1. Uncertainty Contents: General Rules for addition and subtraction Whiteboards for addition and subtraction Rule for multiplication and division Examples of multiplication and division

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

3. Rule for addition and subtraction TOC 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

4. Whiteboards Uncertainty with + and - TOC

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

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

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

8. Rule for multiplication and division TOC 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%)

9. Whiteboards Uncertainty with x and / in % TOC

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

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

12. Rule for multiplication and division TOC 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…

13. Rule for multiplication and division TOC 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

14. Whiteboards Uncertainty with x and / TOC

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

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

17. Rule for powers TOC If y = a n then

18. Rule for powers TOC If y = a n then A cube measures 2.52 ±.05 cm on a side. What is its volume in cc? Volume = 16.00 cc dV =.95256 16.00 ±.95 cc

19. Whiteboards Uncertainty with Powers TOC

20. Express the answer with the correct uncertainty (8.1 ± 1.0) 2 = ?? W 8.1 2 = 65.61 uncty = 65.61(2*1/8.1) = 16.2 66 ± 16 66 ± 16??

21. 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 x r W  r 2 =  4.5 2 = 63.6173 uncty = 63.6173(.1/4.5+.1/4.5) = 2.83 63.6 + 2.8 cm 2

22. Express the answer with the correct uncertainty = ?? W √(25.0) = 5.00 uncty = 5.00*(.5*.2/25) =.02 5.00 ±.02