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 • The fractional uncertainty is 2/5 (or 40%)

Rule for addition and subtraction The uncertainty of a sum or difference is always the sum of the absolute 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

Whiteboards Uncertainty with + and -

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

Express the answer with the correct uncertainty (12. 1 ±. 3) - (4. 5 ±. 6) 7. 6 ±. 9 = ? ?

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

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%)

Whiteboards Uncertainty with x and / in %

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

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

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…

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 cm 2

Whiteboards Uncertainty with x and /

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 = ? ?

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

Rule for powers If y = an then

Rule for powers If y = an then A cube measures 2. 52 ±. 05 cm on a side. What is its volume in cc? 16. 00 ±. 95 cc

Whiteboards Uncertainty with Powers

Express the answer with the correct uncertainty (8. 1 ± 1. 0)2 = ? ? 8. 12 = 65. 61 uncty = 65. 61(2*1/8. 1) = 16. 2 66 ± 16? ?

Express the answer with the correct uncertainty A circle has a radius of 4. 5 +. 1 cm. What is its area? Area = r 2 = x r r 2 = 4. 52 = 63. 6173 uncty = 63. 6173(. 1/4. 5+. 1/4. 5) = 2. 83 63. 6 + 2. 8 cm 2

Express the answer with the correct uncertainty = ? ? √(25. 0) = 5. 00 uncty = 5. 00*(. 5*. 2/25) =. 02 5. 000 ±. 020