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Name ___________________ Period ___________________ Significant Figures Calculations, Version 5 Hauck and Ligon Answer all question below based on the tables provided. Refer to the previous significant figures lesson if necessary. Group 1 (Multiplication) 1 2 3 4 Multiplication I 3.1 x 4.5 125 x 3.31 3.66 x 2.0 2.1 x 5.6984 Correct Calculator answer Answer? 14 414 7.3 12 Division II 1 2 3 4 15 / 2 12 / 2.3695 2004 / 2 0.0375/0.50 Correct answer 8 5.1 1000 7.5e-2 Calculator Answer? Critical Thinking Questions, CTQ 1. Perform the calculations above on your calculator (and write them in the tables) and compare what you get on your calculator to the correct ones listed above. Discuss the differences if any and write those down. 2. How many significant figures are in each of the correct answers? List them here 1. Group I Group II Multiplication Division 1 1 2 2 3 3 4 4 3. Compare your answers to CTQ 2 with the number of significant figures in the numbers in the problem itself. Develop a rule or explanation as to why the correct answer given is the way it is? Write your explanation here: Group 3 (challenging multiplication & division) Operation Calculator Answer Correct Answer 1 15 x 305 4.6 x 103 2 15000.0 / 0.0003 5 x 107 3 1.230 x 103 x 0.0006 0.7 4 (15 x 3.200 x 10-6) / 3 2 x 10-5 # SF in correct answer 4. Perform the calculations on your own (place answers in the calculator answer column for Group 3) and compare your answers to the correct ones. List the #SF in the answer in the last column of the table. Discuss the differences if any and write those down. 5. Is this still consistent with your explanation from CTQ 3? Explain. Group 4 (addition and subtraction) Operation Calculator answer Correct Answer 1 2+5 7 2 2.90 +14.123 17.02 3 35.00 – 2.0 33.0 4 21. 00987 – 0.87 20.14 5 14.9 + 21.0087 + 3 39 # SF in correct answer 6. Perform the calculations on your own and compare your answers to the correct ones. Discuss the differences if any and write those down. 7. What do you think is the deciding factor in determining how many significant figures the answer must be reported in for addition and subtraction problems? Now…here’s a wrench to throw into your rule you made in #7… Problem: 4050 + 24.4 Answer = 4070 Revamp your rule in #7 to include this new type of addition here: 8. Discuss and explain the difference between multiplication/division & addition/subtraction rules for sig figs and write a rule here that describes these differences. Group 5 (Mixed addition and subtraction with multiplication and Division) 1 Operation Calculator answer Correct Answer (2.09 x 9.1) – 12.89 6.129 2 6.1 # SF in correct answer 2 22.94 15.1269 + (2.50 x 3.12500) 3 519 1.002 + 652.10 – (0.269 / 0.00200) 4 33.04 (9.04-8.23+21.954+81.0)/3.1416 5 0.21 8.27 (4.987-4.962) 9. How do you think you should report an answer when an operation involves BOTH addition/subtraction and multiplication/division? Explain. 10. Revise and complete your set of rules that you have developed accordingly, IF they must be amended. Exercises: Perform the following operations and report your answers in the correct number of significant figures. 1. 34 x 19.770 = 2. 120 x 0.081 = 3. 2.300 x 106 / 19 = 4. 12.0 + 12.547 = 5. 0.0090/ 3.0 = 6. 9.00 x .0020 = 7. (0.00089 x 320.3) – 0.190125 = 8. 3.5000 x 108 / 1.2 x 10-4 = Scientific Notation/Exponential Notation 9. 0.14 x 6.022 x 1023 = 10. 2.00x 10 -6 / 3.00 x 10-7 = In a series of calculations, carry the extra digits through to the final result then round. If adding or subtracting the power of 10 must be the same for all numbers. Rounding: if 5 or higher round up. Do not round your answer until all calculations have been made. 11. Add the following to 3 sig figs: (5.22 x 10 4) + (3.21 x 10 2) = 12. Subtract the following to 3 sig figs: (6.25 x 10 -2) + (5.77 x 10 -3) = More Exercises: mixed operations 13. 4.184 x 100.62 x (25.27-24.16) = 14. 9.2 x 100.65 / 8.321+ 4.026 = A website with more explanation of Significant figure rules: http://www.ruf.rice.edu/~kekule/SignificantFigureRules1.pdf