Why are there Latin words on US money?
Presumably you are referring to the Latin phrases on the back of the one dollar bill. The pictures on the back of the one show the front and back faces of the great seal of the United States. The seal was designed shortly after the revolution. At that time Latin was the universal language of educated men. To know Latin was a sign of being genteel and sophisticated. Thus using Latin on the seal gave it a sense of seriousness and also permitted the ideas expressed to be read and understood by educated men from every country in Europe. The phrases are: "E Pluribus Unum" that means "Out of many, one" and is a reference to the several states joining together to form one nation; "Annuit Coeptis" which means "He favors our endeavors" which is a reference to the apparent favor that America has received from God since the founding; and "Novus Ordo Seclorum" which means "A new order for the ages," which is written immediately beneath the Latin numerals for 1776 and symbolizes the historic nature of that date as the beginning of republican self rule in the world.
(an explanation written by someone named Michael Montagne [edited by me] which can be read at this web-address:)

source: http://wiki.answers.com/Q/Why_are_there_Latin_words_on_US_money#ixzz1X5R7pH9g

For additional and more specific information on the meaning and source of each phrase, see

Novus ordo seclorum - http://www.greatseal.com/mottoes/seclorum.html
E pluribus unum - http://www.greatseal.com/mottoes/unum.html
Annuit coeptis - http://www.greatseal.com/mottoes/coeptis.htmll

And for those of you who read French tolerably well, here is a very nice discussion of these issues:

http://enseignement-latin.hypotheses.org/3338
with this helpful quotation from the historian Bernard Bailyn:
« ce qui est le plus manifeste dans les écrits de la période révolutionnaire, c’est l’héritage de l’antiquité classique. La connaissance des auteurs classiques était universelle chez les auteurs en question, quel que soit leur degré d’instruction, et les références aux classiques et à leurs œuvres abondent dans la littérature. De l’école primaire, du collège, de tuteurs particuliers et de lectures personnelles venait une familiarité générale avec eux ainsi que l’habitude de faire référence à des auteurs anciens ainsi qu’à des personnalités héroïques ou des évènements du monde ancien : Homère, Sophocle, Platon, Euripide, Hérodote, Thucydide, Xénophon, Aristote, Strabon, Lucien, Dion, Polybe, Plutarque et Epictète pour les grecs ; Cicéron, Horace, Virgile, Tacite, Lucain, Sénèque, Tite-Live, Cornélius Népos, Salluste, Ovide, Lucrèce, Caton, Pline, Juvénal, Marc Aurèle, Quinte Curce, Marc Aurèle, Pétrone, Suétone, César, les juristes Ulpien et Gaius, ainsi que Justinien chez les romains. Tous sont nommés dans la littérature révolutionnaire et beaucoup ont droit à des citations. Tout obscur pamphlétaire pouvait mobiliser au moins une ressemblance à l’antiquité ou un précepte ancien. »

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This went up 9/5/11 (except for the French thing [9/18/11]) after a quiz of first and second year students, asking first for the identification and meaning (in English) of the three Latin expressions on the dollar, and requesting second a response to the question why were these expressions in Latin, i.e., what reasons could be offered why there should be Latin used in the design of our money. I reviewed this page and the three links with them Tuesday (Monday was an official holiday) and re-administered the same quiz Friday (9/9/11). Here are the responses to the second inquiry grouped by grade level (with errata just highlighted).
Tenth grade -
JS - Latin is the root of many languages, so many people could look at it and know what is says all over the world.
SH - The Latin sayings on the dollar bill mean something to the United States and it's history.
AG - Latin is consider sophisticated by many. Latin speakers were among the first to hold a republic form of government. Also Latin is the root of English.
HW - Latin was put on the money because it means something and it's important.
KA - The Latin language is on the dollar bill because of the heritage and also it was used by the first republic the Romans.
HS - To open our minds to Latin.
Ninth grade -
KT - They are common Latin phrases that Amerians live by.
RS - The guy felt like putting it on there and no one ever changed it.
KK - We use latin on our money because when money was first made, latin was a language that was widely spoken. Latin is a dead language that has influenced english and many other languages. This is why I feel we have latin on our dollar bill.
HS - I think they used Latin because it was a more serious language and it was used by smarter and more sofisticated people.
LD - There should be Latin used in the design of our money because many words from English come from Latin and the words that are on it are very important to some people and it must have been important to the people who put that Latin on our money.
KM - Because Rome was a very well known and established empire and they would want America to have a reference to another empire.
IK - Latin was put on money because alot of English come from Latin. Also the Americans may not have wanted to put something in English because they wanted something that was different from England.
JW - The Roman Empire lasted the longest so mabey they thought that writing in the Roman's language they would prolong the standing of the U.S.A. Maybe they put the sayings in Latin so Ignorant Americans couldn't argue against it.
MO - Back then, a man who could speak in Latin showed that they were intelligent and great. So maybe they put Latin on our money to show that the United States was made & formed by great men, so therefor our nation will be great too.
MH - The reason we use Latin on our money in my opinion is because, Latin is a difficult language. But being that most of the English langauge came from . . . Latin, to put on the Dollar.