Subtracting, significant figures

Note that five significant figures have been retained for the reciprocals of the squares of the quantum numbers because, as you can see in the calculation, two of these figures are lost when the reciprocals are subtracted. 

In addition or subtraction, there should be in each number only as many significant figures as there are in the least accurately known number. Thus the addition... 

The isotopic molar masses are precise to five or more significant figures, so we are tempted to express the result with five significant figures. The mass defect is determined by addition and subtraction, however, and two of the isotopic molar masses are known to just three decimal places, so the mass defect is precise to three decimal places, and the... 

For addition or subtraction, the limiting term is the one with the smallest number of decimal places, so count the decimal places. For multiplication and division, the limiting term is the number that has the least number of significant figures, so count the significant figures. 

Total score = sum of parts a-d. If any of the final answers has the incorrect number of significant figures, subtract one point. 

The total is 10 points for this question. Subtract one point if any answer has an incorrect number of significant figures. 

Total your points there are 10 points possible. Subtract one point if all answers do not have the correct number of significant figures. 

You get 1 point for the prediction that the reaction is spontaneous. The setup (plugging into the equation) is worth 1 point if you remember to change the temperature to kelvin and convert joules to kilojoules. An additional 1 point comes from the answer. If you got the wrong value in either part (a) or (b), but used it correctly, you will still get the point for the answer. The free-energy equation is part of the material supplied in the exam booklet. Subtract one point if all your answers do not have the correct number of significant figures. 

No problem. Follow the normal order of operations, doing multiplication and division first, followed by addition and subtraction. At each step, follow the simple significant-figure rules, and then move on to the next step. 

In addition to the rules cited above, there is another full set of rules to be followed for significant figures when two or more measured numbers are subtracted, added, divided, or multiplied. These rules are summarized in the appendix of the Conceptual Chemistry Laboratory Manual. 

Different rounding off rules are needed for addition (and its reverse, subtraction) and multiplication (and its reverse, division). In both procedures we round off the answers to the correct number of significant figures. 

When we add or subtract numbers, the number of significant figures in the answer is limited by the number with the smallest number of significant figures to the right of the decimal, e.g.,... 

The answer should be rounded off after adding or subtracting, so as to retain digits only as far as the first column containing estimated figures. (Remember that the last significant figure is estimated.)... 

Notice that our assumption about the acetic acid concentration was valid. If we subtract the hydrogen ion concentration from the formal concentration, the difference, expressed to the correct number of significant figures, remains at 0.10 M. 

The manipulation of significant figures in multiplication, division, addition, and subtraction is important. It is particularly important when using electronic calculators which give many more digits than are useful or significant. If you keep in mind the principle that the final answer can be no more accurate than the least accurate measurement, you should not go wrong. A few examples will demonstrate this. 

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