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### Sig Figs: Addition and Subtraction

Posted: Sat Oct 06, 2018 2:10 pm
In mathematical operations involving significant figures, the answer is reported in such a way that it reflects the reliability of the least precise operation. Let's state that another way: a chain is no stronger than its weakest link. An answer is no more precise that the least precise number used to get the answer. Let's do it one more time: imagine a team race where you and your team must finish together. Who dictates the speed of the team? Of course, the slowest member of the team. Your answer cannot be MORE precise than the least precise measurement.
For addition and subtraction, look at the decimal portion (i.e., to the right of the decimal point) of the numbers ONLY. Here is what to do:

1) Count the number of significant figures in the decimal portion of each number in the problem. (The digits to the left of the decimal place are not used to determine the number of decimal places in the final answer.)

2) Add or subtract in the normal fashion.

3) Round the answer to the LEAST number of places in the decimal portion of any number in the problem.

This doesn't make much sense to me, since the digits to the left of the decimal point can also be significant. If you add 12345.6 and 1.008, your final answer would be 12346.6, which has 6 sig figs, even though 1.008 only has 4. Am I making a conceptual error here?

### Re: Sig Figs: Addition and Subtraction

Posted: Sat Oct 06, 2018 2:33 pm
For addition, the rule is to go with the number that has the least digits after the decimal point, so 12345.6 + 1.008 would have an answer that has only one digit after the decimal point, so the answer will be 12346.6. The rule about having the least amount of sig figs in the answer is for multiplication and division.

### Re: Sig Figs: Addition and Subtraction

Posted: Sat Oct 06, 2018 3:50 pm
Addition and subtraction takes the Least significant figures after the decimal point. In this case, I think that one of the reasons is that you can't accurately say that the answer is 123456.608 because the .6 means that you estimated the measurement to .5 through .7 (or +/- .1). So if you keep the other sig fig decimals (.008) you are falsifying how accurate your measurement really is.

### Re: Sig Figs: Addition and Subtraction

Posted: Mon Oct 08, 2018 7:38 pm
To provide more clarification:

Addition/Subtraction : The answer should have the "smallest number of decimal places."
For example: 10.2 + 1.005 + 2.35 = 13.555 = 13.6. (10.2 has one decimal present, thus, we "follow" it)
4.505 - 2.3 = 2.205 = 2.2
*Thus, for answers regarding subtraction and addition, your main concern is the # of decimal places, not the overall number of SF.

Multiplication/Division : One picks the least amount of significant figures.
For example: 2.3 x 3.570 = 8.211 = 8.2
1.3006 x 3.6 = 4.68216 = 4.7