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# Need help with significant figures in basic uncertainty calculation

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1. The following is from a book:

The fractional uncertainty of a product or quotient of 2 quantities is the sum of the fractional uncertainties of those 2 quantities, i.e.

r = xy or r = x/y
dr/r = dx/x + dy/y

e.g. Two lengths are reported as: x = 18.5 +/- 0.5 mm, y = 12.5 +/- 0.5 mm

dr/r = 0.5/18.5 + 0.5/12.5 = 0.067
r = 18.5 x 12.5 = 231.25
dr = 0.067 x 231.25 = 15.49 = 20 mm (1 sf)

r = 230 +/- 20 mm

(the underlines are mine)

I'm confused as to how the rounding ups come about.
How did 231.25 become 230? Where does the 2 sf come from? Why not 3 sf and 231 since it's multiplication and the quantity with the lowest sf has 3 sf?
Shouldn't dr/r be 0.07? 0.5/18.5 = 0.03 (1 sf, following number of sf in 0.5 for division), 0.5/12.5 = 0.04, 0.03 + 0.04 = 0.07

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