7/8 diameter drill or .875
To accommodate a 3/8 bolt, drill a hole that is 3/8 inch in diameter.
A threaded hole with a minor diameter of approximately 2.61 inches and a thread pitch of 11 threads per inch (TPI) indicates it is likely a 2.5-inch nominal size with a coarse thread. The actual major diameter can be calculated based on the TPI and the thread profile. In this case, the major diameter would be around 2.75 inches, consistent with standard measurements for 11 TPI threads.
by using a drill
The recommended drill bit size for a 15/64 inch hole is a 15/64 inch drill bit.
The recommended size of the drill bit for a 7/16 inch hole is a 7/16 inch drill bit.
I drill a pilot hole the size of the 'barrel' of the screw. -I always use a combination drill bit for sinking screwheads. The first part of the bit is the diameter of the 'barrel' of the screw and the step, one inch higher is the size of that screw's head. (The barrel is the diameter inside threads) -I have a set of these drill bits for #6, #8, and #10 screws and they are great.
A 3/16 inch pilot hole drill bit should be used for installing a 1/4 inch screw into hardwood.
For all practical purposes an 8mm drill is equal to 5/16 inch.
A 10 cm hole is almost 4 inches ! ! - IF you meant 10mm, then that's a little over 3/8 of an inch, or 13/32 for a clearance hole.
To drill out a hole that has a diameter of 0.055 inches, you would typically use a drill bit that is slightly larger than 0.055 inches, depending on the desired final size. If you need to increase the hole size, you can consider using a 1/16 inch (0.0625 inches) drill bit, which is a common size for this purpose. Always ensure to check the specifications for the application to avoid oversizing.
Drill bits not only come in fractional number sizes they also come in letter sizes. The F size drill bit is .257 thousandths of an inch in diameter. A 1/4 inch drill bit is .250 thousandths of an inch in diameter, so size F is .007 thousandths of an inch bigger than a 1/4 inch drill bit.
For a clearance hole you need a 9/64 drill bit.