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Uncertainty Contents: General Rules for addition and subtraction

Uncertainty Contents: General Rules for addition and subtraction Whiteboards for addition and subtraction Rule for multiplication and division Examples of multiplication and division. Concept 0. Consider: 5 ± 2 m The (absolute) uncertainty is 2

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Uncertainty Contents: General Rules for addition and subtraction

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  1. UncertaintyContents: • General • Rules for addition and subtraction • Whiteboards for addition and subtraction • Rule for multiplication and division • Examples of multiplication and division

  2. Concept 0 • Consider: 5 ± 2 m • The (absolute) uncertainty is 2 • The fractional uncertainty is 2/5 (or 40%) TOC

  3. Rule for addition and subtraction The uncertainty of a sum or difference is always the sum of the uncertainties If y = a + b then y = a + b  - uncertainty in (2.3 ± .1) + (3.6 ± .3) 5.9 ± .4 (7.6 ± .4) - (2.5 ± .3) 5.1 ± .7 TOC

  4. Whiteboards Uncertainty with + and - TOC

  5. Express the answer with the correct uncertainty (45 ± 3) + (12 ± 2) = ?? 57 ± 5 W 57 ± 5

  6. Express the answer with the correct uncertainty (12.1 ± .3) - (4.5 ± .6) = ?? 7.6 ± .9 W 7.6 ± .9

  7. Express the answer with the correct uncertainty (11 ± 3) - (7 ± 2) = ?? 4 ± 5 Ummm? W ??????

  8. Rule for multiplication and division The fractional uncertainty of a product or quotient is the sum of the fractional uncertainty of the operands: (??) Example - (5 ± 10%) x (20 ± 15%) (100 ± 25%) TOC

  9. Whiteboards Uncertainty with x and / in % TOC

  10. Express the answer with the correct % uncertainty (6 ± 3%) x (8 ± 2%) = ?? 6x8 = 48 uncty = 3% + 2% = 5% 48 + 5% W 48 + 5%

  11. Express the answer with the correct % uncertainty (72 ± 5%)  (9 ± 2%) = ?? 72/9 = 8 uncty = 5% + 2% = 7% 8 + 7% W 8 + 7%

  12. Rule for multiplication and division • The fractional uncertainty of a product or quotient is the sum of the fractional uncertainty of the operands: (??) • If y = ab, then y = a + b + c • c y a b c •  - uncertainty in… TOC

  13. Rule for multiplication and division • If y = ab, then y = a + b + c • c y a b c • Example: • A metal plate measures 21.1 + .5 cm by 15.3 + .1 cm. What is its area? • Find the area: • 21.1 x 15.3 = 322.83 • Use the formula: • y = .5 + .1 • 322.83 21.1 15.3 • y = 9.76 ≈ 9.8 (2 SF?) • 322.8 + 9.8 cm2 TOC

  14. Whiteboards Uncertainty with x and / TOC

  15. Express the answer with the correct uncertainty (45 ± 1) x (12 ± 1) = ?? 12 x 45 = 540 uncty = 540(1/45+1/12) = 57 540. ± 57 W 540. ± 57

  16. Express the answer with the correct uncertainty (30.0 ± .7)  (1.2 ± .1) = ?? 30/1.2 = 25 uncty = 25(.7/30+.1/1.2) = 2.66666 25.0 ± 2.7 W 25 ± 2.7

  17. Express the answer with the correct uncertainty A circle has a radius of 4.5 + .1 cm. What is its area? Area = r2 = x r x r r2 = 4.52 = 63.6173 uncty = 63.6173(.1/4.5+.1/4.5) = 2.83 63.6 + 2.8 cm2 W 63.6 + 2.8 cm2

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