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In a measurement, ◦ All of the digits known with certainty and one “uncertain” or estimated digit Related to the precision of the measuring instrument ◦ The smallest divisions on the scale determine the number of certain digits ◦ Estimate one place past the smallest division on the scale Rules 1. Non zero digits are significant 2. A zero is significant if it is a.“terminating AND right” of the decimal [must be both] b.“sandwiched” between significant figures c. Has a bar over it 3. Exact or counting numbers have an amount of significant figures as do constants and conversion factors Give the number of significant figures for each of the following results. a. A student’s extraction procedure on tea yields 0.0105 g of caffeine. b. A chemist records a mass of 0.050080 g in an analysis. c. In an experiment, a span of time is determined to be 8.050 × 10-3 s . × and ◦ The term with the least number of significant figures determines the number of significant figures in the answer. 4.56 × 1.4 = 6.38 = 6.4 limiting term + and (−) ◦ The term with the least number of decimal places determines the number of significant figures in the answer. 12.11 18.0 limiting term +1.013 31.123= 31.1 pH – the number of significant figures in least accurate measurement determines the number of decimal places on the pH (and vice versa). [H+]=0.10M 2 significant figures pH=-log[H+]=-log(0.10)= 1=1.00 2 decimal places Round at the end of all calculations Look at the significant figure one place beyond your desired number of significant figures ◦ Carry AT LEAST one extra digit through intermediate calculations ◦ Usually just look at the given data and round your final answer to the least number of sig figs in data ◦ When in doubt, round to 3 sig figs ◦ Scientific notation is your friend ◦ No points lost as long as you are within +/- one sig. figure ◦ if >5 round up; <5 drop the digit. Don’t “double round” !! ◦ 4.348 to 2 SF = 4.3 (NOT the 8 makes the 4 a 5 then the 5 makes the 3 a 4 =4.4)