ENGR 107 – Introduction to Engineering

1. Estimation, Accuracy and Precision, and Significant Figures (Lecture #3) ENGR 107 – Introduction to Engineering ENGR 107 - Introduction to Engineering

2. ENGR 107 - Introduction to Engineering Estimation

3. A rough calculation, often using incomplete or uncertain data, that is still close enough to be useful. Definition courtesy of Wikipedia Synonym: approximation Estimation ENGR 107 - Introduction to Engineering

4. ENGR 107 - Introduction to Engineering Estimation • Estimations are used when • Insufficient information is available • Available information is uncertain • Problem is too difficult to solve analytically • Problem is impossible to solve using available analysis tools. • Estimations are used when • An inexact result is useful • A range (i.e. upper and lower bounds) is useful

5. Exercise: Calculate the volume of a box to the nearest cubic meter. The dimensions of the box are: W = 3.75 m L = 1.675 m H = 2.35 m Estimation ENGR 107 - Introduction to Engineering

6. Exercise: Calculate the density of a material to the nearest kg / m3. The mass and volume of the material are: Mass = 489.54 kg Volume = 7.5 m3 Estimation ENGR 107 - Introduction to Engineering

7. Exercise: Determine the number of tiles, to the nearest integer number, needed to tile a wall. Dimensions of the tile: 4.5 in. x 4.5 in. Dimensions of the wall: 7.5 ft. x 11 ft. Estimation ENGR 107 - Introduction to Engineering

8. Calculate the volume of the classroom, using your height as a “measuring stick”. Estimation ENGR 107 - Introduction to Engineering

9. ENGR 107 - Introduction to Engineering Accuracy and Precision

10. In measurements, accuracy and precision have different meanings and cannot be used interchangeably. Accuracy and Precision ENGR 107 - Introduction to Engineering

11. The degree of closeness of a measurement to the actual or true value. Definition courtesy of Wikipedia Accuracy ENGR 107 - Introduction to Engineering

12. The degree to which repeated measurements under unchanged conditions show the same results. Definition courtesy of Wikipedia Also called reproducibility or repeatability. Precision ENGR 107 - Introduction to Engineering

13. Accurate Accuracy vs Precision ENGR 107 - Introduction to Engineering

14. Precise Accuracy vs Precision ENGR 107 - Introduction to Engineering

15. Accurate and Precise Accuracy vs Precision ENGR 107 - Introduction to Engineering

16. ENGR 107 - Introduction to Engineering Accuracy vs Precision

17. ENGR 107 - Introduction to Engineering Measurements

18. ENGR 107 - Introduction to Engineering Measurements • Engineers must be able to measure physical quantities and express these measurements in numerical form. • Engineers must have confidence that the measurements and subsequent calculations and decisions made based on the measurements are reasonable.

19. ENGR 107 - Introduction to Engineering Measurements • Any physical measurement that is not a countable number will be approximate. • Errors are likely to be present regardless of the precautions used when making the measurements. • Significant digits are used to express, numerically, the accuracy of a measurement.

20. ENGR 107 - Introduction to Engineering Measurement Estimation • There is a finite accuracy to which every engineering measurement can be made. • There is a limited number of significant digits that can be included in the numerical representation of a measurement. • The engineer must estimate the measurement between the smallest graduations on the instrument.

21. ENGR 107 - Introduction to Engineering Measurement Estimation

22. ENGR 107 - Introduction to Engineering Errors

23. ENGR 107 - Introduction to Engineering Errors • Systematic • A bias in the measurement leading to the mean of a set of measurements differing significantly from the expected value. • Can be identified and eliminated • Random • An error in the measurement leading to inconsistent values for repeated measurements of the same attribute. • Caused by unpredictable fluctuations in the readings of the measurement equipment, in the environment, etc. • Cannot be eliminated

24. ENGR 107 - Introduction to Engineering Significant Digits

25. ENGR 107 - Introduction to Engineering Numerical Values • For numbers less than one, a zero is written in front of the decimal point. • A space, not a comma, is used to divide numbers of three orders of magnitude or more. • For very large or very small numbers, use scientific notation to reduce the unwieldy nature of these numbers.

26. A significant digit, or significant figure, is defined as any digit used in writing a number, except those zeros that are used only for location of the decimal point or those zeros that do not have any nonzero digit to their left. Significant Digits ENGR 107 - Introduction to Engineering

27. ENGR 107 - Introduction to Engineering Significant Digits • Numbers 10 or larger that are not written in scientific notation and that are not counts (exact values) can cause difficulties in interpretation when zeros are present. • If uncertainty results from using standard decimal notation, use scientific notation so that the reader will clearly understand your intent.

28. ENGR 107 - Introduction to Engineering Significant Digits

29. Rounding: Increase the last digit retained by 1 if the first digit dropped is greater than 5. Significant Digits ENGR 107 - Introduction to Engineering

30. Multiplication and Division: The product or quotient should contain the same number of significant digits as the number with the fewest significant digits. Significant Digits ENGR 107 - Introduction to Engineering

31. Addition and Subtraction: The sum or difference should include significant digits only as far to the right as in the least precise number. Significant Digits ENGR 107 - Introduction to Engineering

32. ENGR 107 - Introduction to Engineering Arithmetic and Significant Digits • In calculator or computer applications it is not practical to perform intermediate rounding (i.e. between arithmetic operations). • It is normal practice to perform the entire calculation and then report a reasonable number of significant figures. • The number of significant digits in the result cannot exceed that in the value with the fewest significant digits. • The result cannot be more precise than any of the values included in the calculation.