Metrology 101
Possom -
You can get a really nice digital 6" caliper at places like Northern Tool or Harbor Freight on Sundays. You may have some of these stores locally, or they both have websites. Calipers usually cost about $25-$35. Look for one that reads in MM and Inches, with a resettable zero, and a carrying case.
Understanding Tolerances
The accuracy needed is inferred. All measurements have a tolerance. When a number like "1/16" is stated, it usually infers a fractional tolerance of the smallest unit on the ruler you are using, say 1/64. So it is really saying "1/16 ±1/64". Follow?
So a number like 1.02" infers a plus/minus tolerance also measured to 2 decimal places, such as 0.01". So it follows that a number like 1.160" infers a tolerance also measured to 3 decimal places, such as 0.005".
The smallest measurement the human eye can detect is generally considered to be 1/64" (~.016"). This is 3 times larger than our 0.005 from above. So when you are given a 3 decimal place OAL, the instructions infer that you MUST get an instrument capable of measuring to 3 decimal places, such as a micrometer or a caliper.
Back in the 50's, reloading used to be the province of machinists and technicians accustomed to working to fine tolerances. All this was innately understood by them at the reading. Now that reloading has moved more into the realm of the hobbyist, this has not been very well explained.
In your particular case, fine tolerances are a must due to the fact that the 9mm Luger case has such a small internal volume. Much smaller than almost any other common round. As I said before, due to the very small case, small changes in OAL make for big changes in chamber pressure. So the 9mm is much more highly sensitive to changes in OAL, and extra special care needs to be exercised.
Other Uses
Calipers can also be handy in detecting over pressure, since one of the signs is case growth at the base. Calipers can also be handy is insuring there is not too much taper crimp, a contributor to higher chamber pressure. So a caliper is a very handy instrument to have. You will never regret the purchase.
Hope this helps!