Determining the reliability of digits and calculations is important, because physical measurements have mathematical limitations. For example, suppose a ruler marked with tenths of inches is used to measure the length of an object. If the measurement is reported as 1.54 inches, the first two digits are certain, and the last digit (4) is an estimate. This represents the most reliable length that can reasonably be obtained for that object using that measuring device. Estimating any additional digits following the 4 would misrepresent the accuracy of the measurement and reduce its reliability.

If a calibrated gravimetric scale is used to measure a weight, and provides a digital answer of 2.328 grams, the measurement is assumed to be precise to one thousandth of a gram and can be reported with reliability. In this case, the reliability of the answer is not limited by the estimating...