Significant figures in measurement

Define significant figure. Discuss the importance of using the proper number of significant figures in measurements and calculations. 

Frequently we need to know the number of significant figures in a measurement reported by someone else (Example 1.2). 

Most measured quantities are not end results in themselves. Instead, they are used to calculate other quantities, often by multiplication or division. The precision of any such derived result is limited by that of the measurements on which it is based. When measured quantities are multiplied or divided, the number of significant figures in the result is the same as that in the quantity with the smallest number of significant figures. 

The numbers 1.8 and 32 are exact Hence they do not limit the number of significant figures in a temperature conversion that limit is determined only by the precision of the thermometer used to measure temperature. 

Determine the number of significant figures in a measured quantity. 

The digits in a reported measurement are called the significant figures. There are two significant figures (written 2 sf) in 1.2 cm3 and 3 sf in 1.78 g. Section A describes how to find the number of significant figures in a measurement. 

We need to introduce a word of caution. Most modem calculators cite an answer with as many as ten significant figures, but we do not know the concentration to more than two or three significant figures. In a related way, we note how the pH of blood is routinely measured to within 0.001 of a pH unit, but most chemical applications... 

For multiplication and division problems, round off the answer to the same number of significant figures in the measurement with the fewest significant figures. 

Assuming three significant figures in the volume measurements, 535 ppm. 

X10 inches. Here, you have to recall that defined quantities (1 foot is defined as 12 inches) have unlimited significant figures. So your calculation is limited only by the number of significant figures in the measurement 345.6 feet. When you multiply 345.6 feet by 12 inches per foot, the feet cancel, leaving units of inches ... 

Only measured quantities >f I may contain a measurement error, which limits the number of significant figures. In addition to counted objects (7 days =... 

The determination of crystal structure in synthetic polymers is often made difficult by the lack of resolution in the diffraction data. The diffuseness of the reflections observed in most x-ray fiber patterns results from the small size and imperfect lattice nature of the polymer crystallites. Resolution of individual reflections is also made difficult from misorientation of the crystallites about the fiber axis. This lack of resolution leads to poor accuracy in measurement of peak positions. In particular, this lack of accuracy makes determination of layer line heights difficult with a corresponding loss of significant figures in evaluation of the repeat distance for the molecular conformation. In the case of helical conformations, the repeat distance may be of considerable length or, as we shall show, indeterminate and, in effect, nonperiodic. This evaluation requires high accuracy in measurements of layer line heights. 

Laboratories use the concept of significant figures in manual calculations for standard and sample preparation, and in data reduction. The rule for determination of the number of significant figures in calculations is as follows When experimental quantities are multiplied and divided, the final result cannot be more accurate than the least precise measurement. 

A couple of comments are in order here. First, did you notice the value of the pH is the same as the absolute value of the exponent This will always be true when the first part of the scientific notation is exactly 1. The second comment relates to significant figures. There are two significant figures in the molarity measurement of 1.0 x 10 3 M. There are also two significant figures in the pH value of 3.00. Finally, pH values have no intrinsic units. Logarithms represent pure numbers, and as such, have no units. 

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