from *The Lore of Large Numbers* by Philip J. Davis

The word *million* is an Italian invention of the 13th century, and means simply "a large thousand." The word *billion* had to wait till the beginning of the 17th century to be adopted in English and then it was more of a curiosity than anything else. It really took the 20th century with the large numbers occurring in science and economics to put billions on the map. Here are the special powers of 10 from the 1960s Webster's Unabridged Dictionary (with the last entry added more recently):

Power |
Number word |
Latin root |
Numerical equivalent of root |

10^{9} |
billion | bi | 2 |

10^{12} |
trillion | tri | 3 |

10^{15} |
quadrillion | quater | 4 |

10^{18} |
quintillion | quintus | 5 |

10^{21} |
sextillion | sex | 6 |

10^{24} |
septillion | septem | 7 |

10^{27} |
octillion | octo | 8 |

10^{30} |
nonillion | novem | 9 |

10^{33} |
decillion | decem | 10 |

10^{36} |
undecillion | undecim | 11 |

10^{39} |
duodecillion | duodecim | 12 |

10^{42} |
tredecillion | tredecim | 13 |

10^{45} |
quattuordecillion | quattuordecim | 14 |

10^{48} |
quindecillion | quindecim | 15 |

10^{51} |
sexdecillion | sexdecim | 16 |

10^{54} |
septdecillion | septendecim | 17 |

10^{57} |
octodecillion | octodecim | 18 |

10^{60} |
novemdecillion | novemdecim | 19 |

10^{63} |
vigintillion | viginti | 20 |

In looking up "large numbers" on the web, I first came across the table of large numbers from Webster's dictionary (extension of the one above, with the addition of centillion or 10^{303}. I then found the Wikipedia page *Names of large numbers*, which fills in the table above up to and above centillion. This page references a great book by Conway and Guy called *The Book of Numbers*, which proposes all sorts of conventions for large numbers. Great stuff! Of course, the terms googol (10100) and googolplex (1010100) are lore now, but only googolplex is of significant value compared to the numbers in these charts. I love how you can make up names for things like numbers – the imagination is really useful when it comes to things that we can only imagine because they are just too big for any realistic evaluation.

Most important for me though was when I read the Davis book and came across this chart, and realized for perhaps the first time why the first few large numbers we learn in school are named what they're named. If I learned it in school, I've long since forgotten. Seems like it should be standard for elementary school math!!