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Unit 7

Unit 7. PRECISION, ACCURACY, AND TOLERANCE. MEASUREMENT. All measurements are approximations Degree of precision of a measurement number depends on number of decimal places used Number becomes more precise as number of decimal places increases

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Unit 7

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  1. Unit 7 PRECISION, ACCURACY, AND TOLERANCE

  2. MEASUREMENT • All measurements are approximations • Degree of precision of a measurement number depends on number of decimal places used • Number becomes more precise as number of decimal places increases • Measurement 2.3 inches is precise to nearest tenth (0.1) inch • Measurement 2.34 inches is precise to nearest hundredth (0.01) inch

  3. RANGE OF A MEASUREMENT • Range of a measurement includes all values represented by the number • Range of the measurement 4 inches includes all numbers equal to or greater than 3.5 inches and less than 4.5 inches • Range of the measurement 2.00 inches includes all numbers equal to or greater than 1.995 inches and less than 2.005 inches

  4. ADDING AND SUBTRACTING • Sum or difference cannot be more precise than least precise measurement number used in computations • Add 7.26 + 8.0 + 1.253. Round answer to degree of precision of least precise number 7.26 + 8.0 1.253 16.513 • Since 8.0 is least precise measurement, round answer to 1 decimal place • 16.513 rounded to 1 decimal place = 16.5Ans

  5. SIGNIFICANT DIGITS • Rules for determining the number of significant digits in a given measurement: • All nonzero digits are significant • Zeros between nonzero digits are significant • Final zeros in a decimal or mixed decimal are significant • Zeros used as place holders are not significant unless identified as such by tagging (putting a bar directly above it) • Zeros are the only problem then…..usually if the zero disappears in scientific notation then it is not significant.

  6. SIGNIFICANT DIGITS • Examples: • 3.905 has 4 significant digits (all digits are significant) • 0.005 has 1 significant digit (only 5 is significant) • 0.0030 has 2 significant digits (only 3 and last 0 are significant) • 32,000 has 2 significant digits (only 3 and 2, the zeros are considered placeholders)

  7. ACCURACY • Determined by number of significant digits in a measurement. • The greater the number of significant digits, the more accurate the number • Product or quotient cannot be more accurate than least accurate measurement used in computations

  8. ACCURACY • Determined by number of significant digits in a measurement. The greater the number of significant digits, the more accurate the number • Number 0.5674 is accurate to 4 significant digits • Number 600,000 is accurate to 1 significant digit • 7.3 × 1.28 = 9.344, but since least accurate number is 7.3, answer must be rounded to 2 significant digits, or 9.3 Ans • 15.7  3.2 = 4.90625, but since least accurate number is 3.2, answer must be rounded to 2 significant digits, or 4.9 Ans

  9. ABSOLUTE AND RELATIVE ERROR • Absolute error = True Value – Measured Value or, if measured value is larger: • Absolute error = Measured Value – True Value

  10. ABSOLUTE AND RELATIVE ERROR EXAMPLE • If the true (actual) value of a shaft diameter is 1.605 inches and the shaft is measured and found to be 1.603 inches, determine both the absolute and relative error • Absolute error = True value – measured value = 1.605 – 1.603 = 0.002 inchAns = 0.1246%Ans

  11. TOLERANCE • Basic Dimension – wanted measurement • Amount of variation permitted for a given length • Difference between maximum and minimum limits of a given length • Find the tolerance given that the maximum permitted length of a tapered shaft is 143.2 inches and the minimum permitted length is 142.8 inches Total Tolerance = maximum limit – minimum limit = 143.2 inches – 142.8 inches =0.4 inchAns

  12. TOLERANCE • Unilateral • Tolerance in one direction • Example: Door, piston, tire to wheel well on your car • Bilateral • Tolerance in two directions • Example: cuts and pilot holes • Total tolerance refers to the amount of tolerance allowed. • Unilateral is all in one direction from Basic Dimension • Bilateral is divided (does not have to be evenly divided always)

  13. TOLERANCE • The basic dimension on a project is 3.75 inches and you have a bilateral tolerance of ±0.15 inches. What are your max and min measurement? • 3.60 to 3.80 inches are allowable. • The total tolerance for a job is 0.5 cm. The basic dimension is 22.45 cm and you are told it is an equal, bilateral tolerance. What are your max and min limits? • 22.20cm to 22.70cm

  14. PRACTICE PROBLEMS • Determine the degree of precision and the range for each of the following measurements: a. 8.02 mm b. 4.600 in c. 3.0 cm • Perform the indicated operations. Round your answers to the degree of precision of the least precise number a. 37.691 in + 14.2 in + 3.87 in b. 2.83 mi + 7.961 mi – 5.7694 mi c. 15 lb – 7.6 lb + 6.592 lb

  15. PRACTICE PROBLEMS (Cont) • Determine the number of significant digits for the following measurements: a. 0.00476 b. 72.020 c. 14,700 • Perform the indicated operations. Round your answers to the same number of significant digits as the least accurate number a. 42.15 mi × 0.0234 b. 16.40  0.224 × 0.0027 c. 4.007555  1.050 × 12.763

  16. PRACTICE PROBLEMS (Cont) • Complete the table below:

  17. PRACTICE PROBLEMS (Cont) • Complete the following table:

  18. PRACTICE PROBLEMS (Cont) • What is the basic dimension of a washer that has total tolerance of 0.3 mm with unilateral tolerance and the max limit is 12.75 mm? • What is the basic dimension if you have an equal bilateral tolerance that has a max limit of 3.5 inches and a min limit of 3.25 inches?

  19. PROBLEM ANSWER KEY • a. 0.01 mm; equal to or greater than 8.015 and less than 8.025 mm b. 0.001 in; equal to or greater than 4.5995 and less than 4.6005 in c. 0.1 cm; equal to or greater than 2.95 and less than 3.05 cm • a. 55.8 in b. 5.02 mi c. 14 lb • a. 3 b. 5 c. 3 • a. .986 mi b. .20 c. 48.71 • a. 0.001 lb; 0.02% b. 1 in; 5.882% c. 0.03 mm; 0.178% • a. 1/8 in b. 0.05 cm c. 1/8 mm

  20. PROBLEM ANSWER KEY • 12.45 mm • 3.375 inches

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