Reading Assignment: Read Chapters 5, 10, and 11 in Thinking Like An Engineer – An Active Learning Approach, by Stephan Unit Conversion Tables – Inside front cover and inside back cover of textSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 441Reading Assignment:Read Chapters 5, 10, and 11 in Thinking Like An Engineer – An Active Learning Approach, by Stephan Unit Conversion Tables – Inside front cover and inside back cover of textHomework Assignment:Homework Assignment #4Lecture #8 EGR 120 – Introduction to EngineeringSignificant Digits and Systems of Units2Lecture #8 EGR 120 – Introduction to EngineeringSignificant DigitsThe use of significant digits in expressing measured quantities gives us the ability to indicate the intended degree of precision. A different degree of precision is implied by 5 gallons versus 5.000 gallons. Three basic rules for significant digits1. All non-zero digits are significant (Example: 54.87 has 4 significant digits)2. Leading zeros are not significant (Example: 0.003 has 1 significant digit)3. Trailing zeros are significant (except with whole numbers where their significance may be uncertain) (Example: 2.20 has 3 significant digits) (Example: 100 has an unclear number of significant digits (1, 2, or 3))Example: How many significant digits are in each number below?1. 241.692 2. 10.0003. 0.000173 4. 0.0440 5. 52503Lecture #8 EGR 120 – Introduction to EngineeringSignificant Digits and AccuracyWhen a measurement is recorded, the number should reflect the accuracy of the measurement. A measurement of 15.3 implies a certain accuracy: that the true value of the quantity being measured is between 15.25 and 15.35. Illustration: Consider the three voltmeters shown to the right. Why would the middle voltmeter read 15.3? It must be that the actual value of the voltage is closer to 15.3 than to 15.2 and is also closer to 15.3 than 15.4. Since the midpoint between 15.2 and 15.3 is 15.25 and the midpoint between 15.3 and 15.4 is 15.35, it follows that: The reading 15.3 implies an accuracy of between 15.25 and 15.35.1 5 .2+V_1 5 .3+V_1 5 .4+V_Example: Determine the accuracy for each measured quantity below. 1. 2.092. 4.803. 2.5004Lecture #8 EGR 120 – Introduction to EngineeringSignificant Digits and Whole NumbersWhole numbers can include trailing zeros that may or may not be significant. For example, the number the zeros in the number 4000 may or may not be significant. It is unclear.Examples: How many significant digits do you think are implied by each of the following?1) A person states that the outside temperature is 100 degrees. Probably all 3 digits are intended to be significant as since expressing temperatures to the nearest degree is common.2) A person states that his swimming pool holds 10000 gallons of water.Probably all digits are not intended to be significant. If all 5 digits were significant, this would imply an unusual accuracy.So, how can the confusion over the number of significant digits be eliminated? By using scientific notation.5Lecture #8 EGR 120 – Introduction to EngineeringSignificant Digits and Scientific NotationUsing scientific notation is a sure way to clear up any possible confusion in the number of significant digits. Trailing zeros are always significant when scientific notation is used. The number 4000 has an unclear number of significant digits, but 4.000 x 103 clearly has 4 significant digits and 4.0 x 103 clearly has only 2 significant digits.Example: Recall the case of the 10,000 gallon swimming pool. The owner could have used scientific notation to make the accuracy of the pool’s volume clear. The possible choices are listed below. Volume of water Number of Impliedin swimming pool sig. digits Accuracy1. x 104 gallons1.0 x 104 gallons1.00 x 104 gallons1.000 x 104 gallons 1.0000 x 104 gallons6Lecture #8 EGR 120 – Introduction to EngineeringSignificant Digits and Percent ErrorThe number of significant digits used in expressing a measured quantity gives an indication of the percent error in the measurement. To illustrate this, consider the case of 3 significant digits used to express a whole number. The smallest whole number that can be expressed using 3 significant digits is 100 and the largest is 999. Note that 100 implies an accuracy of 99.5 - 100.5 and 999 implies an accuracy of 998.5 - 999.5.So, a number expressed using 3 significant digits has a percent error somewhere between 0.1% and 1% or a maximum percent error of 1%. A similar process could be used in other cases:Number of significant digits Maximum Error123456If error is defined as Then when the display shows the value of 100 the errormax value - min valueerror = 100%nominal value100.5 - 9 is And when the display sho9.5 100% = 1%10ws the value o 990f xx999.5 - 998.5 100% 0.1%99 th9e error s 9 i x 7Lecture #8 EGR 120 – Introduction to EngineeringMathematical operations involving significant digitsMeasured data is often used in calculations and the number of significant digits used to express the result depends on the type of calculations performed. There are 2 basic rules to consider:1) When multiplying or dividing numbers, the results should be expressed using the fewest number of significant digits contained in any of the numbers.2) When adding or subtracting numbers, the results should be expressed using the smallest number of digits to the right of any common(*) decimal point contained in any of the numbers.* Note that using scientific notation allows the user to move the decimal point as desired(such as 0.123 x 103 = 1.23 x 104 = 12.3 x 105 , etc) so be sure to use the same exponent when determining the number of significant digits to the right of any common decimal point. Example: Express the result below using the proper number of significant digits. 78 x 878Lecture #8 EGR 120 – Introduction to Engineering3.729 x 1.6 0.0064 28.2 =Example: Express the result below using the proper number of significant digits.Example: Express the result below using the proper number of significant digits.9Lecture #8 EGR 120 –