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Significant Figures

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. Integer and Real Values.

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Significant Figures

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  1. Significant Figures

  2. 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

  3. Integer and Real Values • Real numbers represent continuousquantities, e.g., length of rod, mass of rock, velocity of a vehicle, etc. • Integer numbers represent discretequantities, e.g., number of marbles, number of people, number of computers, etc. L

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

  5. Rat 7

  6. 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.

  7. Team Exercise 7.1: (3 minutes) • The density of HCFC-22 (R-22 Freon) at 40oF was measured as 72.000 lbm/ft3. • The actual (true) value is 79.255 lbm/ft3. • Calculate: • True error • Fractional error • Percent error

  8. 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 2.0001 gallons 100,393 people 600 pages 100,000 ft2 581 pages 128,462 ft2

  9. Rules for SignificantDigits • 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!

  10. 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 12.0000…in/ft • The formula: is equivalent to

  11. Team Exercise 7.3 • 301.33 + 698. = ? • 7.0700 / 30 = ? • 70700 / 30.0 = ? • (-0.6643 + 0.00497)/1792 = ? • 3.14/(693.3 - 693.27) = ?

  12. Accuracy • 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 A5.03% B 4.96% C 2.98%

  13. Precision • 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 A5.03%, 4.97%, 5.07% B 4.49%, 5.52%, 5.01% C 2.98%, 7.98%, 9.23%

  14. Precision vs. Accuracy

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

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

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