A #4-40 machine screw goes through a 1/8" hole without touching the sides. 7/64 makes a much tighter fit, but hard to slide in and out. I usually drill my #4-40 clearance holes to 1/8".
If you want to drill a hole to tap for #4-40, you need to drill a hole using a #43 drill bit, which is roughly 0.089".
- Jon