1. Attend to Precision © 2012 Project Lead The Way, Inc.Introduction to Engineering Design

2. Precision Engineers communicate precisely to others Use clear definitions State the meaning of variables Are careful about specifying units Calculate accurately Express answers with a degree of precision appropriate for the problem context

3. Precision of Answers How precisely should you report a measured value? Digital Instruments—Read and record all digits, including zeros after the decimal point, exactly as displayed. Decimal Scaled Instruments—Record all digits that you can certainly determine from the scale markings and estimate one more digit. 6.33 cm

4. Precision of Answers How precisely should you report a calculated value? Specified precision Common sense Accepted Convention Least precisely measured value used

5. Precision of Answers A cylinder has a height of 6 inches and a diameter of 3 inches. What is the volume of the cylinder? Precision = 0.00 If the cylinder weights 4.5 pounds, what is the density of the material? How precisely should you report a calculated value? Specified precision

6. Precision of Answers How precisely should you report a calculated value? Common sense How many people on a train? How many gallons of paint should you buy? 9.3, say 9 people 4.4? Buy 5 gallons

7. Precision of Answers How precisely should you report a calculated value? Accepted Convention – Money $237.8996 – Lumber 3.4 in. x 5.2 in. $237.90 4 x 6 Can you think of any other accepted conventions?

8. Precision of Answers Accepted Convention—Rounding Statistics General Rule: Don’t round until the final answer. Mean—Round to one more decimal place than the original data. Standard Deviation—Round to one more decimal place than the original data.

9. Precision of Answers How precisely should you report a calculated value? Least precisely measured value used 3 cm 30 cm 2 OR 28 cm 2

10. Think About Precision It is only an ESTIMATE. Assume a minimum radius of 2.5 cm 3 cm Assume a maximum radius of 3.5 cm The true value of the area is 19.6 cm 2 < A < 38.5 cm 2 30 cm 2 OR 28 cm 2

11. How precise? BUT, if you will use your answer in further calculations It is best to keep an intermediate value in your calculator without rounding. If you record an intermediate value, use a level of precision greater than the final answer dictates to eliminate compounding errors.

12. How precise? In general (if it makes sense) use the following rules: If you are adding or subtracting measured values, use the precision of the least precise measured value. – Example: Find the perimeter of a rectangle with side lengths 3.2 in. and 4.76 in. – Perimeter = 2(3.2 in. + 4.76 in.) = 15.92 in. If you are multiply or dividing measured values, use the least number of digits in any of the measured values. – Example: Find the area of a rectangle with sides lengths 13 in. and 4.76 in. – Area = (13 in.)(4.76 in.) = 61.88 in. 2 15.9 in. 61 in. 2 tenths place 2 digits

13. Calculation Precision—Example If a carpet, represented by the below parallelogram, was measured by pacing out steps, calculate the area. h A = bh = 3 ft x 6 ft b = 3 feet A = 18 ft 2 = 18.00 ft 2 = 20 ft 2 h = 6 feet Which answer is appropriate? OR 18 ft 2

14. Calculation Precision—Example The same carpet has now been measured using a ruler. Calculate the area. h A = bh = (3.48 ft)(6.21 ft) b = 3.48 feet A = 21.6108 ft 2 = 21.6 ft 2 = 22 ft 2 h = 6.21 feet Which answer is appropriate? = 20 ft 2

15. It is just an estimate! All measured values are estimates. And therefore, all calculated values resulting from measured values are estimates. You can’t be CERTAIN of the answer to a level of precision greater than the information you use to calculate it, so don’t give an answer that implies that you are.

16. Precision of Answers How precisely should you report a calculated value? Specified precision Common sense Accepted Convention Least precisely measured value used And don’t forget units!