Generally, the number system is favored in fields where you typically report experimental field or lab work. Technical fields such as materials science, aerospace engineering, and chemistry tend to favor the number system.
When you use the number system, your responsibility is to indicate in your text—either in parentheses or brackets—a number that corresponds to a source on your references page. The first source you cite in your text receives the number 1, the second number 2, and so on. If you repeat a reference to a source later in the text, it retains its original number—thus, all references to source number 4 receive a 4 after them in parentheses or brackets. You delay the appropriate punctuation until after the parentheses or brackets:
If the load on the thrust bearing can be decreased by some means, the life of the turbodrill can be significantly increased (1).
Many authors prefer to identify the source at the beginning of the reference, perhaps including the author’s name directly in the text:
Gould et al. (5) found a clear relation between. . .
The number system is especially handy for citing equations, because you can simply insert the citation number logically as you introduce the equation to avoid confusion with any other numbers:
The line’s slope is used in the following equation (7) to calculate. . .
Other In-Text Citation Practices
Slight but important mechanical differences exist among in-text citation practices, in particular when you are trying to conform to a specific style, such as MLA (Modern Language Association) or APA (American Psychological Association). For example, MLA style requires you to provide the page number of your citation in-text, but not the year, while APA style asks you to place a comma between author and year. Please feel welcome to explore all of these nuances for yourself if you wish, and recognize that some professors will insist that you conform to a particular style. When professors do not dictate a particular style, they will usually simply expect you to use the author-year or number system with consistency throughout the paper.
Remember, too, that journals within you field have already made informed decisions about which in-text citation practices they use. To settle on citation particulars, many writers model a journal in their field—mandatory, of course, if you submit material to a journal hoping for publication.
Read up on the specifics of various citation styles, in particular MLA and APA, at the following pages:
"Research and Citation Resources" article from Purdue's Online Writing Lab (OWL)
"Citation Style for Research Papers" article from Long Island University