1. 1 Significant Figures (Sig Figs) Quantity includes all known digits plus one estimated digit = last digit of # Indicates precision 500 vs 500.01

2. 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. 3 Rule 3: Middle zeros are always significant. SANDWICH RULE measurementnumber of sig figs 5.029 m_________ 306 cm_________ 410.0 g_________ 4 3 4

4. 4 Rule 4: A leading zero is never significant. The zeros are place holders only. measurementnumber of sig figs 0007 g ________ 0.00783 kg ________ 5.00783 kg ________ 1 3 6

5. 5 Rule 5: Trailing zeros are significant only when to the right of decimal point. measurementnumber of sig figs 47200 km ________ 4.7200 km ________ 82.0 m ________ 3 5 3

6. 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 3.600 x 10 3 m _________ 1.02 x 10 -9 g _________ 4 3

7. 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____50 002 pennies____ 0.00783 kg____ 3 2 3 3 3 1 5

8. 8 Practice: how many sig figs in each quantity? 45.35 km ____ 6.2100 dag ____ 1.22 us ____ 8 000 000 m/s ____ 0.034567 ML ____ 4 5 3 1 5

9. 9 # of sig figs in answer is based on # sig figs in least precise measurement Which is the least precise, 7.22 m or 7.22555 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 3.215 cm = answer w/ sig figs _________ 4.62 g = 15.00 cm 3 answer w/ sig figs __________ 2.124 mm X 65mm = answer w/ sig figs _____________________________ 7.22 m 76 cm 3 140 mm 2 or 1.4 x 10 2 mm 2 0.308 g/cm 3 75.8097 cm 3 0.308 g/cm 3 138.06 mm 2

10. 10 Rule for addition and subtraction: Look for the last significant place; the answer matches that last sig place. Examples: 100.5 dm51.25 L + 50 dm- 1.5 L 150.5 dm49.75 L answer w/ sig figs _________ __________ 150 dm49.8 L

11. 11 Rule for addition and subtraction: Look for the last significant place; the answer matches that last sig place. Examples: 25002 mm1.520 g 105 mm2.15 g + 4.25 mm +9.5515 g 25111.25 mm 13.2215 g answer w/ sig figs _________ __________ 25111 mm13.22 g

12. 12 Precision of equipment limits accuracy of a measurement 100.5321 100.5321 + 50.4 +50.3572 150.9321150.8893 w/ sf 150.9 Answer with 1/10 th place precision is less accurate. Answer with 1/10,000 th place precision is more accurate.