“a” or “the” when specifying a number/parameter/factor

Question

Please clarify me on the following. When I specify a number, parameter, factor and so on, what is the right article to be used? For example, "the or a factor of 5 ... / the or a ratio of 4 to 3 .../ the or an angle of 90 ../.

Since the number is specified I though that "the" should be used as opposed to the cases: a proportion around/ close to 2/ so on. But there are also many cases when a particular number is specified, but nevertheless "a" is used as if there is some uncertainty. "An angle with a measure of 90". Please help me with this rule. Thank you a lot, Sincerely yours, Alexander

Answer 1

The answer is this: It depends on what you are trying to say....It can be either.

A general proposition is this:

1 - Ratios of 4 to 3 are common in these contexts. [forgive the math, just making up a sentence].

OR this:

2 - A ratio of 4 to 3 is common in these contexts. 1 and 2 mean the same thing.

After the general proposition is understood or implied, the /the/ is used. The ratio of 4 to 3 [for example, in this paper, context, situation, etc.] is common.

So, are you discussing or writing about this thing in a general or in a specific situation? Often, in writing, one starts with a singular (a this or that) or the plural of the noun (plural noun), and the next occurrence of the word will take a /the/. Note how a general proposition can be (in some cases) /a factor/ or [factors] and then TURNS INTO /the factor/ when mentioned the second time.

Another example: An angle that measures 90 degrees is a right angle. That is the same as: Angles that measure 90 degrees are right angles. Same idea. But the 90 degree angle you drew on the page is not a right angle and not the same as the ones I'm describing. :)