Objectives To learn how uncertainty in a measurement arises To learn to indicate a measurement’s uncertainty by using significant figures To learn to determine the number of significant figures in a calculated result To learn the difference between accuracy and precision of a measurement

A. Uncertainty in Measurement A measurement always has some degree of uncertainty. How long is this nail?

A. Uncertainty in Measurement Different people estimate differently. Record all certain numbers and one estimated number. Whenever we measure in chemistry we always record one extra decimal place (estimated number) beyond the markings on the measurement device.

B. Significant Figures Numbers recorded in a measurement. All the certain numbers plus the first estimated number Accuracy of a measurement – how close your number comes to the actual value similar to hitting the bull's-eye on a dart board Precision of a measurement – how close your repeated measurements come to each other (not necessarily the actual value) how closely grouped are your 3 darts on the board (even if they’re not close to the bull's-eye) It is possible for measurements to be precise but not accurate, just as it is possible to be accurate but not precise

Accuracy and Precision

B. Significant Figures Rules for Counting Significant Figures (Simple Method) If the number has a decimal point, attack it from the left; if the number has no decimal point, attack it from the right. Pass through all zeros until you hit the first non-zero number The zeros you passed through are NOT significant digits! Every number you encounter from now on is a significant digit! Including any zeros!

Rules for Counting Significant Figures (Simple Method) B. Significant Figures Rules for Counting Significant Figures (Simple Method) Pacific if a number has a Period (decimal), come from the Pacific side Atlantic if a period (decimal) is Absent, come from the Atlantic side

B. Significant Figures Rules for Counting Significant Figures (Simple Method) 100 attack from _____ __ sig figs 410100 attack from _____ __ sig figs 100. attack from _____ __ sig figs 100.8 attack from _____ __ sig figs 100.80 attack from _____ __ sig figs 0.00287 attack from _____ __ sig figs 0.002870 attack from _____ __ sig figs 1.0805 x 104 attack from _____ __ sig figs 1.0805 x 10-12 attack from _____ __ sig figs 1.205670 x 10-6 attack from _____ __ sig figs

B. Significant Figures Rules for Counting Significant Figures (Hard Method) Nonzero integers always count as significant figures. 1457 4 significant figures

B. Significant Figures Rules for Counting Significant Figures (Hard Method) Zeros Leading zeros - never count 0.0025 2 significant figures Captive zeros - always count 1.008 4 significant figures Trailing zeros - count only if the number is written with a decimal point 100 1 significant figure 100. 3 significant figures 120.0 4 significant figures

B. Significant Figures Rules for Counting Significant Figures (Both Methods) Exact numbers - unlimited significant figures Exact counts have unlimited (infinite) sig figs; they are obtained by simple counting (no uncertainty): 3 apples, 12 eggs, 1 mole Conversion Factors have unlimited sig figs also: 1 in. = 2.54 cm 1 mole = 6.022 x 1023 atoms

B. Significant Figures

B. Significant Figures Rules for Multiplication and Division The number of significant figures in the answer is the same as in the measurement with the smallest number of significant figures.

B. Significant Figures Rules for Addition and Subtraction The number of decimal places in the result is the same as in the measurement with the smallest number of decimal places (not sig figs!).

B. Significant Figures Rules for Counting Significant Figures VITALLY IMPORTANT: For the rest of the year, all calculations must include the correct number of significant figures in order to be fully correct! on all homework, labs, quizzes, and tests, etc. even if the directions don’t specifically tell you so