Today I made a block with one of these, so I though I would share how I deal with cutting at this size.
This block is in honor of the Kentucky Derby and I call it May Roses. For some of the units in this block you need to cut two squares, one red and one green that measure 5 and 3/16 inches square to cut into four triangle units.
The first thing to realize is that 3/16 of an inch is just slightly smaller than 1/4 of an inch. My first cut is to remove a square of my fabric from the main piece that is just a bit larger than this:
I then rotate the square around so the two cut sizes are under the ruler. The small hash marks on my ruler are 1/8 of an inch apart, so the 3/16 I need to cut is between the 1/8 (2/16) and the 1/4 (4/16 mark).
I make sure that both sides of my square are lined up between the two marks and trim my square to the correct size. Now it is ready to cut diagonally both directions to give me 4 triangles. The benefit to cutting this way is that it keeps the bias edges all on the inside of the square so that you have the grain of the fabric on the outside edges, keeping everything nice and square and stable!
The next step is to make sure your pieced triangles are exactly the same size as your large triangle:
If it is not, you need to check your seam allowance and adjust if necessary. Now sew the large triange to the pieced triangle along the long side:
(I didn't notice before I took this picture, but I ran out of bobbin thread before I got to the end of the seam! Whoops!) Press the seam toward the larger side.
Check to make sure your square measures 4 1/2 inches.
Trim your dog ears (those triangles hanging off the edges!) Voila!
I hope this helps you deal with those super tiny increments of measuring! Just remember to count 2 sixteenths for every 1/8 mark and you can do it! Who knew that fractions could be so useful? Boy, am I glad I got A's in math when I was in school!
Here is the finished block: