2. Lesson 7 Reliability, Significant Figures and Percent Error

3. I.Reliability of Measurements A.Measurements must be made with care 1.No measurement is completely exact a.Human error b.Instrument error c.Method error 2. These errors should be accounted for in any report on an experiment.

4. B.Accuracy differs from precision 1.Accuracy is the extent to which a measurement approaches the exact value and is free from error 2.Precision is how exactly or sharply stated a measurement is. 3.Precision can also indicate how close together a group of measurements are. 4.You can have measurements which are both accurate and precise, not accurate or precise, or precise but not accurate (measurements close together, but not close to the correct value)

8. Significant figures: a definition Significant figures, sometimes called significant digits, or even sig. figs. for short, are digits in a measurement which have actually been measured by comparison with scale, plus one estimated digit. This is a direct indication of how accurate your measurements or calculations are.

9. Rules for determining whether a digit is significant or not. Rule 1: All non-zero numbers are significant. Ex. 1,2,3,4,5,6,7,8,9 Rule 2: Zeroes appearing between significant figures are also significant. Ex. 202, 40009, 2.4401 Rule 3: Zeros at the very end of a decimal are significant. Ex. 4.80,.123000012.13020 Rule 4: Zeros that are place holders only are NOT significant. They are not in between sig figs or at the end of the decimal. Ex. 200 0.0000312

10. Examples: 1. 0.02 2.0.020 3.501 4.501.0 5.5,000 6.5,000. 7.6,051.00 8.0.0005 9.0.1020 10.10,001 1 2 3 4 1 4 6 1 4 5

11. In the case of unclarity, you may indicate the last significant figure with a bar above it. A decimal may also be used to indicate significance of zeros: 8040 9100

12. Rules for Calculations in terms of Significant Figures: In scientific calculations, your answers are only allowed to be as accurate as your least accurate measurement in the problem. This is of utmost importance when doing research. Answers in which significant figures rules are not followed are considered COMPLETELY INVALID AND MEANINGLESS!!! Learn these rules now and live by them! You will be held to them in all calculations in my class, in physics next year and any math based science class you ever take from now on.

13. Rules for Multiplication or Division: Look at all the numbers in the math problem. Identify how many significant figures are in each of the factors. Your answer to the problem may only have as many significant figures as the smallest number in the original math problem.

14. Example: 12.239 x 8.30 The first factor has 5 sig figs and the second factor has 3 sig figs. When you type this into your calculator, it gives an answer of : 101.584 This number has 6 significant figures. Our final answer is only allowed to have 3. Round your answer using normal rounding rules. Final answer is :102

15. Rules for Calculations with Addition or Subtraction: In an addition or subtraction problem, we are not concerned with the number of significant figures in each term, but how many decimal places are present in each. The final answer may only have as many decimal places as the fewest present in the original problem.

16. Example: 12.34 + 56.8 + 13.111 = 82.251 82.3

17. III.Percent Error A.Percent Error shows the accuracy of experimental data obtained in the laboratory. B.To Calculate Percent Error 1.First take the absolute value of the experimental number (number obtained in your experiment) and subtract the accepted value (theoretical value) This difference is called the Error 2.Percent error is then the (Error divided by the accepted value) times 100 to give you a percentage. (Error) ------------------- X 100 (Accepted Value)

18. Example: Your experiment predicts the mass of an oxygen atom to be 17.5562 and you are told that the known value is actually 15.9994 what is the percent error of your calculation? 9.7304 %

19. Example 2: Your calculation predicts the mass of a product to be 5.00 g and you physically, in an experiment, massed the product to be 4.5 g. What is the percent error of your calculation? 10 %

20. Accuracy vs. Precision Questions: –Compare and Contrast Accuracy and Precision. –Tell whether each of the following situations describes accuracy, precision, both, or neither: a. 15 cm, 2.16 cm, 2.12 cm, 2.21 cm (Actual length 2.19 cm) b. 81.1 L, 92.8 L, 56.0 L (Actual volume 79.1 L) c. 21.81 g, 21.23 g, 21.56 g (Actual mass 24.23 g) d. 121.21 mL, 126.12 mL, 92.23 mL, 81.22 mL (Actual volume 115.12 mL)

23. Level 1 1.How many significant figures are there in each of the following measurements? A.23 cm B.1.498 g C.248.3 s D.9.855 mL E.76.414 kg F.32.8 m G.107 mm H.0.238 km I.8.0335 cm J.0.05587 m 2.Express the answer to each of the following calculations with the correct number of significant figures. Remember the rules for addition and subtraction. A.3.42 cm + 8.13 cm B.4.939 g + 3.822 g C.17.8 cm + 12.11 cm D.4.552 kg + 3.14 kg E.1.966 s + 3.4422 s F.3.882 g - 2.114 g G.4.894 cm - 2.33 cm H.15.6674 m - 12.838 m I.11.22 g - 8.8 g J.133 L - 6.45 L 3.Express the answer to each of the following calculations with the correct number of significant figures. Remember the rules for multiplication and division. A.1.2 cm x 1.3 cm B.2.1 m x 1.8 m C.1.45 m x 2.2 m D.2.5 mm x 1.33 mm E.4.3324 km x 1.2 km F.32.88 m2 / 4.288 m G.16.5 km2 / 1.8 km H.84.99 m2 / 2.63 m I.9.9 mm2 / 3.4484 mm J.3.085 cm2 / 2.77448 cm

24. Level 2 1.How many significant figures are there in each of the following measurements? A.722 g B.93.302 mL C.1.00282 hL D.8.231 L E.22.22 cm F.8.2300 mm G.83.20 km H.2.231012 g I.8.2303 kg J.90.021 m 2.Express the answer to each of the following calculations with the correct number of significant figures. Remember the rules for addition and subtraction. A.72 cm + 48 cm B.641.1 m + 23.13 m C.888 g + 81.123 g D.5.213 mm + 98.98 mm E.0.00121 mg + 1.23 mg F.8.732 cm - 2.81 cm G.4.2 kg - 2.22 kg H.883 m - 23.24 m I.55.234 cm - 2.2 cm J.0.00224 g - 0.00017 g 3.Express the answer to each of the following calculations with the correct number of significant figures. Remember the rules for multiplication and division. A.8.3 cm x 87 cm B.76.0 m x 45 m C.5.133 mm x 0.0023 mm D.81.22 km x 13.1 km E.711 m x 8.3 m F.0.0023 mm2 / 83.3 mm G.7.34 m2 / 0.25 m H.912.4 mm2 / 76 mm I.0.231 km2 /.12423 km J.67.2 km2 / 123.32 km

25. Level 3 1. How many significant figures are there in each of the following measurements? A.307 g B.1.40082 cm C.0.00058900 g D.0.00300900870 mm E.4500 km F.350,000 cm G.180.00 s H.3.50 x 103 cm I.1.604 x 10-4 m J.0.0459 x 103 g 2. Express the answer to each of the following calculations with the correct number of significant figures. A.80 cm + 13.0 cm B.72.60 m + 0.0950 m C.13.89 cm + 6.8932 cm D.1.30 x 10-2 cm + 2.4 x 10-4 cm E.8.99 x 103 m + 1.400 x 104 m F.750. cm – 677.4 cm G.10,000 m – 940 m H.0.0890 cm – 0.0666 cm I.0.340 x 10-1 g – 1.20 x 10-2 g J.4.5 x 105 km – 3.00 x 103 km 3. Express the answer to each of the following calculations with the correct number of significant figures. A.3.0 cm x 4.000 cm B.2.005 cm x 5.0 cm C.400 m x 87,488 m D.2.3 x 10-6 m x 1.40 x 10-2 m E.8.70 x 10-2 mm x 40. x 10-1 mm F.0.0045 mm2 / 0.90 mm G.120 km2 / 8.56 km H.0.7600 mm3 / 1.50 mm I.4.80 x 105 m2 / 8.5 x 103 m J.0.630 x 10-1 m3 / 0.0804 x 102