This is exactly why I strongly suggest buying a dial or digital caliper (or a micrometer) to anyone who needs to drill a precision hole.Zonie, I think these HF bits are miss-marked, the next step up in the set is 7/32, it measures a perfect .2090 and appears to be exactly what I need, even though I have a very good set of calipers and this bit appears to be correct, I am going to buy a #4 bit just to be sure. Picky, picky that is me when it comes to this stuff.
Don't trust HF's number drill sizes. Always check them with a micrometer or caliper. I got so frustrated with the complete lack of quality control that I threw the whole set in the trash! Some were actually bent. McMaster-Carr is where I go to for quality bits. Pricey? Not really. Quality? Absolutely! I also have a Starrett tap drill chart hanging on the wall of my shop.Go to harbor freight and get a set of bits. HF bits are not great, they are cheap. Pre drill smaller. The final bit will drill to size regardless of the point not being evenly sharpened. I get the one below every few years. The cheaper sets make holes too.
https://www.harborfreight.com/cobalt-drill-bit-set-115-pc-61886.html
By the tap drill charts I use, the 13/64” drill seems a bit too small for a 1/4-32 tap. A 7/32” (.2187”) tap drill would give you a theoretical 77% of thread.1/4" WL liner with tap but no #4 drill bit which is .2090. The closest I have is a 13/64" bit that is .2031. Suppose the 13/64" drill bit is sufficient to use to run a 1/4/32 tap into?