why and how did No. become an abreviation for number when there is not an "o" in the word number?

Answer 1

"no." is not based on the English word "number." It means 'number', but like MANY of our abbreviations (such as etc., i.e., e.g., viz.) it is based on a LATIN word, the word "numero".

Actually, the basic form of the word in Latin is "numerus". "Numero" is the "ablative case" form. Why? Well, the ablative form was used here because that fit the usage English writers needed when they introduced the form into English in the 17th century (in expressions of the sort "men, in number three").

A couple of notes on this form & how to use it:

1) The numero sign used to always use a RAISED (or "superscript") O. (Typewriters could not handle this very well, unless you wanted to manually move the carriage up and down. But wordprocessing, personal computing make it much easier.)
http://en.wikipedia.org/wiki/Numero_sign

This use of a superscript at the end is another indicator that the letter stands for the case ENDING, rather than, say, the second letter of the word. (The practice of abbreviating a word by its first letter or two plus the case ending is ancient. For example, in the early church --by the 2nd century-- copies of the Greek New Testament would abbreviate the divine names by using the first letter or two followed by the case ending, with a line over the whole to mark it as an abbreviation.)
http://www.skypoint.com/~waltzmn/NominaSacra.html

2) Even though the abbreviation is borrowed from the Latin, you should never SAY the Latin word when you see it. That's just an unusual habit in English -- to use Latin abbreviations to stand for English words.

In the same way, when you see "e.g." you say "for example"; for "i.e." say "that is", for "viz." say "namely"; for "cf." say "compare"; and for "etc." say "and so forth". (Many other European languages have equivalent abbreviations, but base them on their OWN language.)
See: http://www.randomhouse.com/wotd/index.pperl?date=19971217
and list - http://list-of-latin-phrases.area51.ipupdater.com/

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Of course, the underlying quesiton is "Why do we use LATIN abbreviations for so many English words?" The basic answer is here:

"Latin was once the universal academic language in Europe. From the eighteenth century authors started using their mother tongue to write books, papers or proceedings. However many Latin abbreviations continued to be used due to their precise simplicity and also Latin's status as a learned language."
http://en.wikipedia.org/wiki/List_of_Latin_abbreviations

Answer 2

Wow, very interesting question (seriously)!

OK, I found this on Wolfram:

To indicate a particular numerical label, the abbreviation "no." is sometimes used (deriving from "numero," the ablative case of the Latin "numerus"), as is the less common "nr." The symbol # (known as the octothorpe) is commonly used to denote "number."

Answer 3

You're assuming that the entire world speaks English.  In French (which was once used so widely, it created the phrase "lingua franca"), it's "nombre".  Thus, the abbreviation "No.".