Chemistry 1. Worksheet 3. Significant Figures in Calculations. 1 MathTutorDVD.com

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1 Chemistry 1 Worksheet 3 Significant Figures in Calculations 1

2 Report all answers on this worksheet with the correct number of significant figures. 1) How many significant figures does each of the following numbers contain? a. 6 b. 75 c. 30 d. 865 e f. 6.0 g. 60 h ) How many significant figures does each of the following numbers contain? a. 3,500 b c d ) How many significant figures does each of the following numbers have? a. 4.2 x 10 3 b x 10 3 c. 4, ) How many significant figures would be in the final answer for the following calculations? a b c. 1, ,000 d e. 7.0 X f

3 5) How many significant figures would be in the final answer for the following calculations? a x 70 b. 458 x 0.06 c X 4.52 d. 9 x 6.21 e x 1.0 f ) How many significant figures are in the following measurements? a. 60 g b km c. 73 balls d ms 7) Complete the following calculations. a = b = c = d = e = f = 8) Complete the following calculations. a. 42 x 6 = b x 532 = c. (5.6 x 10 4 )(1) = 3

4 9) Convert 1.0 x 10 3 kg to g. 10) Convert 5.0 x 10 5 m/s to km/hr using the correct number of significant figures. 11) Challenge: Perform the following calculation. Use the correct number of significant figures in your answer x 5.2 = 4

5 12) Challenge: Perform the following calculation. Use the correct number of significant figures in your answer x = 13) Challenge: a. Convert 50 km to m. b. Use the answer you obtained in Part a in the blank in the calculation below. ( m +4 m 5 m) x 34 m = 5

6 Answer Key Rules for significant figures: 1) Any non-zero number is always significant. 2) Zeroes directly before a decimal place are not counted (unless a non-zero number is located anywhere to its left). 3) Leading zeroes (numbers before a non-zero number) to the right of a decimal place are not counted. 4) Trailing zeroes (zeroes that come after a non-zero number) are counted. 5) Zeroes between other significant digits are counted. 6) For scientific notation, only count digits prior to the power of 10. 7) For addition and subtraction, the answer will have the same number of significant figures after the decimal as the number in the problem with the fewest numbers after the decimal. 8) For multiplication and division, the final answer will have the same number of significant digits as the number in the problem with the fewest significant digits. 1) How many significant figures does each of the following numbers contain? a. 6 1 b c d e f g h ) How many significant figures does each of the following numbers contain? a. 3,500 2 b c d

7 3) How many significant figures does each of the following numbers have? a. 4.2 x b x c. 4, ) How many significant figures would be in the final answer for the following calculations? a b c. 1, ,000 1 d e. 7.0 X f ) How many significant figures would be in the final answer for the following calculations? a x 70 1 b. 458 x c X d. 9 x e x f ) How many significant figures are in the following measurements? a. 60 g 1 b km 3 c. 73 balls N/A d ms 2 7) Complete the following calculations. a = 12 b = _14 c = 6 7

8 d = 5 e = 45 f = 93 8) Complete the following calculations. a. 42 x 6 = _300_ b x 532 = _5_ c. (5.6 x 10 4 )(1) = _6 x 10 4 _ 9) Convert 1.0 x 10 3 kg to g. Very important note: Conversion factors are NOT considered when counting the number of significant figures in a calculation. For instance, the 1,000 g/1kg term below is not important as far as significant figures are concerned. Only actual measured values are important (1.0 x 10 3 kg, in this problem). 1.0 x 10 3 kg 1,000 g = 1.0 x 10 6 g 1 kg Correct answer: 1.0 x 10 6 g 10) Convert 5.0 x 10 5 m/s to km/hr using the correct number of significant figures. The original value (5.0 x 10 5 m/s) only has two significant figures, so the final answer will only have two. 5.0 x 10 5 m 1 km 3,600 s = 1.8 x 10 6 km/hr S 1,000 m 1 hr Correct answer: 1.8 x 10 6 km/hr 8

9 11) Challenge: Perform the following calculation. Use the correct number of significant figures in your answer x 5.2 = In the case of multiple operations, the final operation performed will determine the number of significant figures. In most cases, addition and subtraction will be the final operation, as in the problem below. Round off intermediate answers and only worry about significant figures for the final operation. Let s take it step-by-step: Operation #1: Multiplication If we were to worry about significant figures at this point, 15.6 would be rounded to 20 (1 significant figure) because 3 only has one significant figure. Operation #2: Addition 23.6 Calculate the answer using order of operations (PEMDAS), to arrive at the answer Since addition was the last operation that was performed, the final answer will follow that rule. Thus, the final answer will be rounded to the least-accurate decimal place of the original number, the tenths. Correct answer:

10 12) Challenge: Perform the following calculation. Use the correct number of significant figures in your answer x = Multiply x 70.2 first to get: Then, perform addition to get: 54.3 Since 54.1 has only one number past the decimal place, the final answer will as well. Correct answer: ) Challenge: a. Convert 50 km to m. 50 km 1,000 m = 50,000 m (or 5 x 10 4 m) 1 km Correct answer: 50,000 m (or 5 x 10 4 m) b. Use the answer you obtained in Part a in the blank in the calculation below. (_50,000 m_ + 4 m 5 m) x 34 m Perform calculations inside parentheses first, then multiply. (49,999 m) x 34 m = 1.7 x 10 6 m 2 Correct answer: 1.7 x 10 6 m 2 10

Tutorial 2: Expressing Uncertainty (Sig Figs, Scientific Notation and Rounding)

Tutorial 2: Expressing Uncertainty (Sig Figs, Scientific Notation and Rounding) Goals: To be able to convert quantities from one unit to another. To be able to express measurements and answers to the correct