Significant Figures

Learning Objectives Learn the differences in: –Accuracy/precision, –Random/systematic error, –Uncertainty/error Compute true, fractional, and percent error Use proper number of significant figures to report work

l Real numbers represent continuous quantities, e.g., length of rod, mass of rock, velocity of a vehicle, etc. l Integer numbers represent discrete quantities, e.g., number of marbles, number of people, number of computers, etc. L Integer and Real Values

Error Error can be associated with real and integer values in measurements and calculations. Engineers generally work with real numbers.

Rat 7

Paired Jigsaw Front pair use Sig_Digits.ppt Back pair use Error.ppt Spend 10 minutes developing a 2-minute summary of your handout (and giving some examples) Spend 5 minutes exchanging 2-minute summaries with the other half of your team.

Team Exercise 7.1: (3 minutes) The density of HCFC-22 (R-22 Freon) at 40 o F was measured as lb m /ft 3. The actual (true) value is lb m /ft 3. Calculate: –True error –Fractional error –Percent error

Team Exercise 7.2: How “good” are these numbers (i.e., state whether each reported number has a large or small error)? 2 gallons 5 billion people gallons 100,393 people 600 pages100,000 ft pages128,462 ft 2

Rules for Significant Digits Combined operations: –If using a calculator or computer, perform the entire operation and then round to the correct number of significant digits. Sometimes, common sense and good judgment is the only applicable rule!

Exact Conversions and Formulas The number of significant digits in a final answer is not affected by the number of digits in an exact conversion factor or formula. Examples: The exact conversion factor 12 in/ft is equivalent to …in/ft The formula: is equivalent to

Team Exercise = ? / 30 = ? / 30.0 = ? ( )/1792 = ? 3.14/( ) = ?

Accuracy l Accuracy - nearness to the correct value. Example: A chemistry instructor makes a 5.00% sugar solution. Using a sugar assay, a team of students analyzes the solution and reports the following results: Student Result A 5.03% B 4.96% C 2.98%

Precision l Precision - repeatability of the measurement indicates scatter in the data Example: A chemistry instructor makes a 5.00% sugar solution. Using a sugar assay, a team of students analyzes the solution in triplicate and reports the following results: Student Result A 5.03%, 4.97%, 5.07% B 4.49%, 5.52%, 5.01% C 2.98%, 7.98%, 9.23%

Precision vs. Accuracy

Uncertainty Uncertainty results from random error and describes lack of precision. Fractional Uncertainty = Uncertainty Best Value Percent Uncertainty = Fractional Uncertainty * 100%

Team Exercise 7.4 Compute the fractional and percent uncertainty of a rod with a reported length of 7.57 to 7.59 cm.