Measurements: Every measurement has UNITS. Every measurement has UNCERTAINTY.

Accuracy and Precision in Measurements Accuracy: how close a measurement is to the accepted value. Precision: how close a series of measurements are to one another or how far out a measurement is taken. A measurement can have high precision, but not be as accurate as a less precise one.

Precision can also mean The number of decimal places assigned to the measured number (The more decimal places, the more precise the measurement) Ex. 2.1 cm 2.10 cm 2.100 cm

the digit farthest to the right is considered to be estimated. Significant Figures are used to indicate the precision of a measured number or to express the precision of a calculation with measured numbers. In any measurement the digit farthest to the right is considered to be estimated. 1 2 2.0 1.3

Sig. Fig. Rules (with measurements): 1. All non-zero digits are significant. 3 sig figs 1222 4 sig figs 0.54 2 sig figs 2. Zeros at the beginning of a measurement are not significant. 0.005 1 sig fig 0.0015 2 sig figs 0.00000887 3 sig figs

3. Zeros in between two significant figures are significant 0.00505 3 sig figs 40065 5 sig figs 4. Final zeros after a decimal point are significant 1.0 2 sig figs 74.00 4 sig figs 105.20 5 sig figs 0.0050 2sig figs 2.000 4 sig figs 20.0 3 sig figs Counted numbers and definitions (2.54 cm = 1 inch) are considered to be exact and have no effect on the number of sig. figs. reported in calculations with measurements.

significant to the 0.1 place Calculations with sig. Figs. Addition and subtraction: Look at decimal places! Answer should have the same amount of decimal places as the measurement with the least amount 3.63 cm 13.129 cm +123.1 cm 139.859 cm = 139.9 cm significant to the 0.1 place

Measurement Calculations with scientific notation. Addition/subtraction: must be placed into the same notation. (2.3 x 103) + (3.2 x 104) = 0.23 x 104 +3.2 x 104 3.43 x 104 = 3.4 x 104

Calculations with Sig. figs. Multiplication and division (measurements): Count sig figs!! Answer should have the same amount of sig figs as the measurement with the least amount. 2.734 cm x 5.2 cm x 8.1294 cm = 115.5740539 cm3 4 s.f. 2 s.f. 5 s.f. written as 120 cm3 2 s.f.’s

1. The term that is related to the reproducibility (repeatability) of a measurement is a. accuracy. b. precision. c. qualitative. d. quantitative. e. property. Let’s take a “Quiz” b. precision. 2. The number of significant figures in the mass measured as 0.010210 g is a. 1. b. 2. c. 3. d. 4. e. 5. e. 5.

3. The number of significant figures in 6.0700 x 10-4… is d. 6. e. 7. c. 5. 4. How many significant figures are there in the value 0.003060? a. 7 b. 6 c. 5 d. 4 e. 3 d. 4

Percent Error your value accepted value Indicates accuracy of a measurement your value accepted value

Percent Error % error = 2.9 % A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. % error = 2.9 %