Question: Let 1 , , n be numbers with j correctly rounded to S j digits. In calculating the sum

Let α₁, · · ·, α_nbe numbers with α_jcorrectly rounded to S_j digits. In calculating the sum α₁ + · · · + α_nretaining S = min S_j significant digits, is it essential that we first add and then round the result or that we first round each number to S significant digits and then add?

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