Multiply or divide the following measurements. Be sure each answer you enter contains the correct number of significant digits. \[ \begin{array}{l}78.08 \frac{\mathrm{~mol}}{\mathrm{~L}} \times 70 \mathrm{~L}=\square \mathrm{mol} \\ 542.0 \mathrm{~mol}+66.611 \mathrm{~L}=\square \frac{\mathrm{mol}}{\mathrm{L}} \\ 7.808 \frac{\mathrm{~g}}{\mathrm{~mL}} \times 3.65 \mathrm{~mL}=\square \mathrm{g}\end{array} \]

Below is one way to work through the problem. (Note: In the second expression the unit of the answer is mol/L—which is what you get for concentration (moles divided by volume). Although a plus sign is shown, the proper operation there is division.) 1) Multiply 78.08 mol/L by 70 L.   Calculation:    78.08 mol/L × 70 L = 5465.6 mol   Now for significant figures: 78.08 has 4 significant figures. For the “70 L” the number of significant figures is ambiguous because it is not written in scientific notation; we assume it has 2 significant figures. When multiplying, the answer must have the same number of significant figures as the factor with the fewest. Therefore the answer must have 2 significant figures.   Rounding 5465.6 mol to 2 significant figures gives 5.5×10³ mol. 2) Divide 542.0 mol by 66.611 L to get the concentration in mol/L.   Calculation:    542.0 mol ÷ 66.611 L ≈ 8.132 mol/L   Now for significant figures: 542.0 has 4 significant figures and 66.611 has 5 significant figures. The result should have 4 significant figures (the smaller count). Thus, 8.132 mol/L is the answer (you might also round to 8.13 mol/L if preferred, but 8.132 already shows 4 significant digits). 3) Multiply 7.808 g/mL by 3.65 mL.   Calculation:    7.808 g/mL × 3.65 mL = 28.4992 g   Now for significant figures: 7.808 has 4 significant figures and 3.65 has 3 significant figures. The answer must be given with 3 significant figures.   Rounding 28.4992 g to 3 significant figures gives 28.5 g. To summarize, the answers (with the proper significant digit treatment) are:   • 78.08 mol/L × 70 L = 5.5×10³ mol   • 542.0 mol ÷ 66.611 L ≈ 8.132 mol/L   • 7.808 g/mL × 3.65 mL = 28.5 g