SOLUTION: HI! I saw this on a webpage: Tutorial on the Use of Significant Figures, page 7 ----------- ----------- ----------- ----------- ----------- ----------- -------- General guid

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Question 263548: HI! I saw this on a webpage:
Tutorial on the Use of Significant Figures, page 7
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General guidelines for using calculators
When using a calculator, if you work the entirety of a long calculation without writing down any intermediate results, you may not be able to tell if an error is made. Further, even if you realize that one has occurred, you may not be able to tell where the error is.
In a long calculation involving mixed operations, carry as many digits as possible through the entire set of calculations and then round the final result appropriately. For example,
(5.00 / 1.235) + 3.000 + (6.35 / 4.0)=4.04858... + 3.000 + 1.5875=8.630829...
The first division should result in 3 significant figures. The last division should result in 2 significant figures. The three numbers added together should result in a number that is rounded off to the last common significant digit occurring furthest to the right; in this case, the final result should be rounded with 1 digit after the decimal. Thus, the correct rounded final result should be 8.6. This final result has been limited by the accuracy in the last division.
Warning: carrying all digits through to the final result before rounding is critical for many mathematical operations in statistics. Rounding intermediate results when calculating sums of squares can seriously compromise the accuracy of the result.
This is on a chemistry webpage dealing with significant figures. What do the two sentences after the word warning mean exactly? I don't understand this.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
It means "just be careful".
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To comply with the sentences you should carry out your
work with at least 6 decimal places at each step if
you are asked to arrive at an answer that is good to
the 3rd decimal place. Don't round off your decimals
to the 3rd place every step along the line while you
are working the problem.
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Hope that helps.
Cheers,
Stan H.