Chapter 5, Part 2 Measurements and Calculations. 5.4 Uncertainty in Measurement Reported data- the last unit is uncertain; it has been estimated. Uncertainty.

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Presentation transcript:

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). Grad. Cylinders, pipets, burets, etc.: you are as good as the calibration + one more digit. (This is very important in Laboratory Exercises!)

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:____________

5.5 Significant Figures (sig figs) 1.All nonzero digits are significant. 2.Any trapped zeros are significant. 3.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.

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 atoms

Example: Sample of OJ w/ g of vitamin C (3 sig figs) Mass of a single hair as g(5 sig figs) Distance of x 10 3 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? a m(3) b x 10 2 L(5) c.480 cars(infinite) Embedded Problems: How many sig figs in each of the following? a ____________e _____________ b ____________f _________ c.1000____________g _____________ d ____________

Sig figs in Calculations Addition & Subtraction- the limiting term is the one with the least certainty (the fewest number of decimal places) Example: =  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 =  6.4 Problems: How many sig figs should be in each of the following? a = ____________(2) b = _________________(3) c.4.6 x = ___________________(2) d = __________________(1)

Embedded Problems: Round each number to three sig figs a.2,444,578 _______________ b x 10 5 _____________ c ______________ Solve the operation; round answer to the correct number of sig figs a.(0.15)(280.62) = ___________________ b = ___________________ c.311/0.011 = ___________________