Math Handbook - Glencoe

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APPENDIX B Math Handbook PRACTICE PROBLEMS 7. Round off the following measurements to the number of significant figures indicated in parentheses. a. 2.7518 g (3) d. 186.499 m (5) b. 8.6439 m (2) e. 634 892.34 g (4) c. 13.841 g (2) f. 355 500 g (2) 8. Perform the following operations. a. (2.475 m) (3.5 m) (4.65 m) b. (3.45 m) (3.658 m) (4.7 m) c. (5.36 10 4 g) (6.381 10 5 g) d. (6.46 10 12 m) (6.32 10 11 m) e. (6.6 10 12 m) (5.34 10 18 m) f. 5. 634 1011 m 3. 0 1012 m g. (4.765 10 11 m)(5.3 10 4 m) 7.0 10 5 m Solving Algebraic Equations When you are given a problem to solve, it often can be written as an algebraic equation. You can use letters to represent measurements or unspecified numbers in the problem. The laws of chemistry are often written in the form of algebraic equations. For example, the ideal gas law relates pressure, volume, amount, and temperature of the gases the pilot in Figure 10 breathes. The ideal gas law is written PV nRT Math Handbook where the variables are pressure (P), volume (V), number of moles (n), and temperature (T). R is a constant. This is a typical algebraic equation that can be manipulated to solve for any of the individual variables. Figure 10 Pilots must rely on additional oxygen supplies at high altitudes to prevent hypoxia–a condition in which the tissues of the body become oxygen deprived. Math Handbook 897
APPENDIX B Math Handbook Table 2 Gas Pressures in Air Pressure (kPa) Nitrogen gas 79.10 Carbon dioxide gas 0.040 Trace gases 0.94 Total gases 101.3 remember that the result never can be more precise than the least precise measurement. That is, your answer cannot have more significant figures than the least precise measurement. Be sure to perform all calculations before dropping any insignificant digits. The following rules determine how to use significant figures in calculations that involve measurements. 1. To add or subtract measurements, first perform the mathematical operation, then round off the result to the least precise value. There should be the same number of digits to the right of the decimal as the measurement with the least number of decimal digits. 2. To multiply or divide measurements, first perform the calculation, then round the answer to the same number of significant figures as the measurement with the least number of significant figures. The answer should contain no more significant figures than the fewest number of significant figures in any of the measurements in the calculation EXAMPLE PROBLEM 2 Math Handbook Air contains oxygen (O 2 ), nitrogen (N 2 ), carbon dioxide (CO 2 ), and trace amounts of other gases. Use the known pressures in Table 2 to calculate the partial pressure of oxygen. To add or subtract measurements, first perform the operation, then round off the result to correspond to the least precise value involved. P O2 P total (P N2 P CO2 P trace ) P O2 101.3 kPa (79.11 kPa 0.040 kPa 0.94 kPa) P O2 101.3 kPa 80.090 kPa P O2 21.210 kPa The total pressure (P total ) was measured to the tenths place. It is the least precise measurement. Therefore, the result should be rounded to the nearest tenth of a kilopascal. The leftmost dropped digit (1) is less than five, so the last two digits can be dropped. The pressure of oxygen is P O2 21.2 kPa. A small, hand-held pressure gauge can be used to monitor tire pressure. EXAMPLE PROBLEM 3 The reading on a tire-pressure gauge is 35 psi. What is the equivalent pressure in kilopascals? P 35 psi 1 01. 3 kPa 14. 7 psi P 241.1904762 kPa There are two significant figures in the measurement, 35 psi. Thus, the answer can have only two significant figures. Do not round up the last digit to be kept because the leftmost dropped digit (1) is less than five. The equivalent pressure is P 240 kPa 2.4 10 2 kPa. 896 Chemistry: Matter and Change
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Math Handbook - Glencoe

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