# Measurement and Uncertainty

**Topics:**Measurement, Vernier scale, Accuracy and precision

**Pages:**3 (1057 words)

**Published:**August 24, 2013

When recording data, each entry should be given a corresponding estimated error, or uncertainty. The uncertainty gives the reader an idea of the precision and accuracy of your measurements. Use the following method for finding the uncertainty associated with any measuring device used in lab. First, find the least count, or the smallest printed increment, of the measuring device. On the meter sticks, the least count is 1 mm. On the double pan balances, the least count is 0.1 g. On the small graduated cylinders, the least count is 25 ml. If you are using the full precision of the instrument, you are probably safe in saying that your measurement is within one least count of the measured value, in either direction.

Figure 1

For example, say you are measuring the object in Figure 1. If you use the meter stick to measure an object's length as being around 86 mm, that means you are pretty sure that the actual value is between 85 mm and 87 mm. Therefore, you should represent your data like this: l = 86 mm ± 1 mm

In this case, your uncertainty is ± 1 mm. However, you may feel that you are able to attain more precision than is indicated by the least count. In that case, you should do some estimating. By estimating, you divide the least count of your measuring device into imaginary increments. In this lab, it is recommended that you divide the least count into five imaginary increments. This is called the one-fifth rule. There will be some occasions when the one-fifth rule seems too generous. If you feel that your confidence in the last significant figure of the measurement is greater than this, then of course it would be more appropriate to use, say one-tenth of the least count. Similarly, if your confidence in the last significant figure is lower, then you might use half the least count. At any rate, you should use good judgment in estimating the error. Always think in terms of having to justify your estimates to your instructor! The...

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