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Transcript of Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a...
![Page 1: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/1.jpg)
Significant Figures: Precision and Accuracy in
Measurement
http://en.wikipedia.org/wiki/Darts#mediaviewer/File:Darts_in_a_dartboard.jpgDarts in a dartboardPublic Domainview termsPeterPan23 - http://en.wikipedia.org/wiki/Image:Darts_in_a_dartboard.jpg
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http://simple.wikipedia.org/wiki/Weighing_scale#mediaviewer/File:Balance_Kern.jpgBalance KernPublic DomainKarelj - Own work
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Target Practice
You have 5 arrows. Mime shooting the bow. Be sure to make a
“thwack” sound each time you shoot. Good luck!
![Page 3: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/3.jpg)
Simple Bow
![Page 4: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/4.jpg)
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![Page 5: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/5.jpg)
Was the shooter accurate?Was the shooter precise?
Why or why not?
![Page 6: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/6.jpg)
Compound Bow
![Page 7: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/7.jpg)
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![Page 8: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/8.jpg)
Was the shooter accurate?Was the shooter precise?
Why or why not?
![Page 9: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/9.jpg)
Cross Bow
![Page 10: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/10.jpg)
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![Page 11: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/11.jpg)
Was the shooter accurate?Was the shooter precise?
Why or why not?
![Page 12: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/12.jpg)
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,
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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.
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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
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Remember: Estimate one digit between the lines.
What is the correct reading for the cylinder?
Meniscus
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
Read the bottom of the meniscus.
![Page 16: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/16.jpg)
Least accurate
Mostaccurate
665 mL
20.00 mL
http://en.wikipedia.org/wiki/Meniscus#mediaviewer/File:Meniscus.jpgMeniscusCC BY-SA 3.0PRHaney - Own work
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Read the graduated cylinders correctly.Which cylinder is the
Which cylinder is the
![Page 17: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/17.jpg)
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
![Page 18: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/18.jpg)
Rules for Significant Figures
![Page 19: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/19.jpg)
Rule 1: Nonzeros are always signficant.
Examples:4.56
23
11,526
3 SF2 SF
5 SF
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Zeros are the problem!!
• There are 3 kinds of zeros:
–CAPTURED: in the middle
–PRECEDING: on the left
–TRAILING: on the right
![Page 21: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/21.jpg)
Rule 2: CAPTURED zeros are ALWAYS
significant.Examples:
101
200,205
7802
3 SF6 SF
4 SF
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Rule 3: PRECEDING zeros are NEVER
significant.Examples:
0.00101
0.200205
0.00007802
3 SF6 SF
4 SF
![Page 23: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/23.jpg)
Rule 4: TRAILING zeros are significant WITH A
DECIMAL present.
Examples:100
100.
0.5000
105.75060
1 SF3 SF
4 SF
8 SF
Challenge: Write one hundred in 2 SF.
![Page 24: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/24.jpg)
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
![Page 25: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/25.jpg)
Multiplying and Dividing
• Rule 5: When multiplying or dividing the answer will have the same SF as the least accurate measurement.
Example:m = 9.567 gV = 10.1 mLD = m/V = 9.567g/10.1 mL = =
0.9472277228 g/mL0.947 g/mL
Note the use of Given, Formula, Substitute, Solve
3 SF
http://www.dreamstime.com/royalty-free-stock-photos-icon-multiply-divide-image10996788
![Page 26: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/26.jpg)
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
Least accurate measurementCounted value has no affect
![Page 27: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/27.jpg)
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
![Page 28: Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.](https://reader034.fdocuments.in/reader034/viewer/2022051316/56649ec95503460f94bd7702/html5/thumbnails/28.jpg)
…for now…
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