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# Measurement & Error

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I split the presentation for the unit into two, as I added so many slides to help with student questions and misconceptions. This one focuses on mathematical aspects of the unit.

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• @GoldenRetro I agree

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• On slide 9, I think there is an error with the measurement all the way to the left hand side. Shouldn't it be 48ml plus or minus 1ml?

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### Measurement & Error

1. 1. Measurement & Error Maths Skills in Science Introductory Chemistry Canadian Academy MrT
2. 2. Measurement & Error• Distinguish between quantitative and qualitative data• State SI units of measurement for mass, length, concentration, temperature, density and other values• Distinguish between accuracy and precision• Determine the uncertainty of digital and analogue measuring tools• Calculate the % error of a given or recorded set of values• State and calculate values to appropriate numbers of significant digits 2
3. 3. Quantitative & Qualitative Data Quantitative • Can be measured, using numbers and units • Mathematical relationships used in analysis and conclusions Qualitative • Observational, not numbers • Colour, smell, texture, observed events 3
4. 4. There’s no such word as ‘amount’ Digital balance Mass (g) solids “Amount” Volume (ml) fluids Concentration 4
5. 5. There’s no such word as ‘amount’ Matter is anything that has mass and volume (takes up space): We measure mass in kilograms (kg), or grams (g). We measure volume in litres (l) or millilitres (ml) (or cm3). But we also describe other quantities: • Time in seconds (s) • Length or distance in metres (m) • Energy in joules (J) or kilojoules (kJ) • Heat/temperature in degrees Celcius (oC) (the SI* unit is Kelvin, K) • Quantity of a substance in moles (mol) • Concentration of a solution in moles per litre (M) • Acidity or alkalinity in pH (0 is a strong acid, 7 is neutral, 14 a strong base) • Electrical conductivity in Siemens (S) 5
6. 6. Chemistry Lab Manual Criterion B: Communication in ScienceWork in groups to practice using the lab By the end of the lesson, make sure you haveequipment correctly and safely. completed these tasks: • Measuring volumeThink about the units and uncertainties • Measuring massof each piece of equipment. • Measuring temperature • Measuring pH • Measuring conductivityYou will also learn about: • Bunsen driving test• Accuracy vs precision• Random vs systematic error If you are waiting for a set or are finished,• Significant digits there are plenty of questions to work on!• Scientific notationCompleted Lab manuals are self-assessed,and handed in at the end of the class. 6
7. 7. Chemistry Lab Manual Criterion B: Communication in Science
8. 8. UncertaintiesAll measurements have uncertainties – a range of values in which the truemeasurement could lie. More precise measuring tools have a smaller degree ofuncertainty.In Science it is important for us to estimate and note the uncertainty in themeasurements that we record. Look at this example measurement: Known Estimated This measurement could be 1.23449 or 1.234 1.2335. Both would get rounded to 1.234. g (±0.001) Therefore with this digital measurement there is an uncertainty of ±0.001. Three decimal places (precision) Uncertainty is ± 1 of the smallest division. Remember the SI units!
9. 9. 36.0ml ± 0.5ml44ml ± 1ml 7.4ml ± 0.1ml 9
10. 10. Uncertainty Measuring equipment that presents more decimal places usually has a lower uncertainty. Uncertainty = ± 0.01g Uncertainty = ± 1g
11. 11. Precision vs Accuracy • Accuracy describes how correct – how close to the true answer – the results are. • Precision describes how repeatable they are. Results A Results B Results C Accuracy Low Precision High Generally, measuring tools with a greater degree of precision have smaller divisions (more decimal places).Image source: Bishop, M. Precision vs Accuracy (Fig 1.12). From Preparatory Chemistry (ebook) via http://preparatorychemistry.com/Bishop_Book_1_eBook.pdf
12. 12. Systematic Error vs Random Error • Systematic errors are repeated in the same way throughout an investigation, such as using a balance incorrectly in the same way for each measurement. This can be corrected. Precision describes how repeatable they are. • Random error cannot easily be corrected as it affects measurements differently. Results A Results B Results C Systematic error None No Random Error No NoneImage source: Bishop, M. Precision vs Accuracy (Fig 1.12). From Preparatory Chemistry (ebook) via http://preparatorychemistry.com/Bishop_Book_1_eBook.pdf
13. 13. What type of error? MrT did not calibrate (set up) the pH probe properly, so every reading was pH 0.5 too high.Something was left on the digital balance for everyrecording, so the results were always too high.
14. 14. Accuracy, Precision and Error • Accuracy describes how correct – how close to the true answer – the results are. • Precision describes how repeatable they are. • Systematic errors are repeated in the same way throughout an investigation, such as using a balance incorrectly in the same way for each measurement. This can be corrected. Precision describes how repeatable they are. • Random error cannot easily be corrected as it affects measurements differently. Results A Results B Results C Accuracy Low High Low Precision High High Low Systematic error High None No Random Error No None HighImage source: Bishop, M. Precision vs Accuracy (Fig 1.12). From Preparatory Chemistry (ebook) via http://preparatorychemistry.com/Bishop_Book_1_eBook.pdf
15. 15. Significant Digits Use this online tutorial from Norton Chemistry to learn about significant digits (figures) and how to use them appropriately in your calculations. http://media.wwnorton.com/college/chemistry/chemtours/interfa ce.asp?chapter=chapter_01&folder=significant_figures How many sig. digs? Number # sig. digits Record the following numbers to 3 sig. digits: 12420 = 53 0.03209 = 5.03 4050.0 = 01.67 0.0101010 = 1.067 Practice calculations with significant digits: 100 • 2.01 - 1.0 = 1000.0 • 123 + 456.789 = • 1.2 x 3.45 = 0.003450 • 34.678 /3.33 =
16. 16. The Sig Fig SongSignificant Digits (AKA Significant Figures)When we write measurements or the results ofcalculations in Science, we need to use the correctnumber of significant digits. This tells us theacceptable level of precision in our measurements.Significant Digits are: • All non-zero digits • All zeroes in-between non-zeroes • All digits after a decimal place http://www.youtube.com/watch?v=ZuVPkBb-z2ILeading zeroes don’t count: Try these numbers: • Count from the left • 123.45 • SigDigs start at the first non-zero • 123000Trailing zeroes in numbers > 1 don’t count: • 1.008 • Unless there is a line over one of them • 01.67 • This shows that it is known, not an • 1000 estimate. • 1000 • 1000.0
17. 17. The Sig Fig SongSignificant Digits (AKA Significant Figures)When we write measurements or the results ofcalculations in Science, we need to use the correctnumber of significant digits. This tells us theacceptable level of precision in our measurements.Significant Digits are: • All non-zero digits • All zeroes in-between non-zeroes • All digits after a decimal place http://www.youtube.com/watch?v=ZuVPkBb-z2ILeading zeroes don’t count: Try these numbers: • Count from the left • 123.45 has 5 SigDigs • SigDigs start at the first non-zero • 123000 has 3 SigDigsTrailing zeroes in numbers > 1 don’t count: • 1.008 has 4 SigDigs • Unless there is a line over one of them • 01.67 has 3 SigDigs • This shows that it is known, not an • 1000 has 1 SigDig estimate. • 1000 has 3 SigDigs • 1000.0 has 5 SigDigs
18. 18. Significant Digits Practice Use the periodic table to write your name as closely as possible. e.g. Ra C He Lu Challenge 1 The wall chart periodic table presents many decimal places. Convert each one to 3 significant digits: Ra = 226 C = 12.011  12.0 He = 4.0062  4.01 Lu = 174.967  175How does this periodic table compare to the IB periodic table?Have the IB presented their table based on sigdigs or decimal places?
19. 19. The Sig Fig Song 2: CalculationsCalculating with SigDigsCalculations will often result in too many decimalplaces or digits in an answer. We need to useappropriate rounding and present our answers tothe correct number of SigDigs.Rule number 1:Carry out all the calculations first and round 6.6the final answer – do not round the numbersas you go, it could mess up the result. http://www.youtube.com/watch?v=kB2szfcwu1AAdding and Subtracting• Identify the measurement with the smallest number of decimal places  this is the number of d.p. to use in the final answer. 2.01 – 1.0 =Multiplying and Dividing• Identify the measurement with the smallest number of SigDigs  this is the number of SigDigs to use in the final answer. 1.2 x 3.45 =
20. 20. The Sig Fig Song 2: CalculationsCalculating with SigDigsCalculations will often result in too many decimalplaces or digits in an answer. We need to useappropriate rounding and present our answers tothe correct number of SigDigs.Rule number 1:Carry out all the calculations first and round 6.6the final answer – do not round the numbersas you go, it could mess up the result. http://www.youtube.com/watch?v=kB2szfcwu1AAdding and Subtracting• Identify the measurement with the smallest number of decimal places  this is the number of d.p. to use in the final answer. 2.01 – 1.0 = 1.01, round to 1.0 1d.p.Multiplying and Dividing• Identify the measurement with the smallest number of SigDigs  this is the number of SigDigs to use in the final answer. 1.2 x 3.45 = 4.14 round to 4.1 2sf.
21. 21. Significant Digits are: • All non-zero digits • All zeroes in-between non-zeroes • All digits after a decimal placeLeading zeroes don’t count: Trailing zeroes in numbers > 1 don’t count: • Count from the left • Unless there is a line over one of them • SigDigs start at the first non-zero • This shows that it is known, not an estimate. Adding and Subtracting • Identify the measurement with the smallest number of decimal places  this is the number of d.p. to use in the final answer. 2.01 – 1.0 = 1.01, round to 1.0 1d.p. Multiplying and Dividing Rule number 1: • Identify the measurement with the smallest number of Carry out all the calculations first SigDigs  this is the number of SigDigs to use in the and round the final answer – do not round the numbers as you final answer. go, it could mess up the result. 1.2 x 3.45 = 4.14 round to 4.1 2sf.
22. 22. When it gets more complicated…(5.00 / 1.235) + 3.000 + (6.35 / 4.0) = 8.630829... = 8.6Try these out: smallest number of SigDigs 1. Complete the calculation 2. Identify the value with the fewest sigdigs 3. Round & present the answer to that many sigdigs 1. (12.67 - 2.2) x 89.00 / 33.1 = = 1. ( 14.2 + 23.00 + 4.566 + 20.00) = ( 12.1 - 1.22) =Tutorial: http://www.chem.sc.edu/faculty/morgan/resources/sigfigs/sigfigs7.html
23. 23. When it gets more complicated…(5.00 / 1.235) + 3.000 + (6.35 / 4.0) = 8.630829... = 8.6Try these out: smallest number of SigDigs 1. Complete the calculation 2. Identify the value with the fewest sigdigs 3. Round & present the answer to that many sigdigs 1. (12.67 - 2.2) x 89.00 / 33.1 = 28.1519637462 = 28 1. ( 14.2 + 23.00 + 4.566 + 20.00) = 5.6770220588 ( 12.1 - 1.22) = 5.68Tutorial: http://www.chem.sc.edu/faculty/morgan/resources/sigfigs/sigfigs7.html
24. 24. Scientific Notation How can we write very small or very large numbers in a clear manner? 3450000000000 = 0.0000000000345 = ? ? 3.45 x 10 3.45 x 10 Always one digit before the decimal in scientific notationExpand the following notations:1.0 X 103 =1.0 X 10-6 =4.56 X 105 =7.01 X 10-4 =Record the following in scientificnotation to 3 significant digits:• 12340000 =• 00012340 =• 10101010 = http://media.wwnorton.com/college/chemistry/chemtours/interface.asp?chapter=chapter_01&folder=scientific_notation
25. 25. Scientific Notation How can we write very small or very large numbers in a clear manner? 3450000000000 = 0.0000000000345 = 12 -11 3.45 x 10 3.45 x 10 Always one digit before the decimal in scientific notation 3 SigDigsExpand the following notations:1.0 X 103 =1.0 X 10-6 =4.56 X 105 =7.01 X 10-4 =Record the following in scientificnotation to 3 significant digits:• 12340000 =• 00012340 =• 10101010 = http://media.wwnorton.com/college/chemistry/chemtours/interface.asp?chapter=chapter_01&folder=scientific_notation
26. 26. Scientific Notation & Significant Figures Compare the following measurements: 3.04 x 104 kJ 3.040 x 104 kJ 3.0400 x 104 kJWrite them out in full. Which is larger?Which is written to the greatest number of significant figures?Which was recorded using equipment with the least uncertainty?
27. 27. Scientific Notation & Significant Digits Compare the following measurements: 3.04 x 104 kJ 3.040 x 104 kJ 3.0400 x 104 kJ 3 SigDigs 4 SigDigs 5 SigDigs12340000 to 3 sigdigs could be 12300000 or 1.23 x 107Present these numbers to 3 sigdigs and in scientific notation.1. 00.0101010101012. 12.34567Calculate the following, presenting the answer to the most appropriate sigdigs & notation:1. 1000 x 3.42. 8.0 x 8.03. 8 x 8
28. 28. How do we learn? and why do we need to practice? Working Memory Long-term Memory Storage… Perception Filter Interpreting Events Rearranging sometimes Observation Comparing branched, s sometimes as Storage Instructions separate Preparation fragments Feedback loop for perception filter So… • Review, ask questions, practice • Come back to it later, has it stuck? • Think about measurement and error in all your lab workFrom “Cultured Pearls of Tasty Truffles: Teaching chemistry for the 21st Century”, by Bill Byers 28http://www3.ul.ie/~childsp/CinA/Issue66/TOC20_truffles.htm
29. 29. For more resources. Please consider a donation to charity via Biology4Good. Click here for more information about Biology4Good charity donations.This is a Creative Commons presentation. It may be linked and embedded but not sold or re-hosted.