Why do we use the article 'a' when referring to 100 items? But we don't use it when referring to any other plural count?

Edit Note:

This question has been linked to these questions about using an article before adjectives modifying numbers. This question here has nothing to do with adjectives at all:

• Indefinite articles used with plural nouns: It was AN amazing TWO DAYS
• Indefinite article in the "An [adjective] [number] [plural noun]" construction

The question

Why do we use the article 'a' when referring to 100, but not when referring to any other plural counting?

Here's an example:

I saw a hundred birds today.

But when talking about other count that 100, we don't use 'a' because it's plural:

• I saw ninety-nine birds today.
• I saw two birds today.
• I saw two thousand birds.
• I saw seventy-five birds.

Is there a grammatical or historical explanation?

Solution 1:

a is replacing one.

That is, in the following pairings, both options are legitimate:

I saw one hundred [and] forty-seven birds today.¹
I saw a hundred [and] forty-seven birds today.¹

I earned one million dollars.
I earned a million dollars.

Preferences for one or the other may vary. To me, using one sounds more precise than a, so that would influence my usage: in the first pairing, "one" sounds better to me, while "a" sounds better in the second, unless I was trying to emphasize that I earned exactly one million dollars.

Regardless, either option is legitimate because a is a synonym for one. The reason your other examples don't work is that they don't start with one.

1. The use of "and" in the first pairing above varies based on region (US vs. UK) and speaker preference. See How do you correctly say large numbers?

Solution 2:

"Hundred" is not plural! It is singular. You have one hundred. Hence the "a" ( or "one").

Consider:

I saw a hundred birds today.
I saw two hundred birds today.
I saw three hundred birds today.

Also:

I saw a dozen birds today.
I saw twelve birds today.