PRECISION, ACCURACY, AND TOLERANCE 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 Measurement 2.3 inches is precise to nearest tenth (0.1) inch Measurement 2.34 inches is precise to nearest hundredth (0.01) inch

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

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 = 16.5 Ans

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.

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)

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

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

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

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 inch Ans = 0.1246% Ans

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 inch Ans

TOLERANCE Unilateral Bilateral 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)

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

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

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

PRACTICE PROBLEMS (Cont) Complete the table below: Actual or True Value Measured Value Absolute Error Relative a. 4.983 lb. 4.984 lb. b. 17 in. 16 in. c. 16.87 mm 16.84 mm

PRACTICE PROBLEMS (Cont) Complete the following table: Maximum Limit Minimum Tolerance a. 4 7/16 in 4 5/16 in b. 14.83 cm 14.78 cm c. 5 5/32 mm 5 1/32 mm

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?

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

PROBLEM ANSWER KEY 12.45 mm 3.375 inches