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In determining a density of a rectangular soilid I might, with my cm ruler
get this data:
l = 3.75 +- .05 cm
w = 1.32 +- .05 cm
h = 0.54 +- .05 cm
all the tools I hav been taught to do this gives the volume as:
2.7 cc +- 0.4 cc (14%)
I do not like this very much as the 0.54 has the same certainty as the
others.
I would prefer:
2.67 =- 0.39 cc
but not
2.673 +- 0.388 cc
I have tried to take the approach that we are multiplying 3.7x by 1.32x by
0.5x (where the x represents an uncetain number). When I do this I get
2.4xxx which I think supports my choice of 2.67 cc.
I wonder if I am misleading my students with what I call a reasonable
approach?