1 Significant Figures (Sig Figs) Quantity includes all known digits plus one estimated digit = last digit of # Indicates precision 500 vs

2 Rule 1: All digits recorded from a lab measurement are called significant figures. Rule 2: All non-zero digits are considered significant. measurementnumber of sig figs 96 g_________ 61.4 g_________ 0.52 g_________ 2 3 2

3 Rule 3: Middle zeros are always significant. SANDWICH RULE measurementnumber of sig figs m_________ 306 cm_________ g_________ 4 3 4

4 Rule 4: A leading zero is never significant. The zeros are place holders only. measurementnumber of sig figs 0007 g ________ kg ________ kg ________ 1 3 6

5 Rule 5: Trailing zeros are significant only when to the right of decimal point. measurementnumber of sig figs km ________ km ________ 82.0 m ________ 3 5 3

6 Rule 6: All significant figures include units. Rule 7: All numbers multiplied by 10 in scientific notation are considered significant. measurementnumber of sig figs x 10 3 m _________ 1.02 x g _________ 4 3

7 SAME RULES: SHORT CUT “The Arrow Rule”: Draw an arrow to the first significant digit and count significant figures. Pacific Ocean Atlantic Ocean decimal Present decimal Absent measurement# sig figsmeasurement# sig figs 61.4 g____306 cm____ 0.52 g____7 000 g____ 82.0 m____ pennies____ kg____

8 Practice: how many sig figs in each quantity? km ____ dag ____ 1.22 us ____ m/s ____ ML ____

9 # of sig figs in answer is based on # sig figs in least precise measurement Which is the least precise, 7.22 m or m? _______ Rules for multiplication and division: 1) Count the # of sig figs in each measurement. 2) Use least # sig figs for # of digits in answer. Examples: 4.5 cm X 2.54 cm X cm = answer w/ sig figs _________ 4.62 g = cm 3 answer w/ sig figs __________ mm X 65mm = answer w/ sig figs _____________________________ 7.22 m 76 cm mm 2 or 1.4 x 10 2 mm g/cm cm g/cm mm 2

10 Rule for addition and subtraction: Look for the last significant place; the answer matches that last sig place. Examples: dm51.25 L + 50 dm- 1.5 L dm49.75 L answer w/ sig figs _________ __________ 150 dm49.8 L

11 Rule for addition and subtraction: Look for the last significant place; the answer matches that last sig place. Examples: mm1.520 g 105 mm2.15 g mm g mm g answer w/ sig figs _________ __________ mm13.22 g

12 Precision of equipment limits accuracy of a measurement w/ sf Answer with 1/10 th place precision is less accurate. Answer with 1/10,000 th place precision is more accurate.