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Did you read the article? He explains very precisely what he means and what his conclusion is. "Rational" in the context of the title means "one integer divided by another to which the first is relatively prime", and the word "useless" indicates that there is no gain in accuracy/complexity in comparison to the decimal notation for a rational number (where you express a rational number as an integer divided by an implicit power of ten).

The point is that you should just memorize whatever precision decimal you need. There's no shortcut like 22/7 that will magically give you more accuracy and be easy to memorize.

(pi - 22/7) < (pi - 3.14). 22/7 is closer to pi than 3.14.

It would have been better if I had specified absolute values in the formula. I hope the point came through. (It appears I'm unable to edit this particular comment.)

Sure, but it's not closer than 3.142. You get less than one digit of bonus accuracy.

The point is that it is easier to remember X digits of PI than a fraction, because the fraction will have more digits in total than X.