2. Measurement and Science He has it down to an exact science…… What the heck does that mean? Science is not about being for sure. Science is about exploring options and always being open to other interpretations. There is no such thing as an exact science! There is only one thing for certain in science  Nothing is for certain!

3. Science cannot exist without quantifiable comparisons: He is tall--- compared to who or what? He is 7 ft in height-- quantifiable Tall, short, fat, skinny, long, short, hot, cold……. …. These are relative terms and not quantities! Comparisons are meaningless in science unless compared to a standard value. And those standard values need to be the same for everyone in order to be widely useful!

4. Fundamental Units of Measure -directly comparable to a standard These are the only units used in Mechanics

5. Fundamental Standards for Units in Mechanics meter (m)  now based on wavelengths of light kilogram (kg)  still a non-reproducible standard- chunk of metal in France second (s)  based upon vibrations of a Cesium atom all other units in Mechanics are combinations (derived) of these three fundamental values!

6. Derived Units - derived from fundamental units  Velocity (m/s)- meter/second  Acceleration (m/s 2 )- meter per second squared  Force (N)- Newton  Energy (J)- Joule  Power (w)- Watt

7. In making measurements, it is important to have a standard for comparison, and to make those measurements with as much precision as possible. 2030 Definitely more than 20 and less than 30 units! 23, 24, 25? Definitely more than 24 and less than 25! 24.2 units, 24.3?Either reading is considered correct.

8. 2030 To call this measurement 20 units would be poor when it is obviously more! To call this measurement 30 units would be equally lousy because it is obviously less! 24 or 25 would be a better effort and be considered more accurate, even though they contain estimated values. There is no such thing as an exact measurement-- All measurements are inherently estimates!

9. All measurements contain some degree of uncertainty depending upon the device. An accurate measurement will contain all the known values of the measurement plus one (and only one) estimated value. Why only one? More than one estimated value becomes wild guesses and have no meaning. An estimate is not a guess-- it is an attempt to approximate and make a reading more precise. All known values of a measurement plus one estimate are called significant figures (digits).

10. Significant Figures/Digits  A method of maintaining accuracy and precision in measurements and calculations.  All known values of a measurement or calculation PLUS one and only one estimated value.  In measurements, SD are totally determined by the device being used.  In calculations, SD in the answer are determined by a basic rule

11. In a given value, what is a SD? All non-zero numbers are SD’s: 12.35cm (4) 4.26 m (3) Zeros between other SD count: 102 s (3) 5.007 (4) Zeros ending decimals count: 12.30 (4).3400 (4) Zeros marked with a bar count: 100 (3) 12,000 (4)

12. When is 0 not a SD? When it merely shows where the decimal is: ending whole numbers (with no bar) 12,000 m (2) 305,000 m (3) starting a pure decimal.0035 cm (2) 0.000240 km (3) part of the magnitude of scientific notation 3.50 X 10 5 J (3)

13. In calculations, only measured (or values calculated from measurements) count for SD! The following would have no SD:  the accepted value used in finding experimental error and deviation  standard/accepted values such as the acceleration due to gravity  constant, non-measured values, such as Newton’s Universal Gravitational Constant, Pi (π), etc.  Counted values

14. 125.6 m x 2.7 m General Rules for Calculating in SD: Find the area in SD: 8 7 9 2 2 5 1 2 0 3 3 9. 1 2 Estimated Values You might assume the answer to be 339.1 m 2 because it is a tenth times a tenth In SD, only one estimated value is kept!! Therefore, the correct, precise and accurate answer is: 340 m 2

15. Rule for Calculating in SD In a calculation done in SD, the answer can never be more precise than the least precise part of the problem!

16. Rules for Adding and Subtracting in SD  Your answer will have its last SD in the same decimal place as the least precise part of the problem! 11.2 cm + 8.66 cm + 2.345 cm = last SD in the tenths column 45.3578 L - 23.26 L = last SD in the hundredths column

17. Rules for Multiplying and Dividing in SD Keep the same number of SD in your answer as the smallest (# SD) part of your problem! (12.6 cm)(11.22 cm)(5.8 cm) = [3SD][4SD][2SD]  2 SD in your answer (55.6g) (11.34cm)(18.345cm)(3.4cm)= 2 SD in your answer

18. 1) 400 2) 200.0 3) 0.00014) 218 5) 320 6) 0.00530 7) 22 568 8) 4755.50 How many significant figures in the following measurements: Complete these addition problems. a)6.201 cm + 7.4 cm + 0.68 cm + 12.0 cm = b)1884 kg + 0.94 kg + 1.0 kg + 9.778 kg = c) 16. 156 g + 28.2 g + 0.0058 g + 9.44 g =

19. Complete these subtraction problems. a)10.8 g – 8.264 g = b)2104.1 m – 463.09 m = c) 16.50 mL – 8.0 mL = Complete these multiplication problems. a)10.19 m x 0.013 m = b)3.2145 km x 4.23 km = c)(7.50 x 10 6 m)(2.2 x 10 -3 m) =

20. Complete these division problems. a) 80.23 m 2.4 s b) 4.301 kg 1.9 cm 3 6.6 x 10 8 m 2.31 x 10 -2 s

21. Accuracy and Precision in Labwork Bad accuracy, good precision Better accuracy, poor precision Bad accuracy and precision Good and good

22. Accuracy and Precision øA way of indicating the the degree of uncertainty in measurements

23. Accuracy  Error Refers to how close a measured value comes to the accepted value for a quantity Absolute error- actual difference E a = |O - A| O  Observed in lab (data) A  Accepted answer Relative Error- comparative miss E r = E a /A 100%

24. Precision  Deviation Refers to how well several measurements agree with each other- about the same average answer each trial Absolute Deviation- difference each trial is from the average answer D a = |O - M| M  mean (average of data) Relative Deviation- percentage D r = D a (average)/M  100%  Only 1 value for D r ! 

25. A student performs a lab in which he tries to find the acceleration due to gravity. His data produces the following values: 9.5 m/s 2, 8.9 m/s 2, 9.9 m/s 2, and 9.1 m/s 2. Find his accuracy and his precision if the accepted value is 9.8 m/s 2. E a = |O - A| = | 9.5 - 9.8 |m/s 2 =.3 m/s 2 = | 8.9 - 9.8 | m/s 2 =.9 m/s 2 = | 9.9 - 9.8 | m/s 2 =.1 m/s 2 = | 9.1 - 9.8 | m/s 2 =.7 m/s 2 E r = E a /A x 100 =.3/9.8 x 100 = 3% =.9/9.8 x 100 = 9% =.1/9.8 x 100 = 1% =.7/9.8 x 100 = 7%

26. M = (9.5 + 8.9 + 9.9 + 9.1) m/s 2 4 = 9.4 m/s 2 D a = |O - M| = |9.5 - 9.4| =.1 m/s 2 D a = |O - M| = |8.9 - 9.4| =.5 m/s 2 D a = |O - M| = |9.9 - 9.4| =.5 m/s 2 D a = |O - M| = |9.1 - 9.4| =.3 m/s 2 Avg. D a = (.1+.5+.5+.3)m/s 2 4 =.4 m/s 2 D r = Avg D a X 100 M =.4 / 9.4 X 100 = 4%

27. Find the accuracy and precision of the following lab done to find the density of a sample of lead (accepted D = 11.6 g/cm 3 ): Trial 1: 12.3 g/cm 3 Trial 2: 11.0 g/cm 3 Trial 3: 10.4 g/cm 3 Trial 4: 12.8 g/cm 3 Trial 5: 13.1 g/cm 3