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Chapter 5, Part 2 Measurements and Calculations

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Page 1: Chapter 5, Part 2 Measurements and Calculations. 5.4 Uncertainty in Measurement Reported data- the last unit is uncertain; it has been estimated. Uncertainty

Chapter 5, Part 2

Measurements and Calculations

Page 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

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!)

Page 3: Chapter 5, Part 2 Measurements and Calculations. 5.4 Uncertainty in Measurement Reported data- the last unit is uncertain; it has been estimated. Uncertainty

Stopper Activity

Analytical BalanceMass 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: ____________

Page 4: Chapter 5, Part 2 Measurements and Calculations. 5.4 Uncertainty in Measurement Reported data- the last unit is uncertain; it has been estimated. Uncertainty

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.

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

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

Page 6: Chapter 5, Part 2 Measurements and Calculations. 5.4 Uncertainty in Measurement Reported data- the last unit is uncertain; it has been estimated. Uncertainty

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?a. 0.00100 m (3)b. 2.0800 x 102 L (5)c. 480 cars (infinite)

Embedded Problems: How many sig figs in each of the following?d. 0.003042 ____________ e. 50.0 _____________e. 1.4030 ____________ f. 10.47020 _________f. 1000 ____________ g. 250. _____________g. 0.060 ____________

Page 7: Chapter 5, Part 2 Measurements and Calculations. 5.4 Uncertainty in Measurement Reported data- the last unit is uncertain; it has been estimated. Uncertainty

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?

a. 3.2 + 4.17 + 1.243 = ____________(2)

b. 1.3478 - 0.02 = _________________(3)

c. 4.6 x 3.435 = ___________________(2)

d. 50 - 0.00473 = __________________(1)

Page 8: Chapter 5, Part 2 Measurements and Calculations. 5.4 Uncertainty in Measurement Reported data- the last unit is uncertain; it has been estimated. Uncertainty

Embedded Problems: Round each number to three sig figs

a. 2,444,578 _______________b. 5.1101 x 105 _____________c. 0.100789 ______________

Solve the operation; round answer to the correct number of sig figs

d. (0.15)(280.62) = ___________________e. 334.2 + 60.1 + 609.01 = ___________________f. 311/0.011 = ___________________

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