1. The problem statement, all variables and given/known data Calculating focal lengths of lenses. s = 144.7 ± 5.52 mm s' = 86.0 + 0.71 mm 2. Relevant equations Focal Length f = (s)(s') / ( s + s' ) Adding/Subtracting two numbers with uncertainties A + B ± root [ (±A)^2 + (±B)^2 ] Multiplying/Dividing AB ± root [ (±A/A)^2 + (±B/B)^2) ] 3. The attempt at a solution I have: s = 144.7 ± 5.52 mm s' = 86.0 + 0.71 mm and am getting: f = 53.94 ± 0.02412 mm My question is, does it make sense that the uncertainty that was obviously significant at the start (5.52mm uncertainty in a 144.7mm magnitude) became so miniscule at the end? The way I am calculating this is 1) Calculating numerator and denominator of focal length equation separately -Top = ( s * s' ) and get uncertainty of 0.039mm using the uncertainty multiplication rule -Bot = ( s + s' ) and get uncertainty of 5.57mm using the uncertainty addition rule. 2) Then I divide the top by the bottom apply the uncertainty division rule. Am I doing everything correctly?