Sig fig: Addition and division at the same time.?

Ok how does one do this kind of problem?



8.934+3.1/2.000



8.934+3.1=12.034



I first added, so I rounded to 12.0 since there was only one decimal place. Then I divided by 2.000 and got 6.00 since there was only 3 sig figs. The choices for answers were 6.0, 6.1, and 6.012. Therefore I chose 6.0. Apparently the answer is 6.01. How do you go about getting that answer?

Sig fig: Addition and division at the same time.?
It is permissible (and recommended) to carry intermediate results to a number of significant figures one or two greater than what you are entitled to to guard against accumulation of roundoff error in the final result.



Nevertheless, you are only entitled to report the result to the number of significant figures justified by the least accurate number in your calculation. For addition and subtraction, this means number of significant figures after the decimal point, which may be negative if the number rounds off before the decimal point. For multiplication and division, this means the number of significant figures, regardless of the position of the decimal point.



If the problem is done as it appears in this transcription, the division should be done first, giving 8.934 + 1.6 (actually, 8.934 + 1.55, but you are entitled to only two significant figures because the quantity 3.1 so limits you.) You may then perform the addition to a precision of one digit after the decimal point, a different rule than for multiplication and division. This gives a final answer of 10.5, whether or not you use 1.55 or 1.6 as one of the addends.



If you instead rewrite the expression as (8.934+3.1) / 2.000, as the answers in your multiple-choice list imply that you should have, you get 12.034 / 2.000, which becomes 6.017. However, after the addition, the numerator is only good to only one figure after the decimal point, or three significant figures. You are therefore entitled to report the final quotient to only three significant figures, which is 6.02.
Reply:Sig figs dont work by decimal plaaces.. they work by significant figures.. the additon would end up being only 12 since 2 sig figs is the greatest amount you can round to.. having 12.0 would be 3 sig figs instead of two.then you divide by 12.034 which would end up being 0.99717467176334 so you round the sig figs to 1 because it would be 0.99 but the seven makes the 9 a ten then th eother 9 a ten too.. so you have one ,.. just leave it like that .. so the answer is 1.. hope this helped you.. you have to remember the rules for sig figs.
Reply:8.934+3.1 = 12.034



12.034/2 = 6.017



So the best answer is 6.01.



From my perspective - it is best to keep all the significant digits (in this case the addition piece has 3 places past the decimal), until the end of the problem and then round at the end.



Hope this information helps.