Personal Finance Grammar and Usage, Part Two

It's time again for that most entertaining of English Major tics, the grammar and/or usage correction! Tired But Happy cites savers striving for "piece of mind" as a pet peeve. Valid, but I'm going to go with another one. What's wrong with the following sentence?

Will you give me a $100 dollars?

Two things!
1. The redundant combination of the dollar sign and the word "dollars." We read "$100" as "a [or "one"] hundred dollars." Theoretically, then, we should read "$100 dollars" as "a [ditto] hundred dollars dollars," implying some sort of exponential math, like compound interest on crack.
2. The redundant combination of "a" and the number 1. The numeral 100 reads as "a hundred," or as "one hundred." It does not need an article, especially an article that technically disagrees with the noun it's working with ("a"? singular. "Dollars"? Plural).

The phrase "a $100 dollars" contains two unnecessary components. It can be correctly rendered either as "$100" or "100 dollars," whichever suits your fancy. The only time you will ever need the "a" is when you are beginning a sentence this way (e.g., "A hundred dollars buys a lot of ramen."), because it is technically incorrect to begin a sentence with a non-letter (but there's no semantic confusion, so I tend to shrug at that rule, despite the fact that I obey it myself). There, of course, you are welcome to swap it for "one."

There! I have just saved you the time of typing "a" and "dollars." Time is money, you know.