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Uncertainty

Uncertainty. Goal: To understand and use uncertainties in physical measurement. Uncertainty. Uncertainties in measurements can be stated as absolute values or percentages Ex 1.0±0.5 or 1.0±50%

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Uncertainty

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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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