1 / 17

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

alair
Télécharger la présentation

Uncertainty Contents: General Rules for addition and subtraction

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related