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Numbers Larger Than Centillion


Date: 04/02/2002 at 05:11:35
From: Lawrence Santiago
Subject: Numbers larger than centillion

Are numbers like bicentillion, tricentillion, or quadracentillion true 
or made up? I found the infamous milletillion. With the prefix mille 
follow the prefixes: micre-, nane-, pike-, femte-, atte-, zepte-, 
yocte-, followed by -tillion. Could you tell me what you know about 
numbers beyond centillion?


Date: 04/02/2002 at 08:49:11
From: Doctor Peterson
Subject: Re: Numbers larger than centillion

Hi, Lawrence.

I assume you found our FAQ on the topic,

   Large Numbers and Infinity
   http://mathforum.org/dr.math/faq/faq.large.numbers.html   

and looked at the various links there that go deeper. You will have 
found that these number names, beyond vigintillion or so, if not even 
beyond decillion, are by no means "official," and anyone can really 
make up his own version without much of a challenge. That's because 
these names are nothing but a curiosity, and are not really used for 
anything. People make them up just because they like orderliness, and 
want to see the pattern continued as far as they can. Some just invent 
their own names, because they recognize that the commonly accepted 
names are not really as orderly as they like; that is true for example 
here:

   Large Numbers - Russ Rowlett
   http://www.unc.edu/~rowlett/units/large.html   

where, to my knowledge, the "Greek-based names" are his own invention.

In Decillion, Vigintillion, Trigintillion...
   http://mathforum.org/dr.math/problems/trichardt12.10.98.html   

we have a summary of a naming scheme proposed by Conway and Guy to 
extend the names far beyond those that are normally used. In this 
scheme, you would use names like "ducentillion" and "trecentillion" 
for "200 and 300 sets of zeroes," to distinguish them from 
"duocentillion" for "102". I haven't seen bicentillion in any 
believable source.

You apparently have found other versions that I haven't seen. All of 
these are "made up," though all of them are attempts to follow an 
orderly scheme, usually to extend the familiar names to larger and 
larger bounds. Some are more nonsensical; the page that suggests the 
"micretillion" seems to come from someone who forgot that "micro-" as 
a metric prefix means "millionth," not "million"! (Lots of other 
things on that page are wrong; for example, it is not "hendecillion" 
but "undecillion," since "hen-" is a Greek prefix that doesn't belong 
with Latin roots; he spells "vigintillion" and "trigintillion" wrong 
as well.) That untrustworthy page is

   Numeric Terms Glossary - D.T.
   http://members.cts.com/hollywood/d/davidtan/site25/25nterms.htm   

I would go with Conway and Guy, if only because they are respected 
mathematicians with knowledge of linguistics as well. This page gives 
their system again, with more detailed rules and examples:

   Large Numbers - Robert Munafo
   http://mrob.com/pub/math/largenum.html   

The rules for extending up to 10^3000 are given in _The Book of 
Numbers_ by Conway and Guy. The name is built out of pieces 
representing powers of 103, 1030 and 10^300, as shown by this table: 

x  10^3 x  10^30 x  10^300 x  10^3000 x  
0  -  -  -   
1  un (n)  deci (nx) centi  mille  
2  duo (ms)  viginti (n)  ducenti   
3  tre (s) (ns)  triginta (ns)  trecenti   
4  quattuor (ns)  quadraginta (ns)  quadringenti   
5  quinqua (ns)  quinquaginta (ns)  quingenti   
6  se (sx) (n)  sexaginta (n)  sescenti   
7  septe (mn) (n)  septuaginta (n)  septingenti   
8  octo (mx)  octoginta (mx)  octingenti   
9  nove (mn)  nonaginta  nongenti   

The rules are: 

   - Take the power of 10 you're naming and subtract 3. 

   - Divide by 3. If the remainder is 0, 1 or 2, put one, ten or one  
     hundred at the beginning of your name (respectively). 

   - Break the quotient up into 1's, 10's and 100's. Find the 
     appropriate name segments for each piece in the table. 

   - String the segments together, inserting an extra letter if the 
     letters shown in parentheses at the end of one segment match a 
     letter in parentheses at the beginning of the next. For example:    
     septe(mn) + (ms)viginti = septemviginti.

   - If the result ends in a, change the a to i. 

   - Add llion at the end. You're done. 

Many of the resulting names are only slightly different. For example 
10^261 is sexoctogintillion and 10^2421 is sexoctingentillion. Then 
there's 10^309 = duocentillion and 10^603 = ducentillion. 

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
Elementary Large Numbers

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