Measured Numbers and Significant Figures

When you make a measurement, you use some type of measuring device. For example, you may use a meterstick to measure your height, a scale to check your weight, or a thermometer to take your temperature. 

Identify the zeros as significant or not significant in each of the following measured numbers  

The number of baseballs is counted, which means 2 is an exact number. 

Identify each of the following numbers as measured or exact and give the number of significant figures (SFs) in each of the measured numbers  

The mass of 42.2 g is a measured number because it is obtained with a measuring tool. There are three SFs in 42.2 g because nonzero digits are always significant. 

For example, a mass of 42.2 g and a length of 5.0 X 10 cm are measured numbers because they are obtained using measnring tools. There are three SFs in 42.2 g because all nonzero digits are always significant. There are two SFs in 5.0 X 10 cm because all the digits in the coefficient of a nnmber written in scientific notation are 

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Measured Numbers and Significant Figures LEARNING GOAL Identify a number as measured or exact determine the number of significant figures in a measured number. 

Calculate the molar concentration of NaCl, to the correct number of significant figures, if 1.917 g of NaCl is placed in a beaker and dissolved in 50 mF of water measured with a graduated cylinder. This solution is quantitatively transferred to a 250-mF volumetric flask and diluted to volume. Calculate the concentration of this second solution to the correct number of significant figures. 

Significant figures provide an indication of the precision with which a quantity is measured or known. The last digit represents, in a quantitative sense, some degree of doubt. For example, a measurement of 8.12 inches implies tliat Uie actual quantity is somewhere between 8.315 and 8.325 inches. This applies to calculated and measured quantihes quantities tliat are known exactly (e.g., pure integers) have an infinite 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. 

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. 

Multiplication and division the answer should not contain a greater number of significant figures than the number in the least precise measurement. 

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

The measurement system that is most widely used in chemistry is the SI system. It incorporates a base unit for the various quantities and then uses prefixes to moderate the value of the base unit. The Unit Conversion Method is a way to generate easily the setup to a problem. Be sure to round off the final answer to the correct number of significant figures and include the units with the final answer. 

We have made references in the foregoing discussion to the precision of data, or how precise the data are. We have also made reference to the accuracy of data. Precision refers to the repeatability of a measurement. If you repeat a given measurement over and over and these measurements deviate only slightly from one another, within the limits of the number of significant figures obtainable, then we say that the data are precise, or that the results exhibit a high degree of precision. The mean of such data may or may not represent the real value of that parameter. In other words, it may not be accurate. Accuracy refers to the correctness of a measurement, or how close it comes to the correct value of a parameter. 

We deal with two types of numbers in chemistry—exact and measured. Exact values are just that—exact, by definition. There is no uncertainty associated with them. There are exactly 12 items in a dozen and 144 in a gross. Measured values, like the ones you deal with in the lab, have uncertainty associated with them because of the limitations of our measuring instruments. When those measured values are used in calculations, the answer must reflect that combined uncertainty by the number of significant figures that are reported in the final answer. The more significant figures reported, the greater the certainty in the answer. 

Because many experiments involve numerical calculations, it s often necessary to manipulate and convert different units of measure. The simplest way to carry out such conversions is to use the dimensional-analysis method, in which an equation is set up so that unwanted units cancel and only the desired units remain. It s also important when measuring physical quantities or carrying out calculations to indicate the precision of the measurement by rounding off the result to the correct number of significant figures. 

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. 

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