There are different naming conventions for numbers used around the world. This system is used in the United States and most scientific communities:

Number of zeros(ex. 10^x)   /    Names (USA & Scientific)

3       thousand
6       million
9       billion
12      trillion
15      quadrillion
18      quintillion
21      sextillion
24      septillion
27      octillion
30      nontillion
33      decillion
36      undecillion
39      duodecillion
42      tredecillion
45      quattudecillion
48      quidecillion
51      sexdecillion
54      septendecillion
57      octodecillion
60      novemdecillion
63      vigintillion
66      unvigintillion
69      dovigintillion
72      trevigintillion
75      quattuvigintillion
78      quinvigintillion
81      sexvigintillion
84      septenvigintillion
87      octovigintillion
90      novemvigintillion
93      trigintillion
96      dotrigintillion
99      dotrigintillion
102     tretrigintillion
105     quattutrigintillion
108     quintrigintillion
111     sextrigintillion
114     septentrigintillion
117     octotrigintillion
120     novemtrigintillion
.
.
.
303     centrillion


There is also a googol, which has 100 zeros (ten dotrigintillion), and a googolplex, which has a googol zeros (10^100 zeros).
A zillion, while commonly used to represent a number with many zeros, does not have an actual value.
After about a quintrillion, no-one actually cares too much. Sure, googol and googolplex are used, but what you say about the other large numbers being used in ... most scientific communities is, as far as I can see, bollocks.

They just use exponent notation, even in speech. ("The speed of light is three-times-ten-to-the-eight metres per second" is usually quoted, not three hundred million metres per second.) The same applies to other large and small numbers.

It's a lot easier to work out how many times 2x1013 goes into 4x1020, than to calculate that for twenty trillion and four quintrillion. (answer: 2x107, or twenty million).

But sure, they sound good!

I will give more information about the American system, and present the French system and the Japanese system.

The American system

The American naming convention is the following:

103(n+1) shall be spelled (n)illion, where (n) is a Latin root for n.

See the write-up by Alias for the examples.

The French system

Webster 1913 is outdated about billion and trillion. Nowadays, the French system is the same as the English system, i.e. 1 billion = 1000 milliards = 1012. The naming convention is the following:

106n shall be spelled (n)illion.

Examples: 1012 = 1 billion, 1018 = 1 trillion, 1024 = 1 quatrillion, and so on.

This rule was enunciated in an appendix of the government decree 61-501 of May 3rd, 1961.

However, common usage says "quadrillion" instead of "quatrillion", and adds intermediate numbers: 1 billiard = 1000 billions, 1 trilliard = 1000 trillions, and so on.

The Japanese system

Not only large numbers have distinct names in Japanese, but they also have distinct characters (kanji), so that you need to learn each of them separately. I will give the pronunciations only.

The basic unit is not 103, but 104. For example, you don't say "3 million yens" in Japanese, but something like "300 tenthousands yens". The numbers are:

    104:  man
    108:  oku
    1012: chou
    1016: kei
    1020: gai
    1024: jo
    1028: jou
    1032: kou
    1036: kan
    1040: sei
    1044: sai
    1048: goku
    1052: kougasha
    1056: asougi
    1060: nayuta
    1064: fukashigi
    1068: muryou
    1072: taisui

See Japanese numbers and counting for more details. gn0sis tells me that they borrowed this system from the Chinese. See Chinese numbers.

Sources: http://www.findtutorials.com/tutorials/japanese/takasugi/largenumber.html
http://www.graner.net/nicolas/nombres/liponombres.html

Donald Knuth and the ancient Chinese have independently come up with exponential number systems:
unit            KNUTH *           ANCIENT CHINA
10^0            one                    一
10^1            ten                    十
10^2            hundred                百
10^4            myriad                 萬
10^8            myllion                億
10^16           byllion                兆
10^32           tryllion               京
10^64           quadryllion            垓
10^128          quintyllion            **
10^256          sextyllion             穣
10^512          septyllion             溝
10^1024         octyllion              澗
10^2048         nonyllion              正
10^4096         decyllion         
10^5096                                載 (calc error??)
10^8192         undecyllion       
10^10192                               極 (calc error??)
10^16384        duodecyllion
10^32768        tredecyllion
10^65536        quattuordecyllion
10^131072       quindecyllion
10^262144       sexdecyllion
10^524288       septendecyllion
10^1048576      octodecyllion
10^2097152      novemdecyllion
10^4194304      vigintyllion
* Knuth's system appears in Mathematical Gardner by David A. Klarner.
** Character not available in Unicode.

Example: 123,456,789 is one hundred twenty three million four hundred fifty six thousand seven hundred eighty nine or one myllion twenty three hundred fourty five myriad sixty seven hundred eighty nine.

Later in the 17th Century, the Chinese have changed their numbering system to increments of eight digits, and also added new places with Sanskrit names. Imported into Japan, the definitions of these units were later changed several times until today's system of increments of four digits emerged, with the definitions of places after fukashigi disagreeing among sources.

The American counting system was a 17th century French invention. The French used this until they reverted back to their 15th century version, more popular in Europe. In the 1970's, England became in sync with the American system for business and financial reasons.

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