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Significant Figures

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

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Significant Figures

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  1. Significant Figures

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

  3. 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

  4. Rule 3: Middle zeros are always significant. SANDWICH RULE measurementnumber of sig figs • 5.029 m _________ • 306 cm _________ • 410.0 g _________ 4 3 4

  5. 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

  6. 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

  7. 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 103 m _________ • 1.02 x 10-9 g _________ 4 3

  8. Pacific Ocean Atlantic Ocean decimal Present decimal Absent SAME RULES: SHORT CUT “The Arrow Rule”: Draw an arrow to the first significant digit and count significant figures. 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 3 2 1 3 5 3

  9. 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

  10. # of sig figs in answer is based on # sig figs in least precise measurementWhich is the least precise, 7.22 m or 7.22555 m? _______ 7.22 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 cm3 answer w/ sig figs __________ 2.124 mm X 65mm = answer w/ sig figs _____________________________ 75.8097 cm3 76 cm3 0.308 g/cm3 0.308 g/cm3 138.06 mm2 140 mm2 or 1.4 x 102 mm2

  11. Rule for addition and subtraction:Look for the last significant place; the answer matches that last sig place. Examples: 100.5 dm 51.25 L + 50 dm- 1.5 L 150.5 dm 49.75 L answer w/ sig figs answer w/ sig figs _________ __________ 150 dm 49.8 L

  12. Rule for addition and subtraction:Look for the last significant place; the answer matches that last sig place. Examples: 25002 mm 1.520 g 105 mm 2.15 g + 4.25 mm+9.5515 g 25111.25 mm 13.2215 g answer w/ sig figs answer w/ sig figs _________ __________ 25111 mm 13.22 g

  13. Precision of equipment limits accuracy of a measurement 100.5321 100.5321 + 50.4 +50.3572 150.9321 150.8893 w/ sf150.9 Answer with 1/10,000th place precision is more accurate. Answer with 1/10th place precision is less accurate.

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