1. PRECISION, ACCURACY, AND TOLERANCE
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 inches and less than inches

4. ADDING AND SUBTRACTING
Sum or difference cannot be more precise than least precise measurement number used in computations
Add 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
rounded to 1 decimal place = 16.5 Ans

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)
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 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 = , 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 inches and the shaft is measured and found to be inches, determine both the absolute and relative error
Absolute error = True value – measured value
= – = inch Ans
= % 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 inches and the minimum permitted length is inches
Total Tolerance = maximum limit – minimum limit
= inches – inches
= 0.4 inch Ans

12. 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)

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 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 mm b in c cm
Perform the indicated operations. Round your answers to the degree of precision of the least precise number
a in in in
b mi mi – mi
c. 15 lb – 7.6 lb lb

15. PRACTICE PROBLEMS (Cont)
Determine the number of significant digits for the following measurements:
a b c. 14,700
Perform the indicated operations. Round your answers to the same number of significant digits as the least accurate number
a mi ×
b  ×
c  ×

16. 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

17. 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

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 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 mm; equal to or greater than and less than mm
b in; equal to or greater than and less than in
c. 0.1 cm; equal to or greater than 2.95 and less than 3.05 cm
a in b mi c. 14 lb
a b c. 3
a mi b c
a lb; 0.02% b. 1 in; 5.882% c mm; 0.178%
a. 1/8 in b cm c. 1/8 mm

20. PROBLEM ANSWER KEY
12.45 mm
3.375 inches