Many times a day I pull out a pocket steel tape and measure something. Usually this is a single and quick comparison as a rigorously accurate value isn’t required. If fit is a consideration, particularly as the economic consequence rises, I am more careful and often follow the “measure twice and cut once” proverb. Even more insurance of accuracy can be achieved by comparing the value I measured with that which a helper measures.
Sometimes I tend to forget that all measurements are approximations or estimations. The variation in value is contributed to by the instrument I use and the characteristics of what I am measuring.
Alternatively I can use a pair of dividers set to guess half the length and scribe off lines starting at both ends and split the difference. This is just like the bisecting a line method we learned in plane geometry. Using a pair of dividers made to mark the golden proportion lengths is another useful analog design device.
When several equal length bars are involved I often find the center point by putting a presto pen mark at the guess point then flipping one bar end to end and splitting the difference between the two marks.
Laying a leather strap on a bar and then folding it in half and marking is another quick way to guesstimate center.
Years ago I acquired some strips of lead about a 16” thick and 3/8” wide a couple of feet long which I use to measure circumference of small objects. Soft wire solder has also been recommended.
I have an antique traveler but it just hangs for display. I suppose if I did a lot of work with circumferences that would be different.
Occasionally if I just need to transfer a length measurement under 3 feet I will use a slide bar quick-clamp as a caliper. It will hold long enough without slipping to make the comparison measurement.
Finding the center of mass, “gravity”, by hanging is a trick I know but don’t recall ever having to use. It is similar to finding the center of a circle with a center finding tool. We use an analog method when locating the center of a rectangle by drawing lines from opposite corners and observing the intersection. But when I check a fabricated rectangle for “square” I use a steel tape or folding metal rule corner to diagonal corner to check the numbers.
I’m pretty sure I’ve skipped a lot of examples of this sort of thing. Outside my blacksmithing realm, digital conquers all - electronic caliper, calculators, etc. I haven’t touched a slide rule in many years.
Integers and fractions have their place. Sometimes I need them, sometimes I don’t. That reminds me of the Mounds and Almond joy candy bar ads of the 1970’s. "Sometimes you feel like a nut, sometimes you don't.”
Hanging to find the center of mass: