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Significant Figures Part 2 Problem Solving Applications Multiplying & Dividing • When multiplying or dividing, your answer may only show as many significant digits as the multiplied or divided measurement showing the least number of significant digits. Examples • 22.37 cm x 3.10 cm x 85.75 cm = 5946.50525 cm3 = 5950 cm3 • (3.0 x 105 m2)/(2.45 x 103 m) = 122.4489…m = 120 m More Examples • 5000 g / 4.25 g = 1176.470588 = 1000 • 2500 N x 40. N = 100000 N2 = 1.0 x 105 N2 Adding and Subtracting • When measured quantities are used in addition or subtraction, the uncertainty is determined by the absolute uncertainty in the least precise measurement (not by the number of significant figures). Sometimes this is considered to be the number of digits after the decimal point. Examples • 3.45 cm + 8.1 cm = 11.55 cm = 11.6 cm • 31.492 g – 30.9481 g = .5439 g = .544 g • 685 N + 3.9 N = 688.9 N = 689 N More Examples • 1060 L – 997.2 L = 62.8 L = 60 L • 890 Kg + 0.874 Kg = 890.874 Kg = 890 Kg Practice Problems 1. 2. 3. 4. 890 / 5.86 = 151.8771331 = 150 8.203 x 4.3 = 35.2729 = 35 300 x 52 = 15600 = 20000 40. x (6.02 x 1023) = 2.408 x 1025 = 2.4 x 1025 5. (3.50 x 102) / (8.2 x 103) = 0.0426829268 = 0.043 or 4.3 x 10-2 Practice Problems 6. 6. 3.00 + 82.890 + 4.8 = 90.69 = 90.7 7. 7. 3.24 – 1.005 – 0.023 = 2.212 = 2.21 8. 81.02 + 25 – 8.023 = 17.997 = 18 9. 30 – 5.9 + 2.45 = 26.55 = 30 10.56.8 + 20. – 42.33 = 34.47 = 34