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Our Objectives: Be able to… Accuracy, Precision and Significant Figures Distinguish between PRECISION and ACCURACY. Determine the number of sig figs in a measurement. Round any measurement to a set number of sig figs. Use scientific notation when necessary. Accuracy: Precision: This is the concept which deals with whether a measurement is correct when compared to the known value or standard for that particular measurement. When a statement about accuracy is made, it often involves a statement about percent error. error. Percent error is often expressed by the following equation: This is the concept which addresses the degree of exactness when expressing a particular measurement. The precision of any single measurement that is made by an observer is limited by how precise the tool (measuring instrument) is in terms of its smallest unit. Actual Experiemental % error Experimental 100 Summary: Accuracy & Precision Accuracy refers to how “correct” a measurement is; how close it is to the accepted value. Precision refers to how exactly a measurement is reported; or how closely repeated measurements will agree. A measurement can be precise, but inaccurate. A measurement can be imprecise, but accurate. Examples: Balances Kilogram bathroom scale. Decigram balance. Centigram balance. Analytical balance. 1 METER BAR Significant Figures Significant Figures are ones that have been accurately measured. Sample Problems: How many significant digits are in each of the following? a. 903.2 b. 0.0090 c. 0.007 d. 0.02 e. 90.3 f. 0.090 0 g. h. i. j. k. l. 0.0080 70 900.0 99 0.049 5.0002 1 Which Digits are Significant Figures? Rule 1: All non-zero numbers are significant. Yep…More Practice Problems 1. 2. Rule 2: All imbedded (flanked) zeroes are significant. Rule 3: Leading zeroes are never significant. Rule 4: Trailing zeroes are ONLY significant if there is a decimal point present in the number. 3. 4. 5. 6. 7. 8. 9. 10. Significant Figures: When someone else has made a measurement, you have no control over the choice of the measuring tool or the degree of precision associated with the device used. You must rely on a set of rules to tell you the degree of precision. Refer to the “Tutorial: Significant Figures, Precision, and Accuracy ” Handout (later) No measurement is exact; there is always some uncertainty. There are always two parts to a measurement: Numerical part Unit/label 5 3 3 3 4 4 2 2 3 3 What if I measured it? You will be expected to use the rules for significant figures… figures… in all your calculations… calculations… ….and in all of your measurements Measurements 3.0800 0.00418 7.09 x 10-5 91,600 0.003005 3.200 x10 9 250 780,000 0.0101 0.00800 Measuring with a Meter Stick We know the object is greater than 2 and less than 3. We know the object is greater than 0.8 and less than 0.9 We can also guess at one more place. So, I’ll guess 0.04 Final answer 2.84 cm. 2 Meter Stick Example 1 What length is indicated by the arrow? • • • • Meter Stick Example 2 What length is indicated by the arrow? More than 4, less than 5. More than 0.5 but less than 0.6 Guess at 0.00 So, 4.50 cm. 9.40 cm Measuring with a Thermometer Meter Stick Example 3 What length is indicated by the arrow? 12.34 cm Thermometer Example 1 What is the temperature? 28.5 °C What is the temperature? Greater than 15, but less than 16. Guess one place. So, 0.0 Final answer = 15.0 °C Thermometer Example 2 What is the temperature? 21.8 °C 3 Measuring with a Graduated Cylinder Thermometer Example 3 What is the temperature? 36.0 °C Graduated Cylinder Example 1 What is the volume? Graduated Cylinder Example 2 What is the volume? 27.5 mL 4.28 mL Multiplication and Division with Significant Figures Graduated Cylinder Example 3 What is the volume? Read to the bottom of the meniscus. Greater than 30, less than 31. Guess at one. So, 0.0 Answer 30.0 mL What is the volume? Rule: Your final answer cannot contain any more significant figures than the least precise measured number; the measured number with the fewest significant figures. 5.00 mL 4 Significant Figures: Multiplication and Division Round to least amount of significant figures 3.22 cm X 2.1 cm 6.762 cm The answer would then be 6.8cm Adding and Subtracting with Significant Figures As always, the answer is never more precise than the numbers used in the math: you can never be more precise than the least precise measurement. In addition and subtraction, only look at the decimal portion of the number. Practice 1. 2. 3. 4. 5. 6. 8.6 2.5 x 3.42 = 14.0 3.10 x 4.520 = 3.0 x 10 1 2.33 x 6.085 x 2.1 = 114 (4.52 x 10-4) / (3.980 x 10-6) = 7 -4 6.17 x 10 10 (3.4617 x 10 ) / (5.61 x 10 ) = (2.34 x 102)(0.012)(5.2345 x 105) = 1500000 Adding and Subtracting with Significant Figures Rules: 1. Count the number of significant digits in the decimal portion of each measured number. 2. Round the answer to the LEAST number of places in the decimal portion. Ex. 24.686 m 2.343 m + 3.21_m_ 30.239 m The correct answer is 30.24 m Practice 3.461728 + 14.91 + 0.980001 + 5.2631 = 24.61 2. 23.1 + 4.77 + 125.39 + 3.581= 156.8 3. 22.101 – 0.9307= 21.170 4. 0.04216 – 0.0004134 = 0.04175 5. 564321 – 264321= 300000 1. Practice Problems 5 Our Goals: Be able to… Determine the number of sig figs in a measurement. Round any measurement to a set number of sig figs. Use scientific notation when necessary. 6