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Chapter 5, Part 2

Chapter 5, Part 2. Measurements and Calculations. 5.4 Uncertainty in Measurement Reported data- the last unit is uncertain; it has been estimated. Uncertainty is recorded as plus or minus (the last unit).

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Chapter 5, Part 2

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  1. Chapter 5, Part 2 Measurements and Calculations

  2. 5.4 Uncertainty in Measurement Reported data- the last unit is uncertain; it has been estimated. Uncertainty is recorded as plus or minus (the last unit). Grad. Cylinders, pipets, burets, etc.: you are as good as the calibration + one more digit. (This is very important in Laboratory Exercises!)

  3. Stopper Activity Analytical Balance Mass of stopper #1 ____________ Mass of stopper #2 ____________ Mass of stopper #3 ____________ Average mass: ____________ Electronic Balance (+ or – 0.01 g) Mass of stopper #1 ____________ Mass of stopper #2 ____________ Mass of stopper #3 ____________ Average mass: ____________ Electronic Balance (+ or – 0.1g) Mass of stopper #1 ____________ Mass of stopper #2 ____________ Mass of stopper #3 ____________ Average Mass: ____________

  4. 5.5 Significant Figures (sig figs) • All nonzero digits are significant. • Any trapped zeros are significant. • Atlantic-Pacific Rule Rounding Off: if < 5, preceding digits stays the same If > 5, the preceding digit is increased by 1. Always carry all digits through your calculations and round off at the end.

  5. Exact numbers- have an infinite # of significant digits. 10 experiments 3 apples 8 molecules Conversion units- have an infinite # of significant digits 1 in = 2.54 cm 100 cm = 1 m 1 mole = 6.02 x 10 23atoms

  6. Example: Sample of OJ w/ 0.0108 g of vitamin C (3 sig figs) Mass of a single hair as 0.0050060 g (5 sig figs) Distance of 5.030 x 103 ft (4 sig figs) 110 riders (an exact number, infinite sig figs) 60riders (an exact number, infinite sig figs) Problems: How many sig figs in the following? • 0.00100 m (3) • 2.0800 x 102 L (5) • 480 cars (infinite) Embedded Problems: How many sig figs in each of the following? • 0.003042 ____________ e. 50.0 _____________ • 1.4030 ____________ f. 10.47020 _________ • 1000 ____________ g. 250. _____________ • 0.060 ____________

  7. Sig figs in Calculations Addition & Subtraction- the limiting term is the one with the least certainty (the fewest number of decimal places) Example: 12.11 + 18.0 + 1.013 = 31.123  31.1 Multiplication & Division- the number of sig figs in the result is the same as that in the number with the fewest number of sig figs. Example: 4.56 x 1.4 = 6.384  6.4 Problems: How many sig figs should be in each of the following? • 3.2 + 4.17 + 1.243 = ____________(2) • 1.3478 - 0.02 = _________________(3) • 4.6 x 3.435 = ___________________(2) • 50 - 0.00473 = __________________(1)

  8. Embedded Problems: Round each number to three sig figs • 2,444,578 _______________ • 5.1101 x 105 _____________ • 0.100789 ______________ Solve the operation; round answer to the correct number of sig figs • (0.15)(280.62) = ___________________ • 334.2 + 60.1 + 609.01 = ___________________ • 311/0.011 = ___________________

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