Associated Topics || Dr. Math Home || Search Dr. Math

### 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
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
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

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search