Target for today

1. Target for today Be able to: define uncertainty, accuracy, precision, error, magnitude of error. calculate magnitude of error and % error. determine the number of sig. figs. in a measurement. re-write a measurement to a certain number of s.f. use the correct number of s.f. when doing math.

2. Sig. Figs. It’s 5007 years old! (Exactly)

3. Basic Principles: Every measurement has some ‘uncertainty’ built in. The last digit only is uncertain. “A chain is no stronger than its weakest link.” A combination of measurements is no more accurate than the least accurate measurement.

4. Accuracy – how close to the “true” value a measurement (or the mean of a set of measurements) is. Measured as a % of the true value. Low accuracy means that you made a mistake, or the measurements contain error.

5. Precision – how closely grouped a set of measurements is one-to-another. Precision is shown through the standard deviation of the measurements. Good precision, poor accuracy Low precision, good accuracy

6. Mistakes – something you do incorrectly: Oops – I skipped step 5. Oops – I measured out 25 mLs of water but wrote down 50 mLs. Oops – I mis-read the thermometer!

7. Mistakes can be re-done or corrected, but error is built in to the measuring equipment. Error can only be eliminated by using better equipment. Error is defined as the inherent degree of inaccuracy of a piece of equipment used to make a measurement.

8. Estimating which equipment contributes the most to the overall error: A balance can be read to the nearest 0.01 gram. The last digit is uncertain. If we weigh a test tube and it weighs 12.73 g, the balance gives us a magnitude of error of 0.01 g / 12.73 g x 100 = 0.08% If we measure 100 mLs of water in a graduated cylinder that’s marked every 1 mL, the magnitude of error is 1 mL / 100 mLs x 100 = 1%

9. Magnitude of error = (readability / measurement) x 100 The readability of a piece of equipment is how it’s marked: Ordinary lab balance: 0.01 grams High-precision balance: 0.0001 grams Thermometer: 0.1oC

10. small graduated cylinder: 0.1 mLs • medium grad. cylinder: 1 mL • largest grad. cylinder: 10 mLs • beaker: 10 mLs, 25 mLs, 50 mLs (depends on • size of the beaker) • buret: 0.01 mLs

11. A medium graduated cylinder is used to measure out 20 mLs of water. What is the magnitude of error of this measurement? • (1 mL / 20 mLs) x 100 = 5% A stopwatch is accurate to the nearest 0.01 s. If a receiver runs 40 yards in 6.51 seconds, what is the magnitude of error of the time measurement? (0.01 x / 6.52 s) x 100 = 0.2%

12. After each lab, you will calculate how close to the true value your experimental result was. This is your % error. This single number incorporates all the measurements errors into one. % error = │1 – (experimental result / true)│ x 100

13. A student does a lab to measure the density of copper (Cu). She determines a density of 9.04 g/cm3, but the true density is 8.94 g/cm3. How far off is she? │ 1 – (9.04 / 8.94) │ x 100 = 1.12% error (She earns an A!)

14. Formative Assessment time! Take out half a sheet of paper and solve this problem: A thermometer reads 58.3oC in water that is actually 60.0oC. What is the % error of the measurement?

15. Target for today Be able to: define uncertainty, accuracy, precision, error, magnitude of error. calculate magnitude of error and % error. determine the number of sig. figs. in a measurement. re-write a measurement to a certain number of s.f. use the correct number of s.f. when doing math.

16. Significant Figures Showing the proper level of accuracy or “confidence” in results.

17. How many days are there in a century? • 7 days/week x 4 weeks/month x 12 months/year x 100 yrs/century = • 12 months/year x 30 days/month x 100 yrs/century = • 7 days/week x 52 weeks/yr x 100 yrs/century = • 365 days/year x 100 yrs/century = • 365.24 days/year x 100 yrs/century = 33,600 days 36,000 days 36,400 days 36,500 days 36,524 days

18. Any non-0 digit is always significant, i.e. an actual part of the measurement. • 12,345 g has 5 s.f. and 789 g has 3 s.f.

19. Zero’s trapped between non-0 digits are significant. • 102 has 3 s.f.

20. Zero’s to the right of the decimal pt. after non-0 digits are significant. • 128.0 mg has 4 s.f. • That final “0” tell us that the measurement • was made with an accuracy of 0.1 mg

21. A “0” by itself to the left of the decimal pt. is not significant (just a place holder) • 0.23 g has 2 sf. • 0’s to the right of a decimal, but in front of non-0 digits are also just place holders (not significant - not a part of the measurement: • 0.0023 g has 2 s.f. also

22. Without a decimal pt., zeros to the right are not significant. • 1000 has 1 s.f. • With a decimal point, however, they become significant. • Write it as 1000. to have 4 s.f., or 1.000 x 103 for 4 s.f. also

23. Exact numbers arise from counting something (7 days/week) or from a definition (1 in = 2.54 cm exactly). These have an unlimited number of sig. figs. • Conversion factors that come from definitions also have unlimited s.f.

24. P resent bsent A

25. How many s.f. are in 3002 mg? 0.00301 sec 1.204 x 103 kg 0.00007 Joules 0.0102050 moles

26. Rewrite… 13 grams to have 4 s.f. 0.04200 mol to have 5 s.f. $52,238 to have 1 s.f. 0.0035229 sec to have 2 s.f. Never change the basic value, only the s.f. 13.00 g 0.042000 mol $50,000 0.0035 sec

27. Doing Math with Sig. Figs. When a measurement with high accuracy (many s.f.) is combined with a low-accuracy measurement (few s.f.), the result can’t be any more accurate than the least-accurate measurement. We shouldn’t try to make the result seem more accurate than it really is.

28. + and - • The result can’t have more digits to the right of the decimal than the measurement w/ the fewest number of digits: 100.2 98.65 10.35 -33.2877 12.655+72 123.2 137

29. x & / • The result can’t have more sig.figs. than the measurement with the fewest s.f. 28.300 x 12.887 x 0.12 = 44

30. Finding the Mean Average: Add the results, keeping the correct sig. figs. for addition rules. Then divide by the number of results (unlimited sig. figs.) Find the mean of 12.35, 12.04, 11.58 Sum is 35.97. Then divide by 3. Result is 11.99