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.