Accuracy, Precision and Significant Figures

Scientific Measurements All of the numbers of your certain of plus one more. –Here it would be 4.7x. –We know it is a little more than 4.7, so the “x” is the guess.

Scientific Measurements All of the numbers of your certain of plus one more. 6.6x mL I would say 6.61 mL

Scientific Measurements For mass, all readings are significant, but the last digit may change due to air flow in the room.

SIGNIFICANT FIGURES Read each measurement: a.28 mL b.28.3 mL c mL

Precision v. Accuracy Precision –how closely individual measurements agree (repeatability) Accuracy – how closely individual measurements agree with the correct or “true” value (bullseye)

Uncertainty in Scientific Measurements Uncertainty: the amount of doubt about the measurement. Sometimes known as the “doubtful digit” The volume is measured as 28 mL, where the “2” is the known value and the “8” is our guess. The uncertainty is written as  1 mL

The volume is measured as 28.3 mL, where the “28” is the known value and the “3” is our guess. The uncertainty is written as  0.1 mL Uncertainty in Scientific Measurements

The volume is measured as mL, where the “28.3” is the known value and the “2” is our guess. The uncertainty is written as  0.01 mL Uncertainty in Scientific Measurements

The volume is measured as mL, where the “28.3” is the known value and the “2” is our guess. The uncertainty is written as  0.01 mL Uncertainty in Scientific Measurements

You Try! How many sig figs in the following: Examples: a) 1001 km b) m c) 129,870 m d) km e) L f) 6.02 x atoms g) 20,000 cm h) g Number of Significant Figures: a) 4 b) 4 c) 5 d) 1 e) 4 f) 3 g) 1 h) 2

Rounding Tips: When rounding number greater than or equal to 5: round up. Ex: 5.76 = = 4.9 When rounding number less than 5: round down. Ex: 5.24 = = 4.1

Rounding Round each of these to 2 sig figs: Examples: a) m b) 34,000 m c) 129,870 m d) km e) L f) 6.02 x atoms g) 20,000 cm h) 1001 km Number of Significant Figures: a) 34 m b) 34,000 m c) 130,000 m d) km e) 1.0 L f) 6.0 x atoms g) 2.0 x 10 4 cm h) 1.0 x 10 3 km

CALCULATIONS WITH SIG FIGS Examples: cm x cm = cm² 73.1 = 73.1 cm² (1.13 m)( m) = m² 5.79 = 5.79 m² cm² / cm = cm = cm RULE: When multiplying or dividing measurements, round off the final answer to the measurement with the smallest number of significant figures.

CALCULATIONS WITH SIG FIGS Examples: 1 1) cm cm cm cm 6 = cm RULE: When adding or subtracting, round the answer to the smallest number of decimal places.

You Try! Addition cm + 8 cm cm = Multiplication 2.6 cm x 3.78 cm = cm 178 cm = 178 cm cm cm 2 = 9.8 cm 2