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#### philonossis

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##### sig fig question with multiple operations
« on: February 14, 2010, 05:32:33 AM »

This problem is from an intro college chemistry book.

"Each of the following calculations contains the numbers 4.2, 5.30, 11, and 28. The numbers 4.2 and 5.30 are measured quantities, and 11 and 28 are exact numbers. Do each calculation and express each number to the proper number of significant figures."

Problem (a) (4.2 + 5.30) X (28 +11)

The first operation is addition so the add/subt rules apply, i.e., sig fig to the 10ths place. The answer is 9.50, but I did not round off yet because the textbook also states that rounding off should only be done when all operations are complete.

The second operation (28 + 11) = 39 but is irrelevant to sig figs, since both numbers are exact.

9.50 X 39 = 370.5.
In mult/div the number with the fewest sig figs is controlling.  This is 9.50 which has 3, therefore 370 is the answer.

Problem (c) 28-4.2/5.30X11

28-4.2: The add/sub rule gives sig fig to the 10th place: 23.8

5.30X11: the mult/div rule gives 3 sig figs. 58.3

Final operation: 23.8/58.3 = 0.40823327615

mult/div rule allows 3 sig figs, therefore 0.408.

Problem (d) 28-4.2/11-5.30 = 23.8/5.70 = 4.175438596649

Since division was the final op, this allows 3 sig figs: 4.18.

My question in these problems is whether sig figs are determined by the nature of the final operation, which I believe to be the case.
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#### philonossis

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##### Re: sig fig question with multiple operations
« Reply #1 on: February 21, 2010, 01:47:47 AM »

well, if nobody minds, I'll just take a quick nap.

But I'll be rested, and ready when those replies start flooding in.
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#### Prozac

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##### Re: sig fig question with multiple operations
« Reply #2 on: February 24, 2010, 01:06:11 PM »

Addition and subtraction - fewest decimal place
Multiplication and division- fewest sig fig

Also 39 is only 2 sig fig why go 3 sig fig when rule says fewest sig fig?

Remember you can state answers as 3.7*102 which is 2 sig fig
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#### philonossis

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##### Re: sig fig question with multiple operations
« Reply #3 on: March 02, 2010, 04:09:27 AM »

Addition and subtraction - fewest decimal place
Multiplication and division- fewest sig fig

Also 39 is only 2 sig fig why go 3 sig fig when rule says fewest sig fig?

the number 39 was obtained by addition of two exact numbers, which are considered to have an unlimited number of sig figs so do not limit the number of sig figs. 39 therefore would not have two sig figs according to my book or my interpretation of my book.

Sig figs would be determined by the measurement numbers. "(4.2 + 5.30)" when you add these you get 9.50. If you reduce these to the sig fig at this point, you get 9.5. But my book says not to round off sequentially but only when all the calculations are done. So do you know if I would leave this as 9.50 until the problem is finished?

Do you multiply 9.50 or 9.5 times 39?  I do not understand why the original number "4.2" would determine sig fig since it was an addition problem and there was a multiplication operation coming after it. My book states that we should not round off sequentially but wait until all calculations were done before rounding off. This would make the last operation control the number of sig figs.
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#### AWK

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##### Re: sig fig question with multiple operations
« Reply #4 on: March 02, 2010, 04:39:49 AM »

Quote
Problem (c) 28-4.2/5.30X11

it means 28-(4.2/5.30)X11

Quote
Problem (d) 28-4.2/11-5.30

it means 28-(4.2/11)-5.30
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