 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 g of caffeine. b. A chemist records a mass of g in an analysis. c. In an experiment, a span of time is determined to be × 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  limiting term = 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= decimal places

 Round at the end of all calculations ◦ 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  Look at the significant figure one place beyond your desired number of significant figures ◦ if >5 round up; <5 drop the digit.  Don’t “double round” !! ◦ to 2 SF = 4.3 (NOT the 8 makes the 4 a 5 then the 5 makes the 3 a 4 =4.4)