Precision - Precision Significant Figures Significant...

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Precision Significant Figures Significant figures are the number of digits required to express the accuracy of a particular measurement or the accuracy of a calculation involving measurements. As a general rule one assumes uncertainty in only the last digit and all other digits are considered to be certain or definite. Consider the measurement of the same solid rod using two different rulers. RULER 1 has graduations (marks) every 1/10 of a cm (i.e. every millimeter). RULER 2 has graduations every centimeter. Assume the left end of the rod and the metric rulers (not shown in the figure) are aligned perfectly. The length of the rod in centimeters is obtained by reading the rulers at the right end of the rod and estimating the last “digit”. The rulers enlarged for clarification and are not depicted to scale. That is the centimeter shown is not actually a centimeter in length. Let us examine what the reading for length would be for each ruler. Ruler 1 Ruler 2 1. Length is definitely between 4 and 5 cm. 1. Length is definitely between 4 and 5 cm. 2. Length is definitely between 4.4 and 4.5 cm. 2. Estimate length is around 4.5 cm. 3. Estimate length between 4.47 and 4.49 cm. 3. Report length as 4.5 ± 0.1 cm. 4. Report length as 4.48 ± 0.01 cm In each measurement there was but one uncertain digit-the last estimated digit. Regardless
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RULER 1 produced the more precise measurement. The value of length utilizing RULER 1 has three “significant figures” while the value of length obtained utilizing RULER 2 has two “significant figures”. Generally for a given measurement, the value with the larger number of “significant figures” is the more precise value. Ruler 1 allows measurements to ± 0.01 cm. Consider a different rod again with the left end of both the rod and ruler perfectly aligned. If the right end of the rod is exactly over the graduation at 3.8, the length of the rod would be reported as 3.80 ± 0.01 cm. The number of significant figures is three with uncertainty found only in the last digit which is zero. This example illustrates the fact that zeros after decimal points are significant. Of course, non-zero digits are always significant in this type of measurement. Generally the numerical value of a measured quantity is reported to only one uncertain figure. The number of digits in the number is called the number of significant figures. One can assume that the non-zero digits of an experimental measurement are significant. With this assumption, rules have been devised to understand whether a zero (0) in a number is significant or not. Significant Figures in a Measurement 1. The significance of zero and non-zero digits in a number. (a) Assume non-zero digits are significant. (b) Zeros between the decimal and a non-zero digit are not significant.
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