And Problem Solving in Chemistry Precision and Accuracy Significant Figures % error Measurement Density

Accuracy vs Precision Accuracy: All the data represents the true measurement. When a measurement is accurate It is very close to the accepted value. Generally, you want to be within 5% or less of the accepted value.

Accuracy vs Precision Precision: All the data is very Similar to the average value. The data is very reproducible. It is not necessarily accurate. The measuring device could be consistent but not accurate. The measurements will have been taken under the same conditions.

To be both Accurate and Precise The data must be consistent AND near the Accepted value.

Precise, Accurate, or both? Trial 1 Arrow # 1 = 0.4 cm Arrow #2 = 0.6 cm Arrow #3 = 1.0 cm Arrow #4 = 1.2 cm Water level Trial 1 Rf1 = 0.4/1.2 = 0.3 Rf2 = 0.6/1.2 = 0.5 Rf3 = 1.0/1.2 =0.83 Trial 2 Arrow # 1 = 0.3 cm Arrow #2 = 0.5 cm Arrow #3 = 0.9 cm Arrow #4 = 1.1 cm Trial 2 Rf1 = 0.3/1.1 = 0.3 Rf2 = 0.5/1.1 = 0.5 Rf3 = 0.9/1.1 =0.8 These are both accurate and precise Rf =.3Rf =.5 Rf =.8

Precise, Accurate, or both? Trial 1 Arrow # 1 = 0.6 cm Arrow #2 = 0.8 cm Arrow #3 = 1.1 cm Arrow #4 = 1.2 cm Water level Trial 1 Rf1 = 0.6/1.2 = 0.5 Rf2 = 0.8/1.2 = 0.7 Rf3 = 1.1/1.2 =0.92 Trial 2 Arrow # 1 = 0.6cm Arrow #2 = 0.8cm Arrow #3 = 0.9 cm Arrow #4 = 1.1 cm Trial 2 Rf1 = 0.6/1.1 = 0.5 Rf2 = 0.8/1.1 = 0.7 Rf3 = 1.0/1.1 =0.91 These are only precise Rf =.3 Rf =.8 Rf =.5

% error – instead of guessing if data is precise or accurate, you can use statistics. Error = Accepted Value – experimental value. In order to use % error, you must be using a substance for which there IS an accepted value. In one of our next chemistry lab, we will be using Appendix A1 to compare our values of density of elements to your experimental values. ErrorAccepted Value – experimental value. Accepted Value % error = x 100% Accepted Value

Significant Figures 1. Non Zero Numbers are significant 2. Zeros in between significant digits are significant 3. Place-holder zeros are NOT significant. All other zeros are. 4. Scientific notation is used if a zero which SHOULD be a place-holder is actually a measured value = 4 sig figs 1.01 = 3 sig figs = 5 sig figs = 1 sig fig = 1 sig fig = 3 sig figs 1.0 x 10 8 = 2 sig figs

Scientific Notation x x x x x x x x x x x x x x x x 10 -8

Test Yourself… x x = 6 sig figs = 1 sig fig = 3 sig figs = 3 sig figs = 3 sig figs = 3 sig figs = 3 sig figs x = 4 sig figs x = 3 sig figs

Test Yourself…. Round each number to two sig figs x x x x x x x x x x x 10 -4

Find the density of a metal Find the mass using a balance Find the volume either using rulers or using measurement by difference. Density = mass/volume Look up the accepted value for density. % error = 100% x Accepted – Experimental Accepted