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Understanding uncertainties in physical measurement

Learn how uncertainties are calculated in measurements, whether in absolute values or percentages, and practice adding, subtracting, multiplying, and dividing with uncertainties. Discover methods for determining maximum uncertainties and applying them in different scenarios.

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Understanding uncertainties in physical measurement

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  1. Uncertainty Goal: To understand and use uncertainties in physical measurement

  2. Uncertainty • Uncertainties in measurements can be stated as absolute values or percentages • Ex 1.0±0.5 or 1.0±50% • Absolute uncertainties are 1 sig fig and match the place value of the least significant digit of the measurement

  3. Determining Uncertainties • A simple approximate method is sufficient to determine maximum uncertainties. • For functions such as addition and subtraction, absolute uncertainties may be added. • For multiplication, division and powers, percentage uncertainties may also be added.

  4. Adding and Subtracting Ex. 1: 4.50±0.01 + 3.22±0.01 4.50 + 3.22 = 7.72 0.01 + 0.01 = 0.02 Answer: 7.72±0.02 Ex. 2: 5.60±0.01 - 3.20±0.02 5.60 - 3.20 = 2.40 0.01 + 0.02 = 0.03 Answer: 2.40±0.03

  5. Practice • 12.5±0.5 + 6±1 = • 12.005±0.001 - 0.039±0.001 = • 75,000±1000 + 5550±50 = • 19±2 • 11.966±0.002 • 81,000±1000

  6. Multiplying and Dividing • Ex 3: 15.0±0.5 x 8.0±0.5 15.0 x 8.0 = 120 0.5 ÷ 15.0 x 100 = 3.333% 0.5 ÷ 8.0 x 100 = 6.250% 3.333% + 6.250% = 9.583% 120 x 0.09583 = 11.4996  10 Answer: 120±10

  7. Try it! • Ex4: 12.5±0.5 ÷ 62±1 12.5 ÷ 62 = 0.20 0.5 ÷ 12.5 x 100 = 4.00% 1 ÷ 62 x 100 = 1.613% 4.00 + 1.613 = 5.613% 0.20 x 0.05613 = 0.011 Answer: 0.20±0.01

  8. How thick is one page? • There are 708 page numbers in the book, so that’s 354 pages.

  9. Practice • 12±8% x 2.3±12% • 400±10 ÷ 0.55±0.01 • 28±20% • 730±30

  10. Task: • Calculate, with uncertainty, the volume of the room. Show ALL measurements and calculations.

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