Duodecillion Tredecillion Quattuordecillion Quindecillion Sexdecillion Septendecillion Octodecillion Novemdecillion Vigintillion How Many? 9

Base-illion Value 30 1093 40 10123 50 10153 60 10183 70 10213 80 10243 90 10273 100 10303 200 10603 300 10903 USA and modern British Trigintillion Quadragintillion Quinquagintillion Sexagintillion Septuagintillion Octogintillion Nonagintillion Centillion Ducentillion Trecentillion How Many? 10

Historical Note • Up until the 1970’s the British defined a Billion to be a Million. i. e. 1 000 000 = 1012 • After this time the world over has generally defined a billion to be One Thousand Million. i. e. 1 000 000 = 109 How Many? 11

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Clara was one in a million, one in a billion, one in a googolplex. Please watch a movie clip from http: //www. math. harvard. edu/~knill/math movies/swf/googolplex. html This clip is from the 1990 Science Fiction Western “Back to the Future Part III”, from writer/director Robert Zemeckis and starring Michael J. Fox and Christopher Lloyd. How Many? 13

The googol family • The names googolplex and were invented by Edward Kasner's nephew, Milton Sirotta, and introduced in Kasner and Newman's 1940 book, Mathematics and the Imaginationthe following , in passage: How Many? 14

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 a 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". How Many? 15

• 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 actually happen if one actually tried to write a googolplex, but different people get tired at different times and it would never do to have Carnera (a champion boxer) a better mathematician than Dr. Einstein, simply because he had more endurance. The googolplex is, then, a specific finite number, with so many zeros after the 1 that the number of zeros is a googol. How Many? 16

The googol family 1 googol = 100 10 1 googolplex = 10 googol = How Many? 17

References / Sources: http: //www. math. harvard. edu/~knill/mathmov ies/swf/onceuponatime_millions. html http: //beemp 3. com/download. php? file=487923 4&song=Man+with+a+Harmonica http: //www. math. harvard. edu/~knill/mathmov ies/swf/googolplex. html http: //beemp 3. com/download. php? file=521747 5&song= http: //en. wikipedia. org/wiki/Names_of_large_ numbers How Many? 18