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Significant Figures: Precision and Accuracy in Measurement

http://commons.wikimedia.org/wiki/File%3AGlass_graduated_cylinders-set.jpgBy Lilly_M [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0-2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons. Significant Figures: Precision and Accuracy in Measurement.

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Significant Figures: Precision and Accuracy in Measurement

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  1. http://commons.wikimedia.org/wiki/File%3AGlass_graduated_cylinders-set.jpgBy Lilly_M [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0-2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons Significant Figures: Precision and Accuracy in Measurement http://simple.wikipedia.org/wiki/Weighing_scale#mediaviewer/File:Balance_Kern.jpgBalance KernPublic Domain Karelj - Own work http://en.wikipedia.org/wiki/Darts#mediaviewer/File:Darts_in_a_dartboard.jpgDarts in a dartboardPublic Domainview terms PeterPan23 - http://en.wikipedia.org/wiki/Image:Darts_in_a_dartboard.jpg

  2. Target PracticeYou have 5 arrows. Mime shooting the bow. Be sure to make a “thwack” sound each time you shoot. Good luck!

  3. Simple Bow

  4. http://commons.wikimedia.org/wiki/File%3A25_Meter_Precision_and_50_Meter_Pistol_Target.svgBy Caiguanhao [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0-2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons

  5. Was the shooter accurate?Was the shooter precise?Why or why not?

  6. Compound Bow

  7. http://commons.wikimedia.org/wiki/File%3A25_Meter_Precision_and_50_Meter_Pistol_Target.svgBy Caiguanhao [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0-2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons

  8. Was the shooter accurate?Was the shooter precise?Why or why not?

  9. Cross Bow

  10. http://commons.wikimedia.org/wiki/File%3A25_Meter_Precision_and_50_Meter_Pistol_Target.svgBy Caiguanhao [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0-2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons

  11. Was the shooter accurate?Was the shooter precise?Why or why not?

  12. Which is Accurate? Which is Precise? Which are neither accurate nor precise? http://commons.wikimedia.org/wiki/File:Accuracy_and_precision_example.jpgPermission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License,

  13. http://commons.wikimedia.org/wiki/File%3A25_Meter_Precision_and_50_Meter_Pistol_Target.svgBy Caiguanhao [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0-2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons So, what do precision and accuracy mean in your labs? • Precision is how close your lab measurements are to each other • Accuracy is how close your measurements are to the correct value.

  14. How do we express accuracy in measurement? • We record the measurement according to the accuracy of the equipment used plus one estimated digit. http://commons.wikimedia.org/wiki/File%3AGlass_graduated_cylinder-50ml_pl.jpgBy Pleple2000 (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0-2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons http://fr.wikipedia.org/wiki/Balance_%28instrument%29#mediaviewer/Fichier:Balance_electronique%281%29.JPGBalance electronique(1)Domaine public

  15. What is the correct reading for the cylinder? Read the bottom of the meniscus. Meniscus Remember: Estimate one digit between the lines. Answer: 100. mL http://commons.wikimedia.org/wiki/File%3AMeasuring_cylinder.svgBy Lucasbosch (Own work) [CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons

  16. Read the graduated cylinders correctly. Which cylinder is the Which cylinder is the Least accurate Most accurate 655 mL 20.0 mL http://en.wikipedia.org/wiki/Meniscus#mediaviewer/File:Meniscus.jpgMeniscusCC BY-SA 3.0 PRHaney - Own work http://commons.wikimedia.org/wiki/File%3APlastic_graduated_cylinder-1000ml.jpgBy Lilly_M [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0-2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons

  17. Which balance is more accurate? Estimated digit http://en.wikipedia.org/wiki/Weighing_scale#mediaviewer/File:Analytical_balance_mettler_ae-260.jpgAnalytical balance mettler ae-260Public Domainview terms http://commons.wikimedia.org/wiki/File%3AWaga_elektroniczna.jpgBy Stan Zurek (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html), CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/) or CC-BY-SA-2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/2.5-2.0-1.0)], via Wikimedia Commons

  18. Rules for Significant Figures

  19. Rule 1: Nonzeros are always signficant. Examples: 4.56 23 11,526 3 SF 2 SF 5 SF

  20. Zeros are the problem!! • There are 3 kinds of zeros: • CAPTURED: in the middle • PRECEDING: on the left • TRAILING: on the right

  21. Rule 2:CAPTURED zeros are ALWAYS significant. Examples: 101 200,205 7802 3 SF 6 SF 4 SF

  22. Rule 3:PRECEDING zeros are NEVER significant. Examples: 0.00101 0.200205 0.00007802 3 SF 6 SF 4 SF

  23. Rule 4:TRAILING zeros are significant WITH A DECIMAL present. Examples: 100 100. 0.5000 105.75060 1 SF 3 SF 4 SF 8 SF Challenge: Write one hundred in 2 SF.

  24. Significant Figures in Calculations http://en.wikipedia.org/wiki/TI-84_Plus_series#mediaviewer/File:TI-84_Plus_Silver_Edition.JPGTI-84 Plus Silver EditionPublic Domain

  25. Multiplying and Dividing http://www.dreamstime.com/royalty-free-stock-photos-icon-multiply-divide-image10996788 • Rule 5: When multiplying or dividing the answer will have the same SF as the least accurate measurement. Example: m = 9.567 g V = 10.1 mL D = m/V = 9.567g/10.1 mL = = Note the use of Given, Formula, Substitute, Solve 3 SF 0.9472277228 g/mL 0.947 g/mL

  26. Rule 6: Counted, known, and accepted values DO NOT affect significant figures. Example: (20 students)(68.18 kg avg. mass) = 1363.6 kg Round answer to 4 sig figs. = 1364 Kg Counted value has no affect Least accurate measurement

  27. Adding and Subtracting • Rule 7: When adding and subtracting, the answer is rounded to most accurate decimal place shared by all the measurements. Example: 209.7 cm 8.004 cm + 1012.39 cm 1230.094 cm Tenths column is the most accurate decimal place shared by all the measurements, so round to tenths. Final answer: 1230.1 cm

  28. http://commons.wikimedia.org/wiki/File%3ALittle_Gray_Mouse_-_The_End_(67).pngBy Dorothy Sherrill (Internet Archive) [Public domain or Public domain], via Wikimedia Commons …for now…

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