By Bob Tinker
This exercise was designed to teach students to never blindly trust their instruments. We created the rulers to exaggerate the errors that are part of any measurement done in science. Scientists must always anticipate the errors in their measurements and report these expected errors along with the measurements.
There are two major types of errors scientists can make, procedural and instrumental. The first three rulers illustrate procedural errors and the last two rulers illustrate instrumental errors.
Ruler A has an offset zero (the zero is not at the end of the ruler). When measuring something that is larger than the ruler, students will generally put two rulers end-to-end and add the partial measurement from the second ruler to the total length of the first. This method produces an inaccurate measurement with this ruler.
To measure accurately with this ruler, students must either change their methodology, (overlapping the rulers, for example), or perform additional calculations (subtracting the length of offset).
The cubit, a non-standard unit, is used on Ruler B. Measuring with this ruler requires students to convert their results into a different measurement unit (the centimeter). While this is easily done, it is an additional step necessary to ensure accurate and common measurements. In this instance, students must convert cubits to inches, and then inches to centimeters.
This procedure raises an important question: what units of measure should be used? Because scientists all over the world (including Global Lab student researchers) need to share their data, they require standard units of measure. The metric system, which includes meters and their subdivisions, is such a standard.
It is hard to get accurate measurements with the grossly marked Ruler C, marked in two centimeter intervals. If a measurement falls between two lines, it must be estimated. Usually, most students cannot interpolate accurately and will report the result of their measurement as the nearest measurement on the ruler.
Using this ruler provides practice at interpolation. With enough practice, students should be able to estimate the measurement fairly accurately to the millimeter. Simply estimate the halfway point between the markings (2 and 4 cm in our example). If the measurement falls at that point, it is 3 cm, or 30 mm. If a bit less, perhaps 29 or 28 mm. If a measurement is one-quarter of the way between the 2 cm and 4 cm marks, estimate whether it is exactly 25 mm, a bit more (26 mm) or a bit less (24 mm). The students' estimations will get more accurate with practice.
Ruler D is non-linear. Its markings are not separated by equal distances. Although some measurements made with this ruler may be accurate, one can never be sure. There is no easy way to correct its measurements. The only thing one can do is to throw out the data obtained with it, an unfortunate but common occurrence in science.
The markings on Ruler E are also inaccurate; they are all decreased by a constant 10%. Once this error is detected, the inaccurate measurements can be easily corrected.
This ruler describes a calibration error. Many instruments, like this ruler, report results that are off by a fixed percent. For example, most car speedometers report speeds that are about 5% too high. Scientists can still use these instruments, but they must then correct their readings by comparing them to a standard and computing a correction factor that can be applied to the data.
Using accurate instruments is extremely important in science. If your instruments are faulty, your results are good to no one and you have wasted valuable time obtaining them. This is why scientists spend an enormous amount of time testing their instruments to make sure they are operating properly.
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