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Estimation, Accuracy, Precision, and Significant Figures in Engineering

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This lecture explores fundamental concepts in engineering, focusing on estimation, accuracy, and precision, along with the importance of significant figures. Students will learn how to make rough calculations under uncertain conditions and the distinction between accurate and precise measurements. Various exercises will help enhance problem-solving skills, such as calculating the volume of a box, determining material density, and using measurements to estimate tiles needed for a wall. Understanding these concepts is crucial for engineers to make informed decisions based on numerical data.

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Estimation, Accuracy, Precision, and Significant Figures in Engineering

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  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.

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