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The -yllion system is a fabricated system invented by Donald Knuth for naming large numbers.[1]

Usage Edit

Numbers up to 999 are named as they are normally.

Numbers from 1000 to 9999 are written without a comma and pronounced "a-ty b hundred c-ty d" for the number abcd. For example, 7283 is pronounced "seventy-two hundred eighty-three." The word thousand is not used in this system.

\(10^4\) is called the myriad. All numbers from the myriad up to 9999,9999 are written with a comma between the ten thousands and thousands place. For example, 54325 would be written 5,4325.

Such numbers are pronounced like so:

  • 45,7839 is pronounced "forty-five myriad seventy-eight hundred thirty-nine."
  • 2423,3000 is pronounced "twenty-four hundred twenty-three myriad thirty hundred."
  • 9999,9999 is pronounced "ninety-nine hundred ninety-nine myriad ninety-nine hundred ninety-nine."

\(10^8\) is called the myllion. It is written 1;0000,0000. Note that a new punctuation mark, a semicolon, was used to represent the myllions place. Numbers up to 9999,9999;9999,9999 are named in the same way as the above numbers are pronounced: each group of four digits is pronounced as written above, and the commas are pronounced "myriad." The only difference is that the semicolon (;) is pronounced "myllion."

\(10^{16}\) is called the byllion. It is written 1:0000,0000;0000,0000. Note that a new punctuation mark, a colon, was used to represent the byllions place. Numbers up to 9999,9999;9999,9999:9999,9999;9999,9999 are pronounced as above, but the colon (:) is pronounced "byllion."

Continuing in this method, we have n-yllion \(= 10^{2^{n+2}}\), allowing the tryllion, quadryllion, quintyllion, etc.

Sources Edit

  1. The Knuth -yllion Notation - Large Numbers (page 2) at MROB

See alsoEdit

The Chinese numeral system also had one scale in which each symbol was the square of the next.

myllion byllion tryllion quadryllion quintyllion
sextyllion septyllion octyllion nonyllion decyllion
undecyllion duodecyllion tredecyllion quattuordecyllion quindecyllion
sexdecyllion septdecyllion octodecyllion novemdecyllion vigintyllion
unvigintyllion duovigintyllion trevigintyllion quattuorvigintyllion quinvigintyllion
sexvigintyllion septemvigintyllion octovigintyllion novemvigintyllion trigintyllion
untrigintyllion duotrigintyllion tretrigintyllion quattuortrigintyllion quintrigintyllion
sextrigintyllion septtrigintyllion octotrigintyllion novemtrigintyllion quadragintyllion
quinquagintyllion sexagintyllion septuagintyllion octogintyllion nonagintyllion
centyllion ducentyllion trecentyllion quadringentyllion quingentyllion
sescentyllion septingentyllion octingentyllion nongentyllion millyllion
myryllion micryllion nanyllion picyllion femtyllion
attyllion zeptyllion yoctyllion googolyllion latinlatinlatinbyllionyllionyllionyllion
Googological affixes

Suffixes: -teen · -ty · -plex · -illion · -yllion · -chime · -toll · -gong · -bong · -throng
Prefixes: gar- · fz- · fuga- · megafuga- · booga-
SI prefixes: deca- · hecto- · kilo- · mega- · giga- · tera- · peta- · exa- · zetta- · yotta-
Obsolete SI prefixes: myria-
Extended SI prefixes: 666 · 105 · 107 · 1027 · 1030 · 1033 · 1036 · 1039 · 1042 · 1045 · 1048 · 1051 · 1054 · 1057 · 1060 · 1063 · 1090 · 10100 · 10120 · 10150 · 10180 · 10210 · 10240 · 10270 · 10300 · 10600 · 10900 · 101200 · 101500 · 101800 · 102100 · 102400 · 102700 · 103000 and higher

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