Step One: Extend the tape

Grab your tape measure and extend the tape. You'll notice that both edges are marked with tiny lines of varying lengths. The image above represents an imperial-only tape simply because metric makes my noggin hurt.

The longest lines, commonly also marked with a number, are full inches. In the illustration above we're looking at a three inch span starting at exactly 4 inches on the far left, extending to 7 inches on the far right.

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Step Two: Understanding Inches

I've drawn a shadow over the sides of the image because for most of this tutorial we'll be focussed* on the span between 5 and 6 inches.

First notice that there are 15 lines evenly spaced between the 5 inch line and the 6 inch line.

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* - Note that it is indeed focussed. We're Canadians. We like colour, flavour and we are focussed.

Step Three: Understanding Halves

The largest, aside from the full inch lines, is smack dab in the middle of the span. Since it's halfway, it's designated the half inch line.

There is only one half-inch line in the span between full-inch lines. According to the diagram, if a measurement fell on this line it would total 5 and a half inches.

Easy, right? Don't get cocky, this was the easy part.

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Step Four: What Happened to 2-Quarters?

If you look a little closer at the pattern, you'll notice that the next longest lines are halfway between the full inch lines and the half inch line. These are called quarter-inch lines, because with the help of the half-inch line they split the inch into quarters.

Here's the tricky part: there is one quarter-inch line on each side of the half-inch line. The first is of course, one-quarter. The other is three-quarters. The middle line is not called two-quarters.

You might recall from school that, just like spelling the Canadian way, simplifying fractions is the proper thing to do. While the middle line does represent two-quarters, it is more properly called one-half.

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Step Five: Smaller and Smaller ...

The groundwork is done ... now we just follow it through.

Each quarter section is divided in half by eighths. Once again, two-eighths is not a proper animal, nor is four-eighths or six-eighths. Proper names are one-quarter, one-half and three-quarters.

Eight-eighths is just silly; we just call that one.

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Step Six: The Final Cut

Our tolerance in the glass industry is plus or minus one-sixteenth. As such, this is the final iteration of accuracy for this tutorial. Each and every eighth is divided into sixteenths.

And again, even numbered sixteenths are adjusted up to the next proper fraction: two-sixteenths = one-eighth; four-sixteenths = one-quarter, etc.

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Step Seven: Examples Part I

Try to work it out before you read on.

The red arrow is pointing at one of the second-longest lines. We therefore know it's a quarter-inch line, and it's the first one between 5 and 6 inches. We add it up and get 5 1/4 inches.

The blue arrow is pointing at the next shortest line, so it's an eighth-inch line. It's the third one after the 5-inch line, and we only count odd-numbers, so it's 1 .. 3 .. 5. Total is 5 5/8 inches.

Green arrow --> same size line as the blue arrow, so we know it's an eigth-inch line. It's the first one after the 6, so the total is 6 1/8 inches.

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Step Eight: Examples Part II

These are a little trickier, but they're about as hard as this gets so bear with me.

Blue arrow --> smallest line, so it's a sixteenth-inch line. It's the second one after the 5, so it's 1 .. 3 sixteenths. Total 5 3/16 inches.

Green arrow --> smallest line again, fourth one past 6 inches, so 1 .. 3 .. 5 .. 7 sixteenths. Total 6 7/16 inches.

Red arrow --> try this one backwards for kicks. The big line beside it is the half inch line again, but it's to the left of the 5 so it's the 4 1/2 inch line. Our target is one sixteenth greater than half an inch, aka (improperly) 8 sixteenths, so it's 9/16ths. Total 4 9/16 inches.

Perhaps not the greatest tutorial in the world, but I hope it helps you out.

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