Measuring and precision

- Much of the math that we do in construction involves measurements. We measure lengths in the field and we have to add them together to get totals. Out in the field we commonly work in inches and feet since this is what we read on a tape measure. Since the question of precision often comes up when I'm discussing measuring and construction math, I'm going to take the opportunity to give you my general rules that I think apply to the majority of common construction operations. When measuring lengths in the field the smallest increment that you'll find on most tape measures is 1/16 of an inch. I believe that this is as accurate as you can get when you're using a tape measure. And even then, depending on what it is you're measuring with that tape measure, the practical accuracy out in the field is probably more like 1/8 of an inch. While I'm talking about tape measures this would be a good time to mention that since I'm in the U.S. my examples will use imperial units like feet and inches. Now all of the math I discuss still applies if you're working in metric but your tape measure will measure centimeters and meters, and your smallest unit of practical measure will be millimeters. You'll also probably not have to work as much in fractions because the metric system lends itself to just staying in decimals. Now back to that tape measure. Think about measuring a length of rebar or cable where the end isn't even cut off square, or measuring a roughed-in opening or a length of conduit. Depending on where you measure to, most of the time your lengths are going to be plus or minus 1/8 of an inch. And you certainly can't measure with any greater accuracy than 1/16 of an inch. Now if something on the drawings or the specifications require something to be located with greater accuracy and precision, I'm not sure you can get there with a tape measure. But if you're doing common tasks like framing and openings for doors and windows or positioning anchor bolts in a slab, and you're doing this with a tape measure, I think a precision of 1/8 of an inch is generally acceptable. And I mentioned that here at the beginning of this math course because I use this rule when I talk about how precise to be in our math problems. In decimal value 1/8 of an inch equals .125 inches. So I don't tend to worry too much about telling somebody that something needs to be four foot 3.125379 inches long, just round that to four foot 3.125 inches which is the same as four foot 3 1/8 inch 'cause they're not going to be able to measure any more precise than that out in the field unless there's a reason to be that precise and they're measuring in the field using more precise instruments like calipers. Following this reasoning I will generally not use numbers carried out to more than three or four decimal places. Any more than that and I'll follow general rounding rules for math, rounding up if the number's after the third or fourth place are greater than five and rounding down if it's less than five. In other words, 7.12555 gets rounded up to 7.126 and 7.12542, that gets rounded off to 7.125. It makes my math easier and even though I'm rounding this level of precision is generally acceptable. But we convert from fractions to decimals and back again frequently when we're doing construction math, and it's important to consider precision when we do this. Now when you're converting from fractions to decimals I do think that you should stick with the level of precisions called out on the construction drawings. This means that if the drawings call out measurements down to increments of 1/8 of an inch, you'll carry your decimal conversions out to three decimal places. If the drawings happen to call out increments down to 1/16 of an inch then you'll to use four decimal places in your conversion. Look at these numbers that explain my reasoning. If I convert 4 1/4 inch to a decimal value I get 4.25. Converting 4 3/8 of an inch to a decimal value I get 4.375. And if I convert 4 5/16 of an inch to a decimal value I get 4.3125. Please keep this discussion on rounding and precision in mind as we continue through the course.