The Names of Really Large Numbers

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
109 billion bi 2
1012 trillion tri 3
1015 quadrillion quater 4
1018 quintillion quintus 5
1021 sextillion sex 6
1024 septillion septem 7
1027 octillion octo 8
1030 nonillion novem 9
1033 decillion decem 10
1036 undecillion undecim 11
1039 duodecillion duodecim 12
1042 tredecillion tredecim 13
1045 quattuordecillion quattuordecim 14
1048 quindecillion quindecim 15
1051 sexdecillion sexdecim 16
1054 septdecillion septendecim 17
1057 octodecillion octodecim 18
1060 novemdecillion novemdecim 19
1063 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 10303. 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!!