Problem 3. [10 pts] Estimate the uncertainty of the following values: (a) 123.201, (b) 5334, and (c) 1.2345 x 10' Solution: Assume the values above come from digital displays. a. The value 123.201 implies an uncertainty of b. The value 5334 implies an uncertainty of + c. The value 1.2345 x 10' implies an uncertainty of 2. Measurement Uncertainty and Significant Figures uncertainty, defined as the inability to measuret isomething exactly. The resolution of the measuring As we discovered in the previous section, all physical measurements have some level of device is only one source of uncertainty as we will discess Vater in the course, the calibration of the device, the measurement process, and environmental conditions, to name a few, can also contribute to a measurement's lack of accuracy. taken in a laboratory: 321.53 + 20 kg. Since the uncertainty of the measurement is + 20 kg, are the last The concept of significant figures is related to uncertainty. Consider the following measurement three digits of the nominal value - 1.53 kg - necessary? After all, if the measurement were to the nearest 20 kg, then 1.53 kg would be impossible to resolve. In fact, only the first two digits of the nominal value are significant, and a more appropriate way to report this measurement would be as 320 + 20 kg. often the uncertainties of measurements are not given, if value of a measurement is given without an Significant figures are important especially in engineering and scientific calculations, because uncertainty, we will use the following rule to estimate the uncertainty: Rule for estimating uncertainty when none is given: If a number is given without an uncertainty, we will treat the number as if it was read off a digital display, and assume the uncertainty to be plus or minus one-half the least count