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Alright this is in my lab book:

The overriding consideration for significant figures in computations is that a result should not be quoted with a precision higher than the absolute uncertainty associated with it.

For example, it makes little sense to write I = (1.56250 +/- 0.01288) x 10^-2 kg.m^2, because the result is already uncertain in the third significant digit. It would be more appropriate to write I = (1.563 +/- 0.013) x 10^-2 kg.m^2 or, even better, I = (1.56 +/- 0.01) x 10^-2 kg.m^2.

I guess I am just confused why its "already uncertain in the third significant digit". Can anyone explain.. like how is this known.