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Name ______KEY_____________ Period ___________________ Significant Figures Calculations, Version 5, Hauck, 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 answer 14 414 7.3 12 Calculator Answer? 13.95 413.75 7.32 11.96664 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? 7.500 5.06436 1002 7.5e-2 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. The calculator had more digits in the answer. The correct answers had the # SF as the least # digits in the operation. 2. How many significant figures are in each of the correct answers? List them here 1. Group 1 Multiplication # SF Group 2 # SF Division 1 2 1 1 2 3 2 2 3 2 3 1 4 2 4 2 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: The answer to the operation only contains the least number of SF in the operation Group 3 (challenging multiplication & division) 1 2 3 4 Operation Correct Answer Calculator Answer 15 x 305 15000.0 / 0.0003 1.230 x 103 x 0.0006 (15 x 3.200 x 10-6) / 3 4.6 x 103 5 x 107 0.7 2 x 10-5 4575.000 5 0.738 1.6 e-5 # SF in answer 2 1 1 1 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. The correct answers do not contain as many digits as the calculator answers. The correct answer has the same # SF as the number in the operation with the least # SF. 5. Is this still consistent with your explanation from CTQ 3? Explain. Yes. In both cases the final answers contain only the least # SF from the operation numbers. Group 4 (addition and subtraction) 1 2 3 4 5 Operation Correct Answer Calculator Answer # SF in answer 2+5 2.90 +14.123 35.00 – 2.0 21. 00987 – 0.87 14.9 + 21.0087 + 3 7 17.02 33.0 20.14 39 7 17.023 33 20.13987 38.9087 1 4 2 4 2 6. Perform the calculations on your own and compare your answers to the correct ones. Discuss the differences if any and write those down. The correct answers have fewer digits than the calculator answer and are rounded up if the last digit is 5 or more at the position of rounding. 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? The correct answer in addition and subtraction is only correct when it contains the least number of digits past the decimal. 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: The numbers in the operation are only 3 SF for both numbers, so the answer can only have 3 SF. Original answer before determining SF would be 4074.4. However, the answer can not have more SF than allowed, so must be only 3SF. 8. Discuss and explain the difference between multiplication/division & addition/subtraction rules for sig figs and write a rule here that describes these differences. Multiplication and Division, the answer can contain the least #SF from the numbers used in the operation. Addition and Subtraction can only have the correct #SF in answer based on the accuracy of the numbers in the operation by looking at the #digits past the decimal. Group 5 (Mixed addition and subtraction with multiplication and Division) 1 Operation Correct Answer Calculator answer # SF in correct answer (2.09 x 9.1) – 12.89 6.1 6.129 2 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 0.20675 8.27 (4.987-4.962) 13. How do you think you should report an answer when an operation involves BOTH addition/subtraction and multiplication/division? Explain. Use the least accurate number. If adding or subtracting, look at the #digits past the decimal. Also, looking at the Multiplication and Division, the answer can contain the least #SF from the numbers used in the operation 14. Revise and complete your set of rules that you have developed accordingly, IF they must be amended. One needs to use both different sets of rules for each operation. A website with more explanation of Significant figure rules: http://www.ruf.rice.edu/~kekule/SignificantFigureRules1.pdf Exercises: Perform the following operations and report your answers in the correct number of significant figures. Answers are reported in such a way that it reflects the reliability of the least precise operation 1. 34 x 19.770 = 1.7 2. 120 x 0.081 = 1.48e+03 3. 2.300 x 106 / 19 = 1.2 e+05 4. 12.0 + 12.547 = 24.5 5. 0.0090/ 3.0 = 3.0 e-3 6. 9.00 x 0 .0020 = 4.5 e3 7. (0.00089 x 320.3) – 0.190125= 9.494 e-2 8. 3.5000 x 108 / 1.2 x 10-4 = 2.9 e 12 Scientific Notation/Exponential Notation 9. 0.14 x 6.022 x 1023 =8.4 e 22 10. 2.00x 10 -6 / 3.00 x 10-7 = 6.67 e 0 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) = 5.25 X 104 12. Subtract the following to 3 sig figs: (6.25 x 10 -2) + (5.77 x 10 -3) = 5.67 X 10-2 More Exercises: mixed operations 13. 4.184 x 100.62 x (25.27-24.16) = 467 14. 9.2 x 100.65 / 8.321+ 4.026 = 75