
I hate the imperial measurement system, and can confidently say that anyone who doesn't recognize the superiority of metric is a freaking idiot. How nice it must be for you Aussies, Germans and Koreans to drill an 8mm hole, realize you need it a smidgen bigger, and yell down the ladder for a 9mm bit. Versus us Yankees drilling a 7/32 hole, then having to do an equation in your head to calculate if you need a 3/16 or a 1/4.
For the non-mathematically-gifted like me, dividing things with fractions is the worst. For example, when doing DIY projects you often have to calculate the midpoint of a particular piece—whether it's wood, fabric or metal—and I'd be constantly scrawling equations onto the piece of wood I was working and having to sand the marks off afterwards. That is, until I learned this simple tip to easily find the exact midpoint without having to divide fractions.
Let's say I want to find the midpoint of the board above. We take a tape measure to it...

...and see it's 17-something. That's all you're looking for, ignore the finer gradations.

Then we take note of the nearest even number, whether higher or lower than the actual measurement. In this case the nearest even number is 18.
In other words, if the measurement had been 16-something (simulated below) we'd round down to 16.

Then you take that even number and divide it in two. Even a relatively thick-headed person like myself can quickly calculate that half of 18 is 9.
So we draw a line at the 9-inch mark on the board.

Then we flip the tape measure around...

...and mark 9 inches going the other way.

Now we have two marks that are less than an inch apart.

If you have managed to graduate with a design degree, or if you build things for a living, or have any visual acuity whatsoever, it's super-easy to eyeball the exact midpoint of two lines less than an inch apart.

Mark it, and that's it, you're done.

If you want to double-check, just run the tape measure, no math necessary. Here we see we've got 8 5/8.

Then flip the tape measure, and confirm we've got 8 5/8 going the other way.

The best part of this system is that it's foolproof. In other words, if I was dumb enough that I divided 18 by 2 and came up with 8, and marked 8 inches from each side, the two marks would be a lot wider than 1 inch apart, and I'd know I screwed up and would recalculate before cutting anything.
I can't remember which magazine, website or blog I first saw this tip on—it was years ago—so I cannot give credit where it's due. Nevertheless, I'm sure this is an old and fairly common carpenter's tip.
Comments
...or you can draw an "X" corner to corner, locate center, and using a square, draw perpendicular from the edge.
There is an even simpler way to find center. Position a scale where 0 is at the left edge of the part, using 0 as the center point, rotate the scale until any even number aligns with the right edge of you part -- divide by 2 and you have the exact center.
You can also just angle the tape measure until both ends of the board are on an easily dividable, then put a dot on the mid point. For example, put the 0 on the far left, then tilt the measure until the 10 is on the far side of the board (or whatever easy number you can get) then mark the 5" point on the angle and you'll be dead center.
What a lot of rigamorole. Just angle the tape to easily divisible increments and mark away. Works great to divide a given space into equal increments as well.
http://www.pushstick.com/webview/mid-point.jpg
Given that the center of a triangle's hypotenuse is over the center of each of its sides you can just hold the ruler/tape-measure between the left side and the right side so that the hypotenuse's length is even and then find the length's center. In your example, make the 18" and make at 9". No fiddling needed.
Take a strip of paper, mark the length, fold it in half. Done.
I've got you all beat...I forgot I had this in my toolbox.
http://www.amazon.com/Lufkin-HI-VIZ-Self-Centering-Measure-L725SCT/dp/B002H6WFJY
Draw the diagonals and use a speed square to transfer the center point to the board's edge?
I know fractions are daunting at first but they're really not that difficult. Rarely do you need to work to tolerances of a 32nd in woodwork. Both imperial and metric have their advantages and disadvantages. Imperial is an easy to read and much easier to eyeball than metric. Metric is simple to divide/multiply. They're all just numbers and you need some knowledge and interest in math in order to truly understand what you're doing. None the less angling your ruler to an easily divisible number, be it 2, 4, 27, 392 or what have you, marking those divisions and tracing them back to the base with a straight edge is not only simpler and faster than your method, it's also more accurate.
All the methods described here only work assuming that your pre cut piece of wood is perfectly rectangular.
From a manufacturing point of view this is never the case.
So stick to two references and just do the very very simple math ;)
Or you could just use a metric tape measure and divide by 2.
Why are you Yankees still using the imperial system, its really stupid. You should start a petition to get this changed.
@Ben. Why don't your road signs read Km/3.6 Kilo-seconds and not Km/hr, which is an imperial unit? That is really stupid.
Or you could just buy a tape that is in both cm and inches. Do it in cm and then check the mark in inches
I don't want to wade in to all this juvenile bickering other than to second the wisdom of the original posters wisdom, this method doesn't need parallel ends, a square, a 'scale' or anything to do with units, hell, it doesn't even need a tape measure: the method works just as well using the nearest piece of scrape marked at roughly half.
I would like to thank the author for being so kind for posting these directions.
As for those posting snotty remarks; really? Did your mama's not teach you anything? If you don't have anything nice to say.......
I'm a financial analyst and can reconcile billion dollar accounts to the penny. Ask me to measure something that's not 1/4, 1/2 or 3/4 and I can't figure it out. That's my husbands job. :)