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Significant Figures Arithmetic: Mixed Calculations?
I know you are supposed to wait until the final calculation to round, but I'm having trouble understanding exactly what that means.
100.055 + (10. x 3.33)
= 100.055 + 33.3 (2 s.f.)
= ?
is it 133? (rounding to the ones place to honor the addition with the number 33.3 (2 s.f.), whose least significant digit is in the ones place - I think this is right...)
or 130? (rounding to 2 s.f. to honor the multiplication that resulted in 2 s.f)
or 133.4? (just rounding to 1 decimal place as you would with the standalone calculation: 100.055 + 33.3)
Is the rule for addition to round to the least precise "place" or the least precise "significant place"? If you choose 133.4 as the answer aren't you accepting the .3 in 33.3 as significant when it is not? That 3 digit was only significant when it was in the hundredth's place, no?
1 Answer
- Old Science GuyLv 79 years agoFavorite Answer
in mixed calculations you must round each time you change type of calculation
and again at the equal sign
so
100.055 + (10. x 3.33) = 100.055 + 33.3 (2 s.f.)
is correct so far
then you get 133.355
which must be rounded to the tenths place because 33.3 is least precise
giving
133.4
note that in addition you round to 'place', not to a number of s.f. as you do in multiplication
