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Significant Figures in Calculations

Significant Figures in Calculations. A calculated answer cannot be more precise than the measuring tool. A calculated answer must match the least precise measurement. 3 SF. Significant Figures in Calculations.

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Significant Figures in Calculations

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  1. Significant Figures in Calculations • A calculated answer cannot be more precise than the measuring tool. • A calculated answer must match the least precise measurement.

  2. 3 SF Significant Figures in Calculations • Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm3)(23.3cm3) = 324.103g 4 SF 3 SF 324g

  3. Learning Check A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 = 1)61.582) 62 3) 60 C. 2.54 X 0.0028 = 0.0105 X 0.060 1) 11.3 2) 11 3) 0.041

  4. Solution A. 2.19 X 4.2 = 2) 9.2 B. 4.311 ÷ 0.07 = 3) 60 C. 2.54 X 0.0028 = 2) 11 0.0105 X 0.060 Continuous calculator operation = 2.54 x 0.0028  0.0105  0.060

  5. Adding and subtracting with sig figs • The last sig fig in a measurement is an estimate. • Your answer when you add or subtract can not be better than your worst estimate. • Round your answer to match the measurement with the leftmost last sig fig.

  6. 27.93 + 6.4 27.93 27.93 + 6.4 6.4 For example 1. Line up the decimal point. 2. Determine thelast sig fig of each measurement. 3. The # with the leftmost last sig fig determines the place of the last sig fig in the answer. 34.33

  7. Significant Figures in Calculations • Add/Subtract - The # with the leftmost last sig fig determines the place of the last sig fig in the answer. 224 g + 130 g 354 g 224 g + 130 g 354 g 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL  350 g  7.8 mL

  8. Adding and Subtracting 25.2 + 1.34 26.54  26.5

  9. Learning Check In each calculation, round the answer to the correct number of significant figures. A. 235.05 + 19.6 + 2.1 = 1) 256.75 2) 256.8 3) 257 B. 58.925 - 18.2 = 1) 40.725 2) 40.73 3) 40.7

  10. Solution A. 235.05 + 19.6 + 2.1 = 2) 256.8 B. 58.925 - 18.2 = 3) 40.7

  11. 5. (15.30 g) ÷ (6.4 mL)  2.4 g/mL 2 SF Significant Figures Practice Problems 4 SF 2 SF = 2.390625 g/mL 6. 18.9 g - 0.84 g  18.1 g 18.06 g

  12. Practice • 4.8 + 6.8765 • 520 + 94.98 • 0.0045 + 2.113 • 6.0 x 102 - 3.8 x 103 • 5.4 - 3.28 • 6.7 - .542 • 500 - 126 • 6.0 x 10-2 - 3.8 x 10-3

  13. Practice • 4.5 x 6.245 • 9.8764 x .043 • 3.876 / 1983 • 16547 / 714 • 4.5 / 6.245

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