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Understanding Significant Figures in Multiplication and Division

This resource covers the essential rules for using significant figures in mathematical operations, focusing on multiplication, division, addition, and subtraction. Learn how to determine the correct number of significant digits in your answers by following the measurements with the least precision. You'll find examples illustrating these concepts, along with practice problems that provide opportunities to apply your knowledge. Mastering significant figures is crucial for accurate calculations in scientific and engineering contexts.

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Understanding Significant Figures in Multiplication and Division

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  1. Significant Figures Part 2 Problem Solving Applications

  2. 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.

  3. 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

  4. More Examples • 5000 g / 4.25 g = 1176.470588 = 1000 • 2500 N x 40. N = 100000 N2 = 1.0 x 105 N2

  5. 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.

  6. 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

  7. More Examples • 1060 L – 997.2 L = 62.8 L = 60 L • 890 Kg + 0.874 Kg = 890.874 Kg = 890 Kg

  8. Practice Problems • 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 • (3.50 x 102) / (8.2 x 103) = 0.0426829268 = 0.043 or 4.3 x 10-2

  9. Practice Problems • 6. 3.00 + 82.890 + 4.8 = 90.69 = 90.7 • 7. 3.24 – 1.005 – 0.023 = 2.212 = 2.21 • 81.02 + 25 – 8.023 = 17.997 = 18 • 30 – 5.9 + 2.45 = 26.55 = 30 • 56.8 + 20. – 42.33 = 34.47 = 34

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