Significant digits/rounding

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I have a bunch of criteria to evaluate for a product, and each is scored on a scale from 0 to 5. Each criterion has a weight associated with it.

If I find the weighted score of a criterion, it is

weighted score = score * weight

Does the significant digits apply here where I should only take one significant digit for my weighted score (since there is only one significant digit in my scoring scale (0-5))? Is it necessary?

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mean and standard deviation: round to one more decimal place than your original data. [...] This suggestion follows Sullivan, Michael, Fundamentals of Statistics 3/e (Pearson Prentice Hall, 2011) page 118.

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So, I suggest keeping one digit after the decimal dot when reporting the weighted average.