Sinmplie Examples From Uncertainty Review Written Out



Simple Examples from Uncertainty Review - Written Out

Addition/Subtraction

(33.8 ± 0.2) m - (18.2 ± 0.1) m

= (33.8 – 18.2) m ± (0.2 + 0.1) m Calculate result as if there is no uncertainty

Result’s unc. = sum of absolute uncertainties

= (15.6 ± 0.3) m Final answer

Multiplication/Division

[(12.4 ± 0.3) cm]/[(2.88 ± 0.07)x10-3 s]

(0.3 cm)/(12.4 cm) = 0.02419 = 2.419% First calculate the relative uncertainties

(0.07x10-3 s)/(2.88x10-3 s) = 0.02431 = 2.431%

= [12.4 cm ± 2.419%]/[2.88x10-3 s ± 2.431%] Equation written with relative uncertainties

= (4305.5556 cm/s) ± 4.85% Do calculation and add relative uncertainties

= (4305.5556 cm/s) ± (208.819 cm/s) Change relative uncertainty into absolute

4.85% of 4305.5556 cm/s = 208.819 cm/s

= (4305.5556 cm/s) ± (210 cm/s) Round uncertainty to 1 significant digit or in

this case, 2 since begins with a “1” or a “2”

= (4310 ± 210) cm/s Round result to same decimal place as unc.

= (4.31 ± 0.21) x103 cm/s Final answer written in scientific notation so

the significant digits are not ambiguous

Powers

[(7.44 ± 0.04) cm]2

(0.04 cm)/(7.44 cm) = 0.005376 = 0.5376% First calculate the relative uncertainty

= [7.44 cm ± 0.5376%]2 Equation written with relative uncertainty

= 55.3536 cm2 ± (2)(0.5376%) Do calculation and multiply power times the

relative uncertainty

= 55.3536 cm2 ± 1.0752%

= (55.3536 ± 0.5952) cm2 Change the relative uncertainty into absolute

1.0752% of 55.3536 cm2 = 0.5952 cm2

= (55.3536 ± 0.6) cm2 Round uncertainty to 1 significant digit

= (55.4 ± 0.6) cm2 Round result to same decimal place as unc.

This is written appropriately for final answer

Perfectly Known Number

2[(12.4 ± 0.3) cm]

= 2(12.4 cm) ± 2(0.3 cm) Multiply both the value and the uncertainty

by the perfectly known number.

= (24.8 ± 0.6) cm Final answer

Never multiply relative uncertainty by the

perfectly known number

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