Uncertainty Contents: • General • Rules for addition and subtraction • Whiteboards for addition and subtraction • Rule for multiplication and division • Examples of multiplication and division
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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
TOC
Consider: 5 ± 2 m •The (absolute) uncertainty is 2•The fractional uncertainty is 2/5 (or 40%)
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
WhiteboardsUncertainty with + and -
TOC
Express the answer with the correct uncertainty
(45 ± 3) + (12 ± 2) = ??
W
57 ± 5
57 ± 5
Express the answer with the correct uncertainty
(12.1 ± .3) - (4.5 ± .6) = ??
W
7.6 ± .9
7.6 ± .9
Express the answer with the correct uncertainty
(11 ± 3) - (7 ± 2) = ??
W
4 ± 5 Ummm?
??????
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%)
WhiteboardsUncertainty with x and / in %
TOC
Express the answer with the correct % uncertainty
(6 ± 3%) x (8 ± 2%) = ??
W
6x8 = 48uncty = 3% + 2% = 5%48 + 5%
48 + 5%
Express the answer with the correct % uncertainty
(72 ± 5%) (9 ± 2%) = ??
W
72/9 = 8uncty = 5% + 2% = 7%8 + 7%
8 + 7%
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…
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 = 322.83Use the formula:
y = .5 + .1 322.83 21.1 15.3 y = 9.76 ≈ 9.8 (2 SF?) 322.8 + 9.8 cm2
WhiteboardsUncertainty with x and /
TOC
Express the answer with the correct uncertainty
(45 ± 1) x (12 ± 1) = ??
W
12 x 45 = 540uncty = 540(1/45+1/12) = 57540. ± 57
540. ± 57
Express the answer with the correct uncertainty
(30.0 ± .7) (1.2 ± .1) = ??
W
30/1.2 = 25uncty = 25(.7/30+.1/1.2) = 2.6666625.0 ± 2.7
25 ± 2.7
Rule for powers
TOC
If y = an
then
a
an
y
y
Rule for powers
TOC
If y = an
then
a
an
y
y
A cube measures 2.52 ± .05 cm on a side. What is its volume in cc?
Volume = 16.00 ccdV = .9525616.00 ± .95 cc
WhiteboardsUncertainty with Powers
TOC
Express the answer with the correct uncertainty
(8.1 ± 1.0)2 = ??
W
8.12 = 65.61uncty = 65.61(2*1/8.1) = 16.266 ± 16
66 ± 16??
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
W
r2 = 4.52 = 63.6173 uncty = 63.6173(.1/4.5+.1/4.5) = 2.83
63.6 + 2.8 cm2
63.6 + 2.8 cm2
Express the answer with the correct uncertainty
= ??
W
√(25.0) = 5.00uncty = 5.00*(.5*.2/25) = .025.00 ± .02
5.00 ± .02
2.00.25
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